Our research activity is motivated by accurate dynamic simulations of fiber-
reinforced materials in light-weight structures. In order to accomplish this, we have to
take various steps. The material behavior is formulated with an anisotropic, polyconvex strain
energy function. We combine different mixed element formulations (e.g. see Ref- erence [2] or
[3]) with a Galerkin time integrator as shown in Reference [5]. This reduces the volumetric
locking effect of an incompressible matrix material as well as the locking effect due to stiff
fibers. In addition, we increase the accuracy by using Galerkin-based higher-order time
integrators. Since in long-term simulations a hugh energy error is a strong problem, we
apply the mixed finite element formulations to an energy-momentum time integration scheme (see
Reference [6]). In the next step, we extend the material formulation by adding a
thermo-mechanical coupling as shown in Reference [7]. Here we also describe the directional heat
conduction of the fiber. As numerical examples with multiple material domains and families of
fibers serve cooks cantilever beam as in Ref- erence [5]. The Dirichlet boundary conditions are
modelled by the Lagrange-multiplier method (see Reference [7]) and as Neumann boundary condition a
pressure distribution
is used
