Non-isothermal energy–momentum time integrations with drilling degrees of freedom of composites with viscoelastic fiber bundles and curvature–twist stiffness

Abstract

3D fiber-reinforced composites demand for a special simulation technique, because they consist of fiber bundles. Therefore, in the corresponding representative volume element of these metamaterials, secondary effects as a micro inertia and a curvature–twist stiffness have to bear in mind. The latter increases the strength-to-weight ratio of thin-walled lightweight structures due to a separate twisting and bending stiffness of the fiber bundles. In this paper, these secondary effects are introduced in a continuum formulation by means of independent drilling degrees of freedom. The resulting non-isothermal constrained micropolar continuum is derived by a principle of virtual power, which simultaneously generates in the discrete setting a mixed B-bar method and a Galerkin-based energy–momentum scheme of higher order. This work also takes into account viscoelastic material behavior in the fiber bundles, which arises from a mixture of organic and inorganic fibers. Here, the viscous evolution equation is solved elementwise by using a mixed field as viscous internal variable. Representative numerical examples demonstrate the inelastic material behavior, the effect of micro inertia on the physical properties of the continuum as well as on its space and time discretization and, finally, the twisting and bending stiffness of the fiber bundles. Further, non-standard boundary conditions are applied in the dynamic simulations performed by higher order energy–momentum schemes.