Energy-momentum time integration of gradient-based models for fiber-bending stiffness in anisotropic thermo-viscoelastic continua

For our research, we are motivated by dynamic simulations of 3D fiber-reinforced materials in lightweight structures. In such materials, the material reinforcement is performed by fiber rovings with a separate bending stiffness, which can be modelled by a second order gradient of the deformation mapping. Therefore, we extend a thermo-viscoelastic Cauchy continuum for fiber-matrix composites with single fibers by an independent field for the gradient of the right Cauchy-Green tensor. On the other hand, we focus on numerically stable dynamic long-time simulations with locking free meshes, and thus use higher-order accurate energy-momentum schemes emanating from mixed finite element methods. Hence, we adapt the variational-based space-time finite element method to the new material formulation, and additionally include independent fields to obtain well-known mixed finite elements. As representative numerical example, Cook’s cantilever beam is considered. We primarily analyze the influence of the fiber bending stiffness, as well as the spatial and time convergence up to cubic order. Furthermore, we look at the influence of the physical dissipation in the material.