periodic_elastoplastic_finite-strain.py
782b7a5e04e5master

periodic_elastoplastic_finite-strain.py
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			import argparse
			import sys

			import GMatElastoPlasticFiniteStrainSimo
			import GMatTensor
			import GooseFEM
			import numpy as np

			# mesh
			# ----

			# define mesh
			mesh = GooseFEM.Mesh.Quad4.Regular(5, 5)

			# mesh dimensions
			nelem = mesh.nelem
			nne = mesh.nne
			ndim = mesh.ndim

			# mesh definitions
			coor = mesh.coor
			conn = mesh.conn
			dofs = mesh.dofs

			# periodicity and fixed displacements DOFs
			# ----------------------------------------

			# add control nodes
			control = GooseFEM.Tyings.Control(coor, dofs)
			coor = control.coor
			dofs = control.dofs
			control_dofs = control.controlDofs
			control_nodes = control.controlNodes

			# extract fixed DOFs:
			# - all control nodes: to prescribe the deformation gradient
			# - one node of the mesh: to remove rigid body modes
			iip = np.concatenate((control_dofs.ravel(), dofs[mesh.nodesOrigin, :].ravel()))

			# get DOF-tyings, reorganise system
			tyings = GooseFEM.Tyings.Periodic(coor, dofs, control_dofs, mesh.nodesPeriodic, iip)
			dofs = tyings.dofs

			# simulation variables
			# --------------------

			# vector definition
			vector = GooseFEM.VectorPartitionedTyings(conn, dofs, tyings.Cdu, tyings.Cdp, tyings.Cdi)

			# element definition
			elem0 = GooseFEM.Element.Quad4.QuadraturePlanar(vector.AsElement(coor))
			elem = GooseFEM.Element.Quad4.QuadraturePlanar(vector.AsElement(coor))
			nip = elem.nip

			# nodal quantities
			disp = np.zeros_like(coor) # nodal displacement
			du = np.zeros_like(coor) # iterative displacement update
			fint = np.zeros_like(coor) # internal force
			fext = np.zeros_like(coor) # external force

			# element vectors / matrix
			ue = np.empty([nelem, nne, ndim])
			fe = np.empty([nelem, nne, ndim])
			Ke = np.empty([nelem, nne * ndim, nne * ndim])

			# DOF values
			Fext = np.zeros([tyings.nni])
			Fint = np.zeros([tyings.nni])

			# material definition
			# -------------------

			kappa = np.ones([nelem, nip])
			mu = np.ones([nelem, nip])
			tauy0 = 0.05 * np.ones([nelem, nip])
			H = np.ones([nelem, nip])

			ehard = mesh.elementgrid[:2, :2].ravel()
			tauy0[ehard, :] = 100

			mat = GMatElastoPlasticFiniteStrainSimo.Cartesian3d.LinearHardening2d(kappa, mu, tauy0, H)

			# solve
			# -----

			# allocate system matrix
			K = GooseFEM.MatrixPartitionedTyings(conn, dofs, tyings.Cdu, tyings.Cdp)
			Solver = GooseFEM.MatrixPartitionedTyingsSolver()

			# array of unit tensor
			I2 = GMatTensor.Cartesian3d.Array2d(mat.shape).I2

			# some shear strain history
			dgamma = 0.001 * np.ones([101])
			dgamma[0] = 0

			# # loop over increments
			for inc in range(dgamma.size):
			# update history
			mat.increment()

			for iiter in range(100):
			# deformation gradient
			vector.asElement(disp, ue)
			elem0.symGradN_vector(ue, mat.F)
			mat.F += I2
			mat.refresh()

			# internal force
			elem.int_gradN_dot_tensor2_dV(mat.Sig, fe)
			vector.assembleNode(fe, fint)

			# stiffness matrix
			elem.int_gradN_dot_tensor4_dot_gradNT_dV(mat.C, Ke)
			K.assemble(Ke)

			# residual
			fres = fext - fint

			# check for convergence (skip the zeroth iteration, as the residual still vanishes)
			if iiter > 0:
			# - internal/external force as DOFs (account for periodicity)
			vector.asDofs_i(fext, Fext)
			vector.asDofs_i(fint, Fint)
			# - extract reaction force
			vector.copy_p(Fint, Fext)
			# - norm of the residual and the reaction force
			nfres = np.sum(np.abs(Fext - Fint))
			nfext = np.sum(np.abs(Fext))
			# - relative residual, for convergence check
			if nfext:
			res = nfres / nfext
			else:
			res = nfres
			# - check for convergence
			if res < 1e-5:
			break
			# - safe-guard from infinite loop
			if iiter > 20:
			raise OSError("Maximal number of iterations exceeded")

			# initialise displacement update
			du.fill(0.0)

			# set fixed displacements
			if iiter == 0:
			du[control_nodes[0], 1] = dgamma[inc]

			# solve
			Solver.solve(K, fres, du)

			# add displacement update
			disp += du

			# update shape functions
			elem.update_x(vector.AsElement(coor + disp))

			# plot
			# ----

			parser = argparse.ArgumentParser()
			parser.add_argument("--plot", action="store_true", help="Plot result")
			parser.add_argument("--save", type=str, help="Save plot (plot not shown)")
			args = parser.parse_args(sys.argv[1:])

			if args.plot:
			import GooseMPL as gplt
			import matplotlib.pyplot as plt

			plt.style.use(["goose", "goose-latex"])

			# strain
			vector.asElement(disp, ue)
			elem0.symGradN_vector(ue, mat.F)
			mat.F += I2
			mat.refresh()

			# average equivalent stress per element
			dV = elem.AsTensor(2, elem.dV)
			Sigav = np.average(mat.Sig, weights=dV, axis=1)
			sigeq = GMatElastoPlasticFiniteStrainSimo.Cartesian3d.Sigeq(Sigav)

			# plot
			fig, ax = plt.subplots()
			gplt.patch(coor=coor + disp, conn=conn, cindex=sigeq, cmap="jet", axis=ax, clim=(0, 0.1))
			gplt.patch(coor=coor, conn=conn, linestyle="--", axis=ax)

			# optional save
			if args.save is not None:
			fig.savefig(args.save)
			else:
			plt.show()

			plt.close(fig)

rGOOSEFEM/docs/examples/statics/periodic_elastoplastic_finite-strain.py782b7a5e04e5master

periodic_elastoplastic_finite-strain.pyView Options

rGOOSEFEM/docs/examples/statics/periodic_elastoplastic_finite-strain.py
782b7a5e04e5master

periodic_elastoplastic_finite-strain.py
View Options