Incorporation of thermal effects into the energy‐momentum consistent elastic model for fiber‐bending stiffness in composites

Owing to the wide acceptance of fiber reinforced composites in the lightweight structure industry, the need to study its thermo‐elastic behavior in dynamical multi‐body systems still remains an open question. Standard continuum models, by virtue of first‐order gradient of deformation, cannot capture curvature effects and hence appropriate extensions of the standard modeling techniques are indispensable to model the accurate physical stiffness. The fiber‐bending curvature are captured by introducing a higher‐order gradient of the deformation as an independent field in the standard continuum. This work explores in detail, a further extension of this continuum to understand the thermal effects on the bending stiffness of fiber bundle in fiber‐reinforced composites. Our proposed model incorporates the temperature of the composite and its bidirectional dependency with the higher‐order gradients of the deformation into the extended mechanical continuum model. The implementation of the model is pursued in the context of multi‐field mixed finite element method and dynamic variational principle. The principle of virtual power enables our extended non‐isothermal continuum to derive an energy‐momentum scheme of higher order. The resulting time‐integrator exhibits physically consistent locking‐ free numerical behavior in dynamical simulations. Our novel approach is illustrated by simple transient dynamic simulations with a hyperelastic, transversely isotropic, polyconvex material behavior. We investigate the conservation of total energy and total momentum in the framework of thermo‐elasticity and study the spatial and temporal convergence for long‐term dynamic simulations with coarser grids and increased accurate numerical solutions.