Variational-based higher-order accurate energy–momentum schemes for thermo-viscoelastic fiber-reinforced continua

Abstract

In this paper, new higher-order accurate energy–momentum schemes are presented, which rely on a discrete mixed principle of virtual power. The schemes are designed for simulating an uni-directional fiber-reinforced continuum, considered as transversally isotropic nonlinear continuum with independent material behavior in and normal to fiber direction. The matrix material is considered as an isotropic thermo-viscoelastic material and the fibers behave thermo-elastic. Hence, the model takes into account an independent conduction of heat according to Duhamel’s law with a transversally isotropic conductivity tensor as well as an independent heat expansion and heat capacity of the matrix and the fibers. The 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 structure-preservation of the schemes. The balance laws are also preserved together with different time scales in the mechanical, thermal and viscous time evolution. By calculating the generalized reactions on the boundary, numerical examples show energy–momentum consistent dynamic simulations of different transient Dirichlet and Neumann boundary conditions.