\caption{Problem domain $\Omega$ with boundary in three dimensions. The Dirchelet and the Neumann regions of the boundary are denoted with $\Gamma_u$ and $\Gamma_t$, respecitvely.\label{fig:smm:boundaries}}
\label{fig:problemDomain}
\end{figure}
Different ways of imposing these boundary conditions exist. A basic
way is to loop over nodes or elements at the boundary and apply local
values. A more advanced method consists of using the notion of the
boundary of the mesh. In the following both ways are presented.
Starting with the basic approach, as mentioned, the Dirichlet boundary
conditions can be applied by looping over the nodes and assigning the
required values. Figure~\ref{fig:smm:dirichlet_bc} shows a beam with a
fixed support on the left side. On the right end of the beam, a load
is applied. At the fixed support, the displacement has a given
value. For this example, the displacements in both the $x$ and the
$y$-direction are set to zero. Implementing this displacement boundary
condition is similar to the implementation of initial displacement
conditions described above. However, in order to impose a displacement
boundary condition for all time steps, the corresponding nodes need to
be marked as boundary nodes as shown in the following code:
\begin{cpp}
Array<bool> & blocked = model.getBlockedDOFs();
const Array<Real> & pos = mesh.getNodes();
UInt nb_nodes = mesh.getNbNodes();
Real epsilon = Math::getTolerance();
/* this tolerance is by default equal to the machine precision but can be changed by using %\code{Math::setTolerance(value)}% */
for (UInt i = 0; i < nb_nodes; ++i) {
if(std::abs(pos(i, 0)) < epsilon) {
blocked(i, 0) = true; //block displacement in x-direction
blocked(i, 1) = true; //block displacement in y-direction
disp(i, 0) = 0.; //fixed displacement in x-direction
disp(i, 1)= 0.; //fixed displacement in y-direction
}
}
\end{cpp}
\begin{figure}[!htb]
\centering
\includegraphics[scale=0.4]{figures/dirichlet}
\caption{Beam with fixed support.\label{fig:smm:dirichlet_bc}}
\end{figure}
For the more advanced approach, one needs the notion of a boundary in
the mesh. Therefore, the boundary should be created before boundary
condition functors can be applied. Generally the boundary can be
specified from the mesh file or the geometry. For the first case, the
function \code{createGroupsFromMeshData} is called. This function
can read any types of mesh data which are provided in the mesh
file. If the mesh file is created with Gmsh, the function takes one
input strings which is either \code{tag\_0}, \code{tag\_1} or
\code{physical\_names}. The first two tags are assigned by Gmsh to
each element which shows the physical group that they belong to. In
Gmsh, it is also possible to consider strings for different groups of
elements. These elements can be separated by giving a string
\code{physical\_names} to the function
\code{createGroupsFromMeshData}. Boundary conditions can also be
created from the geometry by calling
\code{createBoundaryGroupFromGeometry}. This function gathers all the
elements on the boundary of the geometry.
To apply the required boundary conditions, the function \code{applyBC}
from the \code{SolidMechanicsModel} needs to be called. This function
gets a Dirichlet or Neumann functor and a string which specifies the
desired boundary on which the boundary conditions is to be
applied. The functors specify the type of conditions to apply. Three
built-in functors for Dirichlet exist: \code{FlagOnly, FixedValue,}
and \code{IncrementValue}. The functor \code{FlagOnly} is used if a
point is fixed in a given direction. Therefore, the input parameter to
this functor is only the fixed direction. The \code{FixedValue}
functor is used when a displacement value is applied in a fixed
direction. The \code{IncrementValue} applies an increment to the
displacement in a given direction. The following code shows the
utilization of three functors for the top, bottom and side surface of
the mesh which were already defined in the Gmsh file:
In the header file the user also needs to declare all the members of
the new material. These include the parameters that a read from the
material input file, as well as any other material parameters that will be computed during the simulation and internal variables.\\
In the following the example of a new damage material will be presented. In this case the parameters in the material will consist of the Young's modulus, the Poisson coefficient, the resistance to damage and the damage threshold. The material will then from these values compute its Lam\'{e} coefficients and its bulk modulus. Furthermore, the user has to add a new internal variable \code{damage} in order to store the amount of damage at each quadrature point in each step of the simulation. For this specific material the member declaration inside the class will look like follows:
During the intializer list the reference to the model and the material id are assigned and the constructor of the internal field is called. Inside the scope of the constructor the internal values have to be initialized and the parameters, that should be printed out, are registered with the function: