A formulation of elasticity and viscoelasticity for fibre reinforced material at small and finite strains Original Research Article

A formulation of elasticity and viscoelasticity for fibre reinforced material at small and finite strains Original Research Article Pages 225-243 M. Kaliske Close preview | Related articles | Related reference work articles Abstract | Figures/Tables | References Abstract The combination of unidirectional fibres embedded in matrix yields a novel material which is heterogeneous on the micro level and exhibits new mean characteristics on the macro level. Due to the fact that the length scale of a composite structure is several orders larger compared to the micro scale, the composite material is assumed to be homogeneous on the structural level. Therefore, a homogeneous anisotropic constitutive formulation has to be introduced in order to represent the material and the composite structure efficiently, for example by a finite element discretization. In case of unidirectional reinforced composites a transversely isotropic idealization is meaningful. One typical class of composites is manufactured, for example, from glass or carbon fibres combined with an epoxy matrix. Usually, structures produced from these materials are subjected to small strains. A geometrically nonlinear description is essential when modelling steel or nylon cord reinforced elastomeric material. The investigation of biomaterials like muscles or bones, which also have a fibrous microstructure, is accomplished on the basis of finite strains, too. The static and the dynamic response of a structure can be simulated with the finite element method. The stiffness is characterized by anisotropic elastic properties. For the dynamic response, the dissipative behaviour, originated in the viscoelastic properties of the polymeric material, is of great importance. Depending on the class of composites investigated, the elastic and the viscoelastic behaviour of fibre reinforced material has to be formulated by a transversely isotropic approach at small and at finite strains respectively. With these models at hand, realistic finite element simulations may be carried out. Article Outline 1. Introduction 2. Linear theory 2.1. Elastic constitutive model 2.2. Viscoelastic constitutive model 3. Finite strain formulation 3.1. Elastic constitutive model 3.2. Viscoelastic constitutive model 4. Numerical examples 4.1. Dynamic response of U-profile 4.2. Elastic analysis of a human cornea 4.3. Viscoelastic simulation of a two layer laminate 5. Conclusions Appendix A A.1. Tensor invariants A.2. Transformation operator References