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.

Abstract

We propose a new variational formulation for large deformations in dynamical systems made of 3D-fiber-reinforced composites. The formulation emanates from the dynamic variational approach based on the principle of virtual power. The use of higher-order gradient theory along with multi-field mixed-finite element method enables us to model the fiber-bending stiffness in fiber reinforced composites for numerical simulations accurately. Our proposed model capture higher-order energy contributions exhibited by fibers that influence the fiber-bending curvature, and consequently the fiber-bending stiffness behaviour. For this, we introduce a higher-order gradient of the deformation mapping as an independent field in the internal energy functional formulation. Along with the energy-momentum scheme, our new time integrator makes possible to perform long-term dynamic simulations with larger time steps and efficient CPU-time. We demonstrate our model using transient dynamical simulations on thre geometrical examples that exhibit hyperelastic, transversely isotropic, polyconvex gradient material behaviour. In the first example, a cantilever beam is self-excited due to its body weight, in the second, a L-shaped block tumbles free in the ambient space after an initial loading phase and in the third a turbine rotor is rotated due to hydrodynamic pressure. It is observed that our model conserves total momenta and total energy and preserves their time evolution in all these examples along with spatial and temporal convergence.

Abstract