Abstract
AbstractIn this paper, novel higher‐order accurate energy‐momentum schemes are presented, emanating from a discrete mixed principle of virtual power. These time‐stepping schemes are designed for simulating an uni‐directional fiber‐reinforced material, considered as transversely isotropic nonlinear continua. The matrix material is considered as an isotropic thermo‐viscoelastic material and the fibers behave thermoelastic. The higher‐order accurate energy‐momentum schemes preserve each balance law of the continuous problem also in the discrete setting, independent of the chosen time step size and the prescribed Neumann and Dirichlet boundary conditions. Therefore, the implemented time step size control with the iteration number as target function does not influence the preservation properties of the time‐stepping schemes. The balance laws are also preserved together with different time scales in the mechanical, thermal and viscous time evolution (different shape functions in time).
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