Locking-free higher-order energy-momentum schemes for thermo-viscoelastic fiber-reinforced materials derived by the principle of virtual power

We present noval higher-order accurate energy-momentum schemes for fiber-reinforced thermo-viscoelastic materials, which additionally includes a new locking-free finite element approximation in space. The well-known locking effect of a standard displacement approximation is avoided by approximating the volume as well as the fiber dilatation with independent fields. Both, the energy-momentum time integration as well as the locking-free finite element approximation are derived by a multi-field principle of virtual power. This variational principle acts as a ‘smart interface’ between the energy-momentum consistent time approximation and the mixed finite element approximation in space. Mechanical as well as thermal fields are approximated in-dependently by higher-order finite elements in space as well as in time. The considered material formulation takes into account thermal volume expansion and heat conduction of a visco-elastic matrix material, and an independent thermal expansion as well as heat conduction of unidirectional fibers. In comparison to a standard time integration with standard finite elements, the fields of deformation, linear momentum, temperature, entropy density as well as volume and fiber strains and stresses are approximated independently in space and time. As numerical examples, we show motions of thin-walled thermo-mechanical structures.