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diff --git a/docs/examples/DynamicsPeriodicDiagonal/laminate/CMakeLists.txt b/docs/examples/DynamicsDiagonalPeriodic/laminate/no_damping/Verlet/CMakeLists.txt
similarity index 87%
rename from docs/examples/DynamicsPeriodicDiagonal/laminate/CMakeLists.txt
rename to docs/examples/DynamicsDiagonalPeriodic/laminate/no_damping/Verlet/CMakeLists.txt
index 5e3f722..e69c369 100644
--- a/docs/examples/DynamicsPeriodicDiagonal/laminate/CMakeLists.txt
+++ b/docs/examples/DynamicsDiagonalPeriodic/laminate/no_damping/Verlet/CMakeLists.txt
@@ -1,47 +1,43 @@
cmake_minimum_required(VERSION 3.1)
# define a project name
project(example)
# set optimization level
set(CMAKE_BUILD_TYPE Release)
add_definitions(-DNDEBUG)
# set C++ standard
set(CMAKE_CXX_STANDARD 14)
set(CMAKE_CXX_STANDARD_REQUIRED ON)
set(CMAKE_CXX_EXTENSIONS OFF)
# load pkg-config
find_package(PkgConfig)
-# find cppmat
+# load HDF5
+find_package(HDF5 COMPONENTS CXX REQUIRED)
+include_directories(${HDF5_INCLUDE_DIRS})
+set(LINK_LIBS ${HDF5_LIBS} ${HDF5_LIBRARIES})
+
+# load header-only modules using pkg-config
+# - cppmat
pkg_check_modules(CPPMAT REQUIRED cppmat)
include_directories(${CPPMAT_INCLUDE_DIRS})
-
-# find GooseFEM
+# - GooseFEM
pkg_check_modules(GOOSEFEM REQUIRED GooseFEM)
include_directories(${GOOSEFEM_INCLUDE_DIRS})
-
-# find GooseMaterial
+# - GooseMaterial
pkg_check_modules(GOOSEMATERIAL REQUIRED GooseMaterial)
include_directories(${GOOSEMATERIAL_INCLUDE_DIRS})
-
-# find eigen3
+# - eigen3
pkg_check_modules(EIGEN3 REQUIRED eigen3)
include_directories(${EIGEN3_INCLUDE_DIRS})
-
-# find HDF5
-find_package(HDF5 COMPONENTS CXX REQUIRED)
-include_directories(${HDF5_INCLUDE_DIRS})
-set(LINK_LIBS ${HDF5_LIBS} ${HDF5_LIBRARIES})
-
-# find HDF5pp
+# - HDF5pp
pkg_check_modules(HDF5PP REQUIRED HDF5pp)
include_directories(${HDF5PP_INCLUDE_DIRS})
-# add executable
+# create executable
add_executable(${PROJECT_NAME} main.cpp)
-
# link libraries
target_link_libraries(${PROJECT_NAME} ${LINK_LIBS})
diff --git a/docs/examples/DynamicsDiagonalPeriodic/laminate/no_damping/Verlet/example.svg b/docs/examples/DynamicsDiagonalPeriodic/laminate/no_damping/Verlet/example.svg
new file mode 100644
index 0000000..13648dd
--- /dev/null
+++ b/docs/examples/DynamicsDiagonalPeriodic/laminate/no_damping/Verlet/example.svg
@@ -0,0 +1,11520 @@
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diff --git a/docs/examples/DynamicsDiagonalPeriodic/laminate/no_damping/Verlet/main.cpp b/docs/examples/DynamicsDiagonalPeriodic/laminate/no_damping/Verlet/main.cpp
new file mode 100644
index 0000000..e40c269
--- /dev/null
+++ b/docs/examples/DynamicsDiagonalPeriodic/laminate/no_damping/Verlet/main.cpp
@@ -0,0 +1,161 @@
+
+#include <HDF5pp.h>
+#include <Eigen/Eigen>
+#include <cppmat/cppmat.h>
+#include <GooseFEM/GooseFEM.h>
+#include <GooseMaterial/AmorphousSolid/LinearStrain/Elastic/Cartesian2d.h>
+
+// -------------------------------------------------------------------------------------------------
+
+using MatS = GooseFEM::MatS;
+using MatD = GooseFEM::MatD;
+using ColD = GooseFEM::ColD;
+
+using vec = cppmat::cartesian2d::vector <double>;
+using T2 = cppmat::cartesian2d::tensor2 <double>;
+using T2s = cppmat::cartesian2d::tensor2s<double>;
+using T2d = cppmat::cartesian2d::tensor2d<double>;
+
+namespace GM = GooseMaterial::AmorphousSolid::LinearStrain::Elastic::Cartesian2d;
+
+// =================================================================================================
+
+class Quadrature
+{
+public:
+ T2s eps, epsdot, sig;
+
+ size_t nhard;
+ GM::Material hard, soft;
+
+ double Ebar, Vbar;
+
+ Quadrature(size_t nhard);
+
+ double density (size_t elem, size_t k, double V);
+ void stressStrain (size_t elem, size_t k, double V);
+ void stressStrainRate (size_t elem, size_t k, double V);
+ void stressStrainPost (size_t elem, size_t k, double V);
+ void stressStrainRatePost(size_t elem, size_t k, double V);
+};
+
+// -------------------------------------------------------------------------------------------------
+
+Quadrature::Quadrature(size_t _nhard)
+{
+ nhard = _nhard;
+ hard = GM::Material(100.,10.);
+ soft = GM::Material(100., 1.);
+}
+
+// -------------------------------------------------------------------------------------------------
+
+double Quadrature::density(size_t elem, size_t k, double V)
+{
+ return 1.0;
+}
+// -------------------------------------------------------------------------------------------------
+
+void Quadrature::stressStrain(size_t elem, size_t k, double V)
+{
+ if ( elem < nhard ) sig = hard.stress(eps);
+ else sig = soft.stress(eps);
+}
+// -------------------------------------------------------------------------------------------------
+
+void Quadrature::stressStrainRate(size_t elem, size_t k, double V)
+{
+}
+// -------------------------------------------------------------------------------------------------
+
+void Quadrature::stressStrainPost(size_t elem, size_t k, double V)
+{
+ Vbar += V;
+
+ if ( elem < nhard ) Ebar += hard.energy(eps) * V;
+ else Ebar += soft.energy(eps) * V;
+}
+
+// -------------------------------------------------------------------------------------------------
+
+void Quadrature::stressStrainRatePost(size_t elem, size_t k, double V)
+{
+}
+
+// =================================================================================================
+
+int main()
+{
+ // set simulation parameters
+ double T = 20. ; // total time
+ double dt = 1.e-2; // time increment
+ size_t nx = 40 ; // number of elements in both directions
+ double gamma = .05 ; // displacement step
+
+ // class which provides the mesh
+ GooseFEM::Mesh::Quad4::Regular mesh(nx,nx,static_cast<double>(nx),static_cast<double>(nx));
+ // reference node
+ size_t nodeRef = mesh.nodesRef();
+
+ // class which provides the constitutive response at each quadrature point
+ auto quadrature = std::make_shared<Quadrature>(nx*nx/4);
+
+ // class which provides the response of each element
+ using Elem = GooseFEM::Dynamics::Diagonal::LinearStrain::Quad4<Quadrature>;
+ auto elem = std::make_shared<Elem>(quadrature);
+
+ // class which provides the system and an increment
+ GooseFEM::Dynamics::Diagonal::Periodic<Elem> sim(
+ elem,
+ mesh.coor(),
+ mesh.conn(),
+ mesh.dofsPeriodic(),
+ dt,
+ 0.0
+ );
+
+ // define update in macroscopic deformation gradient
+ T2 dFbar(0.);
+ dFbar(0,1) = gamma;
+
+ // update the displacement according to the macroscopic deformation gradient update
+ for ( size_t i = 0 ; i < sim.nnode ; ++i )
+ for ( size_t j = 0 ; j < sim.ndim ; ++j )
+ for ( size_t k = 0 ; k < sim.ndim ; ++k )
+ sim.u(i,j) += dFbar(j,k) * ( sim.x0(i,k) - sim.x0(nodeRef,k) );
+
+ // output variables
+ ColD Epot(static_cast<int>(T/dt)); Epot.setZero(); // potential energy
+ ColD Ekin(static_cast<int>(T/dt)); Ekin.setZero();
+ ColD t (static_cast<int>(T/dt)); t .setZero();
+
+ // loop over increments
+ for ( size_t inc = 0 ; inc < static_cast<size_t>(Epot.size()) ; ++inc )
+ {
+ // - compute increment
+ sim.Verlet();
+
+ // - post: energy based on nodes
+ // -- store time
+ t(inc) = sim.t;
+ // -- kinetic energy
+ for ( size_t i = 0 ; i < sim.ndof ; ++i )
+ Ekin(inc) += .5 / sim.Minv(i) * std::pow( sim.V(i) , 2. );
+ // -- potential energy
+ quadrature->Ebar = 0.0;
+ quadrature->Vbar = 0.0;
+ sim.post();
+ Epot(inc) = quadrature->Ebar;
+ }
+
+ // write to output file
+ H5p::File f = H5p::File("example.hdf5");
+ f.write("/global/Epot",Epot );
+ f.write("/global/Ekin",Ekin );
+ f.write("/global/t" ,t );
+ f.write("/mesh/coor" ,mesh.coor());
+ f.write("/mesh/conn" ,mesh.conn());
+ f.write("/mesh/disp" ,sim.u );
+
+ return 0;
+}
diff --git a/docs/examples/DynamicsDiagonalPeriodic/laminate/no_damping/Verlet/plot.py b/docs/examples/DynamicsDiagonalPeriodic/laminate/no_damping/Verlet/plot.py
new file mode 100644
index 0000000..e83c20c
--- /dev/null
+++ b/docs/examples/DynamicsDiagonalPeriodic/laminate/no_damping/Verlet/plot.py
@@ -0,0 +1,52 @@
+
+import sys,os,re
+import h5py
+import numpy as np
+import matplotlib.pyplot as plt
+import goosempl as gplt
+import matplotlib as mpl
+
+plt.style.use(['goose','goose-latex'])
+
+# --------------------------------------------------------------------------------------------------
+
+name = 'example.hdf5'
+f = h5py.File(name,'r')
+
+fig = plt.figure(figsize=(20,10))
+fig.set_tight_layout(True)
+
+# --------------------------------------------------------------------------------------------------
+
+ax = fig.add_subplot(1,2,1)
+
+t = f['/global/t' ][:]
+E = f['/global/Ekin'][:] + f['/global/Epot'][:]; ax.plot(t,E,color='k',label=r'$E_\mathrm{pot} + E_\mathrm{kin}$')
+E = f['/global/Epot'][:] ; ax.plot(t,E,color='r',label=r'$E_\mathrm{pot}$')
+E = f['/global/Ekin'][:] ; ax.plot(t,E,color='b',label=r'$E_\mathrm{kin}$')
+
+plt.legend(loc='lower right')
+
+plt.xlabel(r'$t$')
+plt.ylabel(r'$E$')
+
+# --------------------------------------------------------------------------------------------------
+
+ax = fig.add_subplot(1,2,2)
+
+coor = f['/mesh/coor'][:]
+conn = f['/mesh/conn'][:]
+u = f['/mesh/disp'][:]
+
+im = gplt.patch(coor=coor+u,conn=conn)
+
+Lx = np.max(coor[:,0])-np.min(coor[:,0])
+Ly = np.max(coor[:,1])-np.min(coor[:,1])
+
+plt.xlim([-0.1*Lx,1.3*Lx])
+plt.ylim([-0.1*Ly,1.3*Ly])
+
+ax.set_aspect('equal')
+
+plt.savefig(re.sub(r'(.*)(\.hdf5)',r'\1.svg',name))
+plt.show()
diff --git a/docs/examples/DynamicsPeriodicDiagonal/laminate2/CMakeLists.txt b/docs/examples/DynamicsDiagonalPeriodic/laminate/no_damping/velocityVerlet/CMakeLists.txt
similarity index 87%
rename from docs/examples/DynamicsPeriodicDiagonal/laminate2/CMakeLists.txt
rename to docs/examples/DynamicsDiagonalPeriodic/laminate/no_damping/velocityVerlet/CMakeLists.txt
index 5e3f722..e69c369 100644
--- a/docs/examples/DynamicsPeriodicDiagonal/laminate2/CMakeLists.txt
+++ b/docs/examples/DynamicsDiagonalPeriodic/laminate/no_damping/velocityVerlet/CMakeLists.txt
@@ -1,47 +1,43 @@
cmake_minimum_required(VERSION 3.1)
# define a project name
project(example)
# set optimization level
set(CMAKE_BUILD_TYPE Release)
add_definitions(-DNDEBUG)
# set C++ standard
set(CMAKE_CXX_STANDARD 14)
set(CMAKE_CXX_STANDARD_REQUIRED ON)
set(CMAKE_CXX_EXTENSIONS OFF)
# load pkg-config
find_package(PkgConfig)
-# find cppmat
+# load HDF5
+find_package(HDF5 COMPONENTS CXX REQUIRED)
+include_directories(${HDF5_INCLUDE_DIRS})
+set(LINK_LIBS ${HDF5_LIBS} ${HDF5_LIBRARIES})
+
+# load header-only modules using pkg-config
+# - cppmat
pkg_check_modules(CPPMAT REQUIRED cppmat)
include_directories(${CPPMAT_INCLUDE_DIRS})
-
-# find GooseFEM
+# - GooseFEM
pkg_check_modules(GOOSEFEM REQUIRED GooseFEM)
include_directories(${GOOSEFEM_INCLUDE_DIRS})
-
-# find GooseMaterial
+# - GooseMaterial
pkg_check_modules(GOOSEMATERIAL REQUIRED GooseMaterial)
include_directories(${GOOSEMATERIAL_INCLUDE_DIRS})
-
-# find eigen3
+# - eigen3
pkg_check_modules(EIGEN3 REQUIRED eigen3)
include_directories(${EIGEN3_INCLUDE_DIRS})
-
-# find HDF5
-find_package(HDF5 COMPONENTS CXX REQUIRED)
-include_directories(${HDF5_INCLUDE_DIRS})
-set(LINK_LIBS ${HDF5_LIBS} ${HDF5_LIBRARIES})
-
-# find HDF5pp
+# - HDF5pp
pkg_check_modules(HDF5PP REQUIRED HDF5pp)
include_directories(${HDF5PP_INCLUDE_DIRS})
-# add executable
+# create executable
add_executable(${PROJECT_NAME} main.cpp)
-
# link libraries
target_link_libraries(${PROJECT_NAME} ${LINK_LIBS})
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new file mode 100644
index 0000000..3511ae9
--- /dev/null
+++ b/docs/examples/DynamicsDiagonalPeriodic/laminate/no_damping/velocityVerlet/example.svg
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diff --git a/docs/examples/DynamicsDiagonalPeriodic/laminate/no_damping/velocityVerlet/main.cpp b/docs/examples/DynamicsDiagonalPeriodic/laminate/no_damping/velocityVerlet/main.cpp
new file mode 100644
index 0000000..350a475
--- /dev/null
+++ b/docs/examples/DynamicsDiagonalPeriodic/laminate/no_damping/velocityVerlet/main.cpp
@@ -0,0 +1,162 @@
+
+#include <HDF5pp.h>
+#include <Eigen/Eigen>
+#include <cppmat/cppmat.h>
+#include <GooseFEM/GooseFEM.h>
+#include <GooseMaterial/AmorphousSolid/LinearStrain/Elastic/Cartesian2d.h>
+
+// -------------------------------------------------------------------------------------------------
+
+using MatS = GooseFEM::MatS;
+using MatD = GooseFEM::MatD;
+using ColD = GooseFEM::ColD;
+
+using vec = cppmat::cartesian2d::vector <double>;
+using T2 = cppmat::cartesian2d::tensor2 <double>;
+using T2s = cppmat::cartesian2d::tensor2s<double>;
+using T2d = cppmat::cartesian2d::tensor2d<double>;
+
+namespace GM = GooseMaterial::AmorphousSolid::LinearStrain::Elastic::Cartesian2d;
+
+// =================================================================================================
+
+class Quadrature
+{
+public:
+ T2s eps, epsdot, sig;
+
+ size_t nhard;
+ GM::Material hard, soft;
+
+ double Ebar, Vbar;
+
+ Quadrature(size_t nhard);
+
+ double density (size_t elem, size_t k, double V);
+ void stressStrain (size_t elem, size_t k, double V);
+ void stressStrainRate (size_t elem, size_t k, double V);
+ void stressStrainPost (size_t elem, size_t k, double V);
+ void stressStrainRatePost(size_t elem, size_t k, double V);
+};
+
+// -------------------------------------------------------------------------------------------------
+
+Quadrature::Quadrature(size_t _nhard)
+{
+ nhard = _nhard;
+ hard = GM::Material(100.,10.);
+ soft = GM::Material(100., 1.);
+}
+
+// -------------------------------------------------------------------------------------------------
+
+double Quadrature::density(size_t elem, size_t k, double V)
+{
+ return 1.0;
+}
+// -------------------------------------------------------------------------------------------------
+
+void Quadrature::stressStrain(size_t elem, size_t k, double V)
+{
+ if ( elem < nhard ) sig = hard.stress(eps);
+ else sig = soft.stress(eps);
+}
+// -------------------------------------------------------------------------------------------------
+
+void Quadrature::stressStrainRate(size_t elem, size_t k, double V)
+{
+ sig.zeros();
+}
+// -------------------------------------------------------------------------------------------------
+
+void Quadrature::stressStrainPost(size_t elem, size_t k, double V)
+{
+ Vbar += V;
+
+ if ( elem < nhard ) Ebar += hard.energy(eps) * V;
+ else Ebar += soft.energy(eps) * V;
+}
+
+// -------------------------------------------------------------------------------------------------
+
+void Quadrature::stressStrainRatePost(size_t elem, size_t k, double V)
+{
+}
+
+// =================================================================================================
+
+int main()
+{
+ // set simulation parameters
+ double T = 20. ; // total time
+ double dt = 1.e-2; // time increment
+ size_t nx = 40 ; // number of elements in both directions
+ double gamma = .05 ; // displacement step
+
+ // class which provides the mesh
+ GooseFEM::Mesh::Quad4::Regular mesh(nx,nx,static_cast<double>(nx),static_cast<double>(nx));
+ // reference node
+ size_t nodeRef = mesh.nodesRef();
+
+ // class which provides the constitutive response at each quadrature point
+ auto quadrature = std::make_shared<Quadrature>(nx*nx/4);
+
+ // class which provides the response of each element
+ using Elem = GooseFEM::Dynamics::Diagonal::LinearStrain::Quad4<Quadrature>;
+ auto elem = std::make_shared<Elem>(quadrature);
+
+ // class which provides the system and an increment
+ GooseFEM::Dynamics::Diagonal::Periodic<Elem> sim(
+ elem,
+ mesh.coor(),
+ mesh.conn(),
+ mesh.dofsPeriodic(),
+ dt,
+ 0.0
+ );
+
+ // define update in macroscopic deformation gradient
+ T2 dFbar(0.);
+ dFbar(0,1) = gamma;
+
+ // update the displacement according to the macroscopic deformation gradient update
+ for ( size_t i = 0 ; i < sim.nnode ; ++i )
+ for ( size_t j = 0 ; j < sim.ndim ; ++j )
+ for ( size_t k = 0 ; k < sim.ndim ; ++k )
+ sim.u(i,j) += dFbar(j,k) * ( sim.x0(i,k) - sim.x0(nodeRef,k) );
+
+ // output variables
+ ColD Epot(static_cast<int>(T/dt)); Epot.setZero(); // potential energy
+ ColD Ekin(static_cast<int>(T/dt)); Ekin.setZero();
+ ColD t (static_cast<int>(T/dt)); t .setZero();
+
+ // loop over increments
+ for ( size_t inc = 0 ; inc < static_cast<size_t>(Epot.size()) ; ++inc )
+ {
+ // - compute increment
+ sim.velocityVerlet();
+
+ // - post: energy based on nodes
+ // -- store time
+ t(inc) = sim.t;
+ // -- kinetic energy
+ for ( size_t i = 0 ; i < sim.ndof ; ++i )
+ Ekin(inc) += .5 / sim.Minv(i) * std::pow( sim.V(i) , 2. );
+ // -- potential energy
+ quadrature->Ebar = 0.0;
+ quadrature->Vbar = 0.0;
+ sim.post();
+ Epot(inc) = quadrature->Ebar;
+ }
+
+ // write to output file
+ H5p::File f = H5p::File("example.hdf5");
+ f.write("/global/Epot",Epot );
+ f.write("/global/Ekin",Ekin );
+ f.write("/global/t" ,t );
+ f.write("/mesh/coor" ,mesh.coor());
+ f.write("/mesh/conn" ,mesh.conn());
+ f.write("/mesh/disp" ,sim.u );
+
+ return 0;
+}
diff --git a/docs/examples/DynamicsDiagonalPeriodic/laminate/no_damping/velocityVerlet/plot.py b/docs/examples/DynamicsDiagonalPeriodic/laminate/no_damping/velocityVerlet/plot.py
new file mode 100644
index 0000000..e83c20c
--- /dev/null
+++ b/docs/examples/DynamicsDiagonalPeriodic/laminate/no_damping/velocityVerlet/plot.py
@@ -0,0 +1,52 @@
+
+import sys,os,re
+import h5py
+import numpy as np
+import matplotlib.pyplot as plt
+import goosempl as gplt
+import matplotlib as mpl
+
+plt.style.use(['goose','goose-latex'])
+
+# --------------------------------------------------------------------------------------------------
+
+name = 'example.hdf5'
+f = h5py.File(name,'r')
+
+fig = plt.figure(figsize=(20,10))
+fig.set_tight_layout(True)
+
+# --------------------------------------------------------------------------------------------------
+
+ax = fig.add_subplot(1,2,1)
+
+t = f['/global/t' ][:]
+E = f['/global/Ekin'][:] + f['/global/Epot'][:]; ax.plot(t,E,color='k',label=r'$E_\mathrm{pot} + E_\mathrm{kin}$')
+E = f['/global/Epot'][:] ; ax.plot(t,E,color='r',label=r'$E_\mathrm{pot}$')
+E = f['/global/Ekin'][:] ; ax.plot(t,E,color='b',label=r'$E_\mathrm{kin}$')
+
+plt.legend(loc='lower right')
+
+plt.xlabel(r'$t$')
+plt.ylabel(r'$E$')
+
+# --------------------------------------------------------------------------------------------------
+
+ax = fig.add_subplot(1,2,2)
+
+coor = f['/mesh/coor'][:]
+conn = f['/mesh/conn'][:]
+u = f['/mesh/disp'][:]
+
+im = gplt.patch(coor=coor+u,conn=conn)
+
+Lx = np.max(coor[:,0])-np.min(coor[:,0])
+Ly = np.max(coor[:,1])-np.min(coor[:,1])
+
+plt.xlim([-0.1*Lx,1.3*Lx])
+plt.ylim([-0.1*Ly,1.3*Ly])
+
+ax.set_aspect('equal')
+
+plt.savefig(re.sub(r'(.*)(\.hdf5)',r'\1.svg',name))
+plt.show()
diff --git a/docs/examples/DynamicsPeriodicDiagonal/laminate/main.cpp b/docs/examples/DynamicsPeriodicDiagonal/laminate/main.cpp
deleted file mode 100644
index af2d76e..0000000
--- a/docs/examples/DynamicsPeriodicDiagonal/laminate/main.cpp
+++ /dev/null
@@ -1,382 +0,0 @@
-
-#include <Eigen/Eigen>
-#include <HDF5pp.h>
-#include <cppmat/cppmat.h>
-#include <GooseFEM/GooseFEM.h>
-#include <GooseMaterial/AmorphousSolid/LinearStrain/ElastoPlastic/Cartesian2d.h>
-
-using MatD = GooseFEM::MatD;
-using ColD = GooseFEM::ColD;
-
-
-
-namespace GM = GooseMaterial::AmorphousSolid::LinearStrain::ElastoPlastic::Cartesian2d;
-
-using vec = cppmat::cartesian2d::vector <double>;
-using T2 = cppmat::cartesian2d::tensor2 <double>;
-using T2s = cppmat::cartesian2d::tensor2s<double>;
-using T2d = cppmat::cartesian2d::tensor2d<double>;
-
-
-// =================================================================================================
-
-class Element
-{
-public:
- // arrays / matrices
- cppmat::tiny::matrix2<double,4,2> xe, ue, ve, xi, xi_n, dNdxi, dNdx;
- cppmat::tiny::vector <double,4> N, w, w_n;
- cppmat::tiny::matrix2<double,8,8> M;
- cppmat::tiny::vector <double,8> fu, fv;
- // tensors
- cppmat::cartesian2d::tensor2 <double> J, Jinv, gradu, gradv;
- cppmat::cartesian2d::tensor2s<double> eps, epsdot, sig;
- cppmat::cartesian2d::vector <double> v;
- // scalars
- double Jdet, V;
- // sizes (nodes per element, dimensions, quadrature points)
- size_t nne=4, ndim=2, nk=4;
-
- // problem definition
- // - density
- double rho;
- // - constitutive model / Rayleigh damping
- GM::Material hard, soft, rayleigh;
- // - number of elements
- size_t nelem;
-
- // output quantities
- double Epotbar; // potential energy
- double Ekinbar; // kinetic energy
- double Vbar; // volume
-
- Element(double eta, size_t nelem);
-
- void computeMassMatrix (size_t elem);
- void computeInternalForce(size_t elem);
- void computeDampingForce (size_t elem);
- void postProcess (size_t elem);
-
-};
-
-// -------------------------------------------------------------------------------------------------
-
-Element::Element(double eta, size_t _nelem)
-{
- // constitutive definition
- hard = GM::Material(100.,10.);
- soft = GM::Material(100., 1.);
- rayleigh = GM::Material(eta ,eta);
- rho = 1.;
- nelem = _nelem;
-
- // integration point coordinates/weights: normal Gauss integration for Quad4
- xi(0,0) = -1./std::sqrt(3.); xi(0,1) = -1./std::sqrt(3.); w(0) = 1.;
- xi(1,0) = +1./std::sqrt(3.); xi(1,1) = -1./std::sqrt(3.); w(1) = 1.;
- xi(2,0) = +1./std::sqrt(3.); xi(2,1) = +1./std::sqrt(3.); w(2) = 1.;
- xi(3,0) = -1./std::sqrt(3.); xi(3,1) = +1./std::sqrt(3.); w(3) = 1.;
-
- // integration point coordinates/weights: integration at the nodes for Quad4
- xi_n(0,0) = -1.; xi_n(0,1) = -1.; w_n(0) = 1.;
- xi_n(1,0) = +1.; xi_n(1,1) = -1.; w_n(1) = 1.;
- xi_n(2,0) = +1.; xi_n(2,1) = +1.; w_n(2) = 1.;
- xi_n(3,0) = -1.; xi_n(3,1) = +1.; w_n(3) = 1.;
-
-}
-
-// -------------------------------------------------------------------------------------------------
-
-void Element::computeMassMatrix(size_t elem)
-{
- // zero-initialize element mass matrix
- M.zeros();
-
- // loop over integration points (coincide with the nodes to get a diagonal mass matrix)
- for ( size_t k = 0 ; k < nne ; ++k )
- {
- // - shape function gradients (local coordinates)
- dNdxi(0,0) = -.25*(1.-xi_n(k,1)); dNdxi(0,1) = -.25*(1.-xi_n(k,0));
- dNdxi(1,0) = +.25*(1.-xi_n(k,1)); dNdxi(1,1) = -.25*(1.+xi_n(k,0));
- dNdxi(2,0) = +.25*(1.+xi_n(k,1)); dNdxi(2,1) = +.25*(1.+xi_n(k,0));
- dNdxi(3,0) = -.25*(1.+xi_n(k,1)); dNdxi(3,1) = +.25*(1.-xi_n(k,0));
-
- // - Jacobian
- J.zeros();
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- J(i,j) += dNdxi(m,i) * xe(m,j);
-
- // - determinant and inverse of the Jacobian
- Jdet = J.det();
- Jinv = J.inv();
-
- // - integration point volume (== volume associated with the node, in this element)
- V = w_n(k) * Jdet;
-
- // - assemble to element mass matrix (use the delta properties of the shape functions)
- for ( size_t i = 0 ; i < ndim ; ++i )
- M(i,i) += rho * V;
- }
-}
-
-// -------------------------------------------------------------------------------------------------
-
-void Element::computeInternalForce(size_t elem)
-{
- // zero-initialize element force
- fu.zeros();
-
- // loop over integration points
- for ( size_t k = 0 ; k < nk ; ++k )
- {
- // - shape function gradients (local coordinates)
- dNdxi(0,0) = -.25*(1.-xi(k,1)); dNdxi(0,1) = -.25*(1.-xi(k,0));
- dNdxi(1,0) = +.25*(1.-xi(k,1)); dNdxi(1,1) = -.25*(1.+xi(k,0));
- dNdxi(2,0) = +.25*(1.+xi(k,1)); dNdxi(2,1) = +.25*(1.+xi(k,0));
- dNdxi(3,0) = -.25*(1.+xi(k,1)); dNdxi(3,1) = +.25*(1.-xi(k,0));
-
- // - Jacobian
- J.zeros();
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- J(i,j) += dNdxi(m,i) * xe(m,j);
-
- // - determinant and inverse of the Jacobian
- Jdet = J.det();
- Jinv = J.inv();
-
- // - integration point volume
- V = w(k) * Jdet;
-
- // - shape function gradients (global coordinates)
- dNdx.zeros();
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- dNdx(m,i) += Jinv(i,j) * dNdxi(m,j);
-
- // - displacement gradient
- gradu.zeros();
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- gradu(i,j) += dNdx(m,i) * ue(m,j);
-
- // - strain tensor (symmetric part of "gradu")
- eps = gradu.astensor2s();
-
- // - constitutive response
- if ( elem < (nelem/4)*nelem ) sig = hard.stress(eps);
- else sig = soft.stress(eps);
-
- // - assemble to element force
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- fu(m*ndim+j) += dNdx(m,i) * sig(i,j) * V;
- }
-}
-
-// -------------------------------------------------------------------------------------------------
-
-void Element::computeDampingForce(size_t elem)
-{
- // zero-initialize element force
- fv.zeros();
-
- // loop over integration points
- for ( size_t k = 0 ; k < nk ; ++k )
- {
- // - shape function gradients (local coordinates)
- dNdxi(0,0) = -.25*(1.-xi(k,1)); dNdxi(0,1) = -.25*(1.-xi(k,0));
- dNdxi(1,0) = +.25*(1.-xi(k,1)); dNdxi(1,1) = -.25*(1.+xi(k,0));
- dNdxi(2,0) = +.25*(1.+xi(k,1)); dNdxi(2,1) = +.25*(1.+xi(k,0));
- dNdxi(3,0) = -.25*(1.+xi(k,1)); dNdxi(3,1) = +.25*(1.-xi(k,0));
-
- // - Jacobian
- J.zeros();
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- J(i,j) += dNdxi(m,i) * xe(m,j);
-
- // - determinant and inverse of the Jacobian
- Jdet = J.det();
- Jinv = J.inv();
-
- // - integration point volume
- V = w(k) * Jdet;
-
- // - shape function gradients (global coordinates)
- dNdx.zeros();
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- dNdx(m,i) += Jinv(i,j) * dNdxi(m,j);
-
- // - velocity gradient
- gradv.zeros();
-
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- gradv(i,j) += dNdx(m,i) * ve(m,j);
-
- // - strain rate tensor (symmetric part of "gradv")
- epsdot = gradv.astensor2s();
-
- // - constitutive response
- sig = rayleigh.stress(epsdot);
-
- // - assemble to element force
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- fv(m*ndim+j) += dNdx(m,i) * sig(i,j) * V;
- }
-}
-
-// -------------------------------------------------------------------------------------------------
-
-void Element::postProcess(size_t elem)
-{
- // loop over integration points
- for ( size_t k = 0 ; k < nk ; ++k )
- {
- // - shape functions
- N(0) = .25*(1.-xi(k,0))*(1.-xi(k,1));
- N(1) = .25*(1.+xi(k,0))*(1.-xi(k,1));
- N(2) = .25*(1.+xi(k,0))*(1.+xi(k,1));
- N(3) = .25*(1.-xi(k,0))*(1.+xi(k,1));
-
- // - shape function gradients (local coordinates)
- dNdxi(0,0) = -.25*(1.-xi(k,1)); dNdxi(0,1) = -.25*(1.-xi(k,0));
- dNdxi(1,0) = +.25*(1.-xi(k,1)); dNdxi(1,1) = -.25*(1.+xi(k,0));
- dNdxi(2,0) = +.25*(1.+xi(k,1)); dNdxi(2,1) = +.25*(1.+xi(k,0));
- dNdxi(3,0) = -.25*(1.+xi(k,1)); dNdxi(3,1) = +.25*(1.-xi(k,0));
-
- // - Jacobian
- J.zeros();
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- J(i,j) += dNdxi(m,i) * xe(m,j);
-
- // - determinant and inverse of the Jacobian
- Jdet = J.det();
- Jinv = J.inv();
-
- // - integration point volume
- V = w(k) * Jdet;
- // - add to total volume
- Vbar += V;
-
- // - shape function gradients (global coordinates)
- dNdx.zeros();
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- dNdx(m,i) += Jinv(i,j) * dNdxi(m,j);
-
- // - displacement gradient
- gradu.zeros();
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- gradu(i,j) += dNdx(m,i) * ue(m,j);
-
- // - strain tensor (symmetric part of "gradu")
- eps = gradu.astensor2s();
-
- // - add to total strain energy
- if ( elem < (nelem/4)*nelem ) Epotbar += hard.energy(eps) * V;
- else Epotbar += soft.energy(eps) * V;
-
- // - velocity
- v.zeros();
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- v(i) += N(m) * ve(m,i);
-
- // - add to total kinetic energy
- Ekinbar += .5 * rho * v.dot(v) * V;
-
- }
-}
-
-// =================================================================================================
-
-int main(int argc, const char** argv)
-{
- // get "eta" and "name" of the output file from the input
- std::string num1 = argv[1]; size_t N = std::stod(num1);
- std::string num2 = argv[2]; double eta = std::stod(num2);
- std::string num3 = argv[3]; double alpha = std::stod(num3);
- std::string num4 = argv[4]; double dt = std::stod(num4);
- std::string name = argv[5];
-
- // define a mesh
- GooseFEM::Mesh::Quad4::Regular mesh(N,N,static_cast<double>(N),static_cast<double>(N));
- // extract a reference node (whose position will stay constant)
- size_t nodeRef = mesh.nodesRef();
-
- // define the problem specific "Element" routines (see above)
- auto elem = std::make_shared<Element>(eta,N);
-
- // define the entire problem
- GooseFEM::Dynamics::Periodic::DiagonalMass<Element> sim(
- elem,
- mesh.coor(),
- mesh.conn(),
- mesh.dofsPeriodic(),
- dt,
- alpha
- );
-
- // define update in macroscopic deformation gradient
- T2 dFbar(0.);
- dFbar(0,1) = .01;
-
- // update the displacement according to the macroscopic deformation gradient update
- for ( size_t i = 0 ; i < sim.nnode ; ++i )
- for ( size_t j = 0 ; j < sim.ndim ; ++j )
- for ( size_t k = 0 ; k < sim.ndim ; ++k )
- sim.u(i,j) += dFbar(j,k) * ( sim.x0(i,k) - sim.x0(nodeRef,k) );
-
- // output : total energy and potential energy
- ColD Epotbar(static_cast<int>(15./dt));
- ColD Ekinbar(static_cast<int>(15./dt));
- ColD t (static_cast<int>(15./dt));
-
- // loop over increments
- for ( size_t i = 0 ; i < static_cast<size_t>(Epotbar.size()) ; ++i )
- {
- // - compute increment
- sim.Verlet();
-
- // - post-process
- // -- zero-initialize averages
- elem->Vbar = 0.;
- elem->Epotbar = 0.;
- elem->Ekinbar = 0.;
- // -- compute sums
- sim.postProcess();
- // -- normalize and store averages
- Epotbar(i) = elem->Epotbar;
- Ekinbar(i) = elem->Ekinbar;
- t (i) = sim.t;
- }
-
- // write to output file
- H5p::File f = H5p::File(name);
- f.write("/global/Epot",Epotbar );
- f.write("/global/Ekin",Ekinbar );
- f.write("/global/t" ,t );
- f.write("/mesh/coor" ,mesh.coor());
- f.write("/mesh/conn" ,mesh.conn());
- f.write("/mesh/disp" ,sim.u );
-
- return 0;
-}
diff --git a/docs/examples/DynamicsPeriodicDiagonal/laminate2/DynamicsDiagonalQuad4.h b/docs/examples/DynamicsPeriodicDiagonal/laminate2/DynamicsDiagonalQuad4.h
deleted file mode 100644
index 94d820c..0000000
--- a/docs/examples/DynamicsPeriodicDiagonal/laminate2/DynamicsDiagonalQuad4.h
+++ /dev/null
@@ -1,328 +0,0 @@
-/* ========================================== DESCRIPTION ==========================================
-
-(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
-
-================================================================================================= */
-
-#ifndef GOOSEFEM_DYNAMICS_DIAGONAL_QUAD4_H
-#define GOOSEFEM_DYNAMICS_DIAGONAL_QUAD4_H
-
-#include "Macros.h"
-#include <cppmat/cppmat.h>
-
-// -------------------------------------------------------------------------------------------------
-
-namespace GooseFEM {
-namespace Dynamics {
-namespace Diagonal {
-
-// -------------------------------------------------------------------------------------------------
-
-using vec = cppmat::cartesian2d::vector <double>;
-using T2 = cppmat::cartesian2d::tensor2 <double>;
-using T2s = cppmat::cartesian2d::tensor2s<double>;
-using T2d = cppmat::cartesian2d::tensor2d<double>;
-
-// =================================================================================================
-
-template <class QuadraturePoint>
-class Quad4
-{
-public:
-
- // variables
- // ---------
-
- // arrays / matrices
- cppmat::tiny::matrix2<double,4,2> xe, ue, ve, xi, xi_n, dNdxi, dNdx;
- cppmat::tiny::vector <double,4> w, w_n;
- cppmat::tiny::matrix2<double,8,8> M;
- cppmat::tiny::vector <double,8> fu, fv;
- // tensors
- cppmat::cartesian2d::tensor2<double> J, Jinv, gradu, gradv;
- // scalars
- double Jdet, V;
- // sizes (nodes per element, dimensions, quadrature points)
- size_t nne=4, ndim=2, nk=4;
- // quadrature point
- std::shared_ptr<QuadraturePoint> quad;
-
- // constructor
- // -----------
-
- Quad4(std::shared_ptr<QuadraturePoint> quad);
-
- // functions
- // ---------
-
- void computeMassMatrix (size_t elem);
- void computeInternalForce(size_t elem);
- void computeDampingForce (size_t elem);
- void postProcess (size_t elem);
-
-};
-
-// =================================================================================================
-
-template <class QuadraturePoint>
-Quad4<QuadraturePoint>::Quad4(std::shared_ptr<QuadraturePoint> _quad)
-{
- // quadrature point routines
- quad = _quad;
-
- // integration point coordinates/weights: normal Gauss integration
- xi(0,0) = -1./std::sqrt(3.); xi(0,1) = -1./std::sqrt(3.); w(0) = 1.;
- xi(1,0) = +1./std::sqrt(3.); xi(1,1) = -1./std::sqrt(3.); w(1) = 1.;
- xi(2,0) = +1./std::sqrt(3.); xi(2,1) = +1./std::sqrt(3.); w(2) = 1.;
- xi(3,0) = -1./std::sqrt(3.); xi(3,1) = +1./std::sqrt(3.); w(3) = 1.;
-
- // integration point coordinates/weights: integration at the nodes
- xi_n(0,0) = -1.; xi_n(0,1) = -1.; w_n(0) = 1.;
- xi_n(1,0) = +1.; xi_n(1,1) = -1.; w_n(1) = 1.;
- xi_n(2,0) = +1.; xi_n(2,1) = +1.; w_n(2) = 1.;
- xi_n(3,0) = -1.; xi_n(3,1) = +1.; w_n(3) = 1.;
-}
-
-// =================================================================================================
-
-template <class QuadraturePoint>
-void Quad4<QuadraturePoint>::computeMassMatrix(size_t elem)
-{
- // zero-initialize element mass matrix
- M.zeros();
-
- // loop over integration points (coincide with the nodes to get a diagonal mass matrix)
- for ( size_t k = 0 ; k < nne ; ++k )
- {
- // - shape function gradients (local coordinates)
- dNdxi(0,0) = -.25*(1.-xi_n(k,1)); dNdxi(0,1) = -.25*(1.-xi_n(k,0));
- dNdxi(1,0) = +.25*(1.-xi_n(k,1)); dNdxi(1,1) = -.25*(1.+xi_n(k,0));
- dNdxi(2,0) = +.25*(1.+xi_n(k,1)); dNdxi(2,1) = +.25*(1.+xi_n(k,0));
- dNdxi(3,0) = -.25*(1.+xi_n(k,1)); dNdxi(3,1) = +.25*(1.-xi_n(k,0));
-
- // - Jacobian
- J.zeros();
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- J(i,j) += dNdxi(m,i) * xe(m,j);
-
- // - determinant and inverse of the Jacobian
- Jdet = J.det();
- Jinv = J.inv();
-
- // - integration point volume (== volume associated with the node, in this element)
- V = w_n(k) * Jdet;
-
- // - assemble to element mass matrix (use the delta properties of the shape functions)
- for ( size_t i = 0 ; i < ndim ; ++i )
- M(i,i) += quad->density(elem,k,V) * V;
- }
-}
-
-// =================================================================================================
-
-template <class QuadraturePoint>
-void Quad4<QuadraturePoint>::computeInternalForce(size_t elem)
-{
- // zero-initialize element force
- fu.zeros();
-
- // loop over integration points
- for ( size_t k = 0 ; k < nk ; ++k )
- {
- // - shape function gradients (local coordinates)
- dNdxi(0,0) = -.25*(1.-xi(k,1)); dNdxi(0,1) = -.25*(1.-xi(k,0));
- dNdxi(1,0) = +.25*(1.-xi(k,1)); dNdxi(1,1) = -.25*(1.+xi(k,0));
- dNdxi(2,0) = +.25*(1.+xi(k,1)); dNdxi(2,1) = +.25*(1.+xi(k,0));
- dNdxi(3,0) = -.25*(1.+xi(k,1)); dNdxi(3,1) = +.25*(1.-xi(k,0));
-
- // - Jacobian
- J.zeros();
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- J(i,j) += dNdxi(m,i) * xe(m,j);
-
- // - determinant and inverse of the Jacobian
- Jdet = J.det();
- Jinv = J.inv();
-
- // - integration point volume
- V = w(k) * Jdet;
-
- // - shape function gradients (global coordinates)
- dNdx.zeros();
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- dNdx(m,i) += Jinv(i,j) * dNdxi(m,j);
-
- // - displacement gradient
- gradu.zeros();
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- gradu(i,j) += dNdx(m,i) * ue(m,j);
-
- // - strain tensor (symmetric part of "gradu")
- for ( size_t i = 0 ; i < ndim ; ++i ) {
- for ( size_t j = i ; j < ndim ; ++j ) {
- quad->eps(i,j) = .5 * ( gradu(i,j) + gradu(j,i) );
- quad->eps(j,i) = quad->eps(i,j);
- }
- }
-
- // - constitutive response
- quad->stressStrain(elem,k,V)
-
- // - assemble to element force
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- fu(m*ndim+j) += dNdx(m,i) * quad->sig(i,j) * V;
- }
-}
-
-// =================================================================================================
-
-template <class QuadraturePoint>
-void Quad4<QuadraturePoint>::computeDampingForce(size_t elem)
-{
- // zero-initialize element force
- fv.zeros();
-
- // loop over integration points
- for ( size_t k = 0 ; k < nk ; ++k )
- {
- // - shape function gradients (local coordinates)
- dNdxi(0,0) = -.25*(1.-xi(k,1)); dNdxi(0,1) = -.25*(1.-xi(k,0));
- dNdxi(1,0) = +.25*(1.-xi(k,1)); dNdxi(1,1) = -.25*(1.+xi(k,0));
- dNdxi(2,0) = +.25*(1.+xi(k,1)); dNdxi(2,1) = +.25*(1.+xi(k,0));
- dNdxi(3,0) = -.25*(1.+xi(k,1)); dNdxi(3,1) = +.25*(1.-xi(k,0));
-
- // - Jacobian
- J.zeros();
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- J(i,j) += dNdxi(m,i) * xe(m,j);
-
- // - determinant and inverse of the Jacobian
- Jdet = J.det();
- Jinv = J.inv();
-
- // - integration point volume
- V = w(k) * Jdet;
-
- // - shape function gradients (global coordinates)
- dNdx.zeros();
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- dNdx(m,i) += Jinv(i,j) * dNdxi(m,j);
-
- // - velocity gradient
- gradv.zeros();
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- gradv(i,j) += dNdx(m,i) * ve(m,j);
-
- // - strain-rate tensor (symmetric part of "gradu")
- for ( size_t i = 0 ; i < ndim ; ++i ) {
- for ( size_t j = i ; j < ndim ; ++j ) {
- quad->epsdot(i,j) = .5 * ( gradu(i,j) + gradu(j,i) );
- quad->epsdot(j,i) = quad->epsdot(i,j);
- }
- }
-
- // - constitutive response
- quad->stressStrainRate(elem,k,V)
-
- // - assemble to element force
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- fv(m*ndim+j) += dNdx(m,i) * quad->sig(i,j) * V;
- }
-}
-
-// =================================================================================================
-
-template <class QuadraturePoint>
-void Quad4<QuadraturePoint>::postProcess(size_t elem)
-{
- // loop over integration points
- for ( size_t k = 0 ; k < nk ; ++k )
- {
- // - shape function gradients (local coordinates)
- dNdxi(0,0) = -.25*(1.-xi(k,1)); dNdxi(0,1) = -.25*(1.-xi(k,0));
- dNdxi(1,0) = +.25*(1.-xi(k,1)); dNdxi(1,1) = -.25*(1.+xi(k,0));
- dNdxi(2,0) = +.25*(1.+xi(k,1)); dNdxi(2,1) = +.25*(1.+xi(k,0));
- dNdxi(3,0) = -.25*(1.+xi(k,1)); dNdxi(3,1) = +.25*(1.-xi(k,0));
-
- // - Jacobian
- J.zeros();
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- J(i,j) += dNdxi(m,i) * xe(m,j);
-
- // - determinant and inverse of the Jacobian
- Jdet = J.det();
- Jinv = J.inv();
-
- // - integration point volume
- V = w(k) * Jdet;
- // - add to total volume
- Vbar += V;
-
- // - shape function gradients (global coordinates)
- dNdx.zeros();
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- dNdx(m,i) += Jinv(i,j) * dNdxi(m,j);
-
- // - displacement gradient
- gradu.zeros();
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- gradu(i,j) += dNdx(m,i) * ue(m,j);
-
- // - strain tensor (symmetric part of "gradu")
- for ( size_t i = 0 ; i < ndim ; ++i ) {
- for ( size_t j = i ; j < ndim ; ++j ) {
- quad->eps(i,j) = .5 * ( gradu(i,j) + gradu(j,i) );
- quad->eps(j,i) = quad->eps(i,j);
- }
- }
-
- // - velocity gradient
- gradv.zeros();
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- gradv(i,j) += dNdx(m,i) * ve(m,j);
-
- // - strain-rate tensor (symmetric part of "gradu")
- for ( size_t i = 0 ; i < ndim ; ++i ) {
- for ( size_t j = i ; j < ndim ; ++j ) {
- quad->epsdot(i,j) = .5 * ( gradu(i,j) + gradu(j,i) );
- quad->epsdot(j,i) = quad->epsdot(i,j);
- }
- }
-
- // - constitutive response
- quad->stressStrainPost(elem,k,V)
- quad->stressStrainRatePost(elem,k,V)
- }
-}
-
-// =================================================================================================
-
-}}} // namespace GooseFEM::Dynamics::Diagonal
-
-#endif
diff --git a/docs/examples/DynamicsPeriodicDiagonal/laminate2/main.cpp b/docs/examples/DynamicsPeriodicDiagonal/laminate2/main.cpp
deleted file mode 100644
index af2d76e..0000000
--- a/docs/examples/DynamicsPeriodicDiagonal/laminate2/main.cpp
+++ /dev/null
@@ -1,382 +0,0 @@
-
-#include <Eigen/Eigen>
-#include <HDF5pp.h>
-#include <cppmat/cppmat.h>
-#include <GooseFEM/GooseFEM.h>
-#include <GooseMaterial/AmorphousSolid/LinearStrain/ElastoPlastic/Cartesian2d.h>
-
-using MatD = GooseFEM::MatD;
-using ColD = GooseFEM::ColD;
-
-
-
-namespace GM = GooseMaterial::AmorphousSolid::LinearStrain::ElastoPlastic::Cartesian2d;
-
-using vec = cppmat::cartesian2d::vector <double>;
-using T2 = cppmat::cartesian2d::tensor2 <double>;
-using T2s = cppmat::cartesian2d::tensor2s<double>;
-using T2d = cppmat::cartesian2d::tensor2d<double>;
-
-
-// =================================================================================================
-
-class Element
-{
-public:
- // arrays / matrices
- cppmat::tiny::matrix2<double,4,2> xe, ue, ve, xi, xi_n, dNdxi, dNdx;
- cppmat::tiny::vector <double,4> N, w, w_n;
- cppmat::tiny::matrix2<double,8,8> M;
- cppmat::tiny::vector <double,8> fu, fv;
- // tensors
- cppmat::cartesian2d::tensor2 <double> J, Jinv, gradu, gradv;
- cppmat::cartesian2d::tensor2s<double> eps, epsdot, sig;
- cppmat::cartesian2d::vector <double> v;
- // scalars
- double Jdet, V;
- // sizes (nodes per element, dimensions, quadrature points)
- size_t nne=4, ndim=2, nk=4;
-
- // problem definition
- // - density
- double rho;
- // - constitutive model / Rayleigh damping
- GM::Material hard, soft, rayleigh;
- // - number of elements
- size_t nelem;
-
- // output quantities
- double Epotbar; // potential energy
- double Ekinbar; // kinetic energy
- double Vbar; // volume
-
- Element(double eta, size_t nelem);
-
- void computeMassMatrix (size_t elem);
- void computeInternalForce(size_t elem);
- void computeDampingForce (size_t elem);
- void postProcess (size_t elem);
-
-};
-
-// -------------------------------------------------------------------------------------------------
-
-Element::Element(double eta, size_t _nelem)
-{
- // constitutive definition
- hard = GM::Material(100.,10.);
- soft = GM::Material(100., 1.);
- rayleigh = GM::Material(eta ,eta);
- rho = 1.;
- nelem = _nelem;
-
- // integration point coordinates/weights: normal Gauss integration for Quad4
- xi(0,0) = -1./std::sqrt(3.); xi(0,1) = -1./std::sqrt(3.); w(0) = 1.;
- xi(1,0) = +1./std::sqrt(3.); xi(1,1) = -1./std::sqrt(3.); w(1) = 1.;
- xi(2,0) = +1./std::sqrt(3.); xi(2,1) = +1./std::sqrt(3.); w(2) = 1.;
- xi(3,0) = -1./std::sqrt(3.); xi(3,1) = +1./std::sqrt(3.); w(3) = 1.;
-
- // integration point coordinates/weights: integration at the nodes for Quad4
- xi_n(0,0) = -1.; xi_n(0,1) = -1.; w_n(0) = 1.;
- xi_n(1,0) = +1.; xi_n(1,1) = -1.; w_n(1) = 1.;
- xi_n(2,0) = +1.; xi_n(2,1) = +1.; w_n(2) = 1.;
- xi_n(3,0) = -1.; xi_n(3,1) = +1.; w_n(3) = 1.;
-
-}
-
-// -------------------------------------------------------------------------------------------------
-
-void Element::computeMassMatrix(size_t elem)
-{
- // zero-initialize element mass matrix
- M.zeros();
-
- // loop over integration points (coincide with the nodes to get a diagonal mass matrix)
- for ( size_t k = 0 ; k < nne ; ++k )
- {
- // - shape function gradients (local coordinates)
- dNdxi(0,0) = -.25*(1.-xi_n(k,1)); dNdxi(0,1) = -.25*(1.-xi_n(k,0));
- dNdxi(1,0) = +.25*(1.-xi_n(k,1)); dNdxi(1,1) = -.25*(1.+xi_n(k,0));
- dNdxi(2,0) = +.25*(1.+xi_n(k,1)); dNdxi(2,1) = +.25*(1.+xi_n(k,0));
- dNdxi(3,0) = -.25*(1.+xi_n(k,1)); dNdxi(3,1) = +.25*(1.-xi_n(k,0));
-
- // - Jacobian
- J.zeros();
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- J(i,j) += dNdxi(m,i) * xe(m,j);
-
- // - determinant and inverse of the Jacobian
- Jdet = J.det();
- Jinv = J.inv();
-
- // - integration point volume (== volume associated with the node, in this element)
- V = w_n(k) * Jdet;
-
- // - assemble to element mass matrix (use the delta properties of the shape functions)
- for ( size_t i = 0 ; i < ndim ; ++i )
- M(i,i) += rho * V;
- }
-}
-
-// -------------------------------------------------------------------------------------------------
-
-void Element::computeInternalForce(size_t elem)
-{
- // zero-initialize element force
- fu.zeros();
-
- // loop over integration points
- for ( size_t k = 0 ; k < nk ; ++k )
- {
- // - shape function gradients (local coordinates)
- dNdxi(0,0) = -.25*(1.-xi(k,1)); dNdxi(0,1) = -.25*(1.-xi(k,0));
- dNdxi(1,0) = +.25*(1.-xi(k,1)); dNdxi(1,1) = -.25*(1.+xi(k,0));
- dNdxi(2,0) = +.25*(1.+xi(k,1)); dNdxi(2,1) = +.25*(1.+xi(k,0));
- dNdxi(3,0) = -.25*(1.+xi(k,1)); dNdxi(3,1) = +.25*(1.-xi(k,0));
-
- // - Jacobian
- J.zeros();
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- J(i,j) += dNdxi(m,i) * xe(m,j);
-
- // - determinant and inverse of the Jacobian
- Jdet = J.det();
- Jinv = J.inv();
-
- // - integration point volume
- V = w(k) * Jdet;
-
- // - shape function gradients (global coordinates)
- dNdx.zeros();
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- dNdx(m,i) += Jinv(i,j) * dNdxi(m,j);
-
- // - displacement gradient
- gradu.zeros();
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- gradu(i,j) += dNdx(m,i) * ue(m,j);
-
- // - strain tensor (symmetric part of "gradu")
- eps = gradu.astensor2s();
-
- // - constitutive response
- if ( elem < (nelem/4)*nelem ) sig = hard.stress(eps);
- else sig = soft.stress(eps);
-
- // - assemble to element force
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- fu(m*ndim+j) += dNdx(m,i) * sig(i,j) * V;
- }
-}
-
-// -------------------------------------------------------------------------------------------------
-
-void Element::computeDampingForce(size_t elem)
-{
- // zero-initialize element force
- fv.zeros();
-
- // loop over integration points
- for ( size_t k = 0 ; k < nk ; ++k )
- {
- // - shape function gradients (local coordinates)
- dNdxi(0,0) = -.25*(1.-xi(k,1)); dNdxi(0,1) = -.25*(1.-xi(k,0));
- dNdxi(1,0) = +.25*(1.-xi(k,1)); dNdxi(1,1) = -.25*(1.+xi(k,0));
- dNdxi(2,0) = +.25*(1.+xi(k,1)); dNdxi(2,1) = +.25*(1.+xi(k,0));
- dNdxi(3,0) = -.25*(1.+xi(k,1)); dNdxi(3,1) = +.25*(1.-xi(k,0));
-
- // - Jacobian
- J.zeros();
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- J(i,j) += dNdxi(m,i) * xe(m,j);
-
- // - determinant and inverse of the Jacobian
- Jdet = J.det();
- Jinv = J.inv();
-
- // - integration point volume
- V = w(k) * Jdet;
-
- // - shape function gradients (global coordinates)
- dNdx.zeros();
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- dNdx(m,i) += Jinv(i,j) * dNdxi(m,j);
-
- // - velocity gradient
- gradv.zeros();
-
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- gradv(i,j) += dNdx(m,i) * ve(m,j);
-
- // - strain rate tensor (symmetric part of "gradv")
- epsdot = gradv.astensor2s();
-
- // - constitutive response
- sig = rayleigh.stress(epsdot);
-
- // - assemble to element force
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- fv(m*ndim+j) += dNdx(m,i) * sig(i,j) * V;
- }
-}
-
-// -------------------------------------------------------------------------------------------------
-
-void Element::postProcess(size_t elem)
-{
- // loop over integration points
- for ( size_t k = 0 ; k < nk ; ++k )
- {
- // - shape functions
- N(0) = .25*(1.-xi(k,0))*(1.-xi(k,1));
- N(1) = .25*(1.+xi(k,0))*(1.-xi(k,1));
- N(2) = .25*(1.+xi(k,0))*(1.+xi(k,1));
- N(3) = .25*(1.-xi(k,0))*(1.+xi(k,1));
-
- // - shape function gradients (local coordinates)
- dNdxi(0,0) = -.25*(1.-xi(k,1)); dNdxi(0,1) = -.25*(1.-xi(k,0));
- dNdxi(1,0) = +.25*(1.-xi(k,1)); dNdxi(1,1) = -.25*(1.+xi(k,0));
- dNdxi(2,0) = +.25*(1.+xi(k,1)); dNdxi(2,1) = +.25*(1.+xi(k,0));
- dNdxi(3,0) = -.25*(1.+xi(k,1)); dNdxi(3,1) = +.25*(1.-xi(k,0));
-
- // - Jacobian
- J.zeros();
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- J(i,j) += dNdxi(m,i) * xe(m,j);
-
- // - determinant and inverse of the Jacobian
- Jdet = J.det();
- Jinv = J.inv();
-
- // - integration point volume
- V = w(k) * Jdet;
- // - add to total volume
- Vbar += V;
-
- // - shape function gradients (global coordinates)
- dNdx.zeros();
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- dNdx(m,i) += Jinv(i,j) * dNdxi(m,j);
-
- // - displacement gradient
- gradu.zeros();
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- for ( size_t j = 0 ; j < ndim ; ++j )
- gradu(i,j) += dNdx(m,i) * ue(m,j);
-
- // - strain tensor (symmetric part of "gradu")
- eps = gradu.astensor2s();
-
- // - add to total strain energy
- if ( elem < (nelem/4)*nelem ) Epotbar += hard.energy(eps) * V;
- else Epotbar += soft.energy(eps) * V;
-
- // - velocity
- v.zeros();
- for ( size_t m = 0 ; m < nne ; ++m )
- for ( size_t i = 0 ; i < ndim ; ++i )
- v(i) += N(m) * ve(m,i);
-
- // - add to total kinetic energy
- Ekinbar += .5 * rho * v.dot(v) * V;
-
- }
-}
-
-// =================================================================================================
-
-int main(int argc, const char** argv)
-{
- // get "eta" and "name" of the output file from the input
- std::string num1 = argv[1]; size_t N = std::stod(num1);
- std::string num2 = argv[2]; double eta = std::stod(num2);
- std::string num3 = argv[3]; double alpha = std::stod(num3);
- std::string num4 = argv[4]; double dt = std::stod(num4);
- std::string name = argv[5];
-
- // define a mesh
- GooseFEM::Mesh::Quad4::Regular mesh(N,N,static_cast<double>(N),static_cast<double>(N));
- // extract a reference node (whose position will stay constant)
- size_t nodeRef = mesh.nodesRef();
-
- // define the problem specific "Element" routines (see above)
- auto elem = std::make_shared<Element>(eta,N);
-
- // define the entire problem
- GooseFEM::Dynamics::Periodic::DiagonalMass<Element> sim(
- elem,
- mesh.coor(),
- mesh.conn(),
- mesh.dofsPeriodic(),
- dt,
- alpha
- );
-
- // define update in macroscopic deformation gradient
- T2 dFbar(0.);
- dFbar(0,1) = .01;
-
- // update the displacement according to the macroscopic deformation gradient update
- for ( size_t i = 0 ; i < sim.nnode ; ++i )
- for ( size_t j = 0 ; j < sim.ndim ; ++j )
- for ( size_t k = 0 ; k < sim.ndim ; ++k )
- sim.u(i,j) += dFbar(j,k) * ( sim.x0(i,k) - sim.x0(nodeRef,k) );
-
- // output : total energy and potential energy
- ColD Epotbar(static_cast<int>(15./dt));
- ColD Ekinbar(static_cast<int>(15./dt));
- ColD t (static_cast<int>(15./dt));
-
- // loop over increments
- for ( size_t i = 0 ; i < static_cast<size_t>(Epotbar.size()) ; ++i )
- {
- // - compute increment
- sim.Verlet();
-
- // - post-process
- // -- zero-initialize averages
- elem->Vbar = 0.;
- elem->Epotbar = 0.;
- elem->Ekinbar = 0.;
- // -- compute sums
- sim.postProcess();
- // -- normalize and store averages
- Epotbar(i) = elem->Epotbar;
- Ekinbar(i) = elem->Ekinbar;
- t (i) = sim.t;
- }
-
- // write to output file
- H5p::File f = H5p::File(name);
- f.write("/global/Epot",Epotbar );
- f.write("/global/Ekin",Ekinbar );
- f.write("/global/t" ,t );
- f.write("/mesh/coor" ,mesh.coor());
- f.write("/mesh/conn" ,mesh.conn());
- f.write("/mesh/disp" ,sim.u );
-
- return 0;
-}

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