Energy-momentum time integration of gradient-based models for fiber-bending stiffness in anisotropic thermo-mechanical continua

Abstract

Accurate dynamic simulations of 3D fiber-reinforced materials in lightweight structures motivate our research activities. In order to accomplish this, the material reinforcement is performed by fiber rovings with a separate bending stiffness, which can be modelled by a second-order gradient of the deformation mapping (see Reference [10]). With an independent field for the gradient of the right Cauchy-Green tensor, we extend the thermoelastic Cauchy continuum for fiber-matrix composites with single fibers. In addition, we use accurate higherorder energy-momentum schemes in combination with mixed finite element methods to obtain numerically stable long-term dynamic simulations and locking free meshes. Therefore, we introduce additional independent fields of well-known as well as new mixed finite elements within a variational-based space-time finite element method and adapt it to the new material formulation. We use Cook's cantilever beam as representative numerical example. We primarily analyze the influence of the fiber bending stiffness as well as the spatial and time convergence up to cubic order, but also look at the influence of Fourier's heat conduction in the matrix and fiber families.

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