No abstract

No abstract

The main goal of this contribution is to provide a simple method for constructing transversely isotropic polyconvex functions suitable for the description of biological soft tissues. The advantage of our approach is that only a few parameters are necessary to approximate a variety of stress-strain curves and to satisfy the condition of a stress-free reference configuration a priori in the framework of polyconvexity. The proposed polyconvex stored energies are embedded into the concept of structural tensors and the representation theorems for isotropic tensor functions are utilized. As an example, the medial layer of a human abdominal aorta is investigated, modeled by some of the proposed polyconvex functions and compared with experimental data. Hereby, the economic fitting to experimental data, and hence the easy handling of the functions is shown.

No abstract

No abstract

A wide class of micro-heterogeneous materials is designed to satisfy the advanced challenges of modern materials occurring in a variety of technical applications. The effective macroscopic properties of such materials are governed by the complex interaction of the individual constituents of the associated microstructure. A sufficient macroscopic phenomenological description of these materials up to a certain order of accuracy can be very complicated or even impossible. On the contrary, a whole resolution of the fine scale for the macroscopic boundary value problem by means of a classical discretization technique seems to be too elaborate. Instead of developing a macroscopic phenomenological constitutive law, it is possible to attach a representative volume element (RVE ) of the microstructure at each point of the macrostructure; this results in a two-scale modeling scheme. A discrete version of this scheme performing finite element (FE) discretizations of the boundary value problems on both scales, the macro-and the micro-scale, is denoted as the FE 2 -method or as the multilevel finite element method. The main advantage of this procedure is based on the fact that we do not have to define a macroscopic phenomenological constitutive law; this is replaced by suitable averages of stress measures and deformation tensors over the microstructure. Details concerning the definition of the macroscopic quantities in terms of their microscopic counterparts, the definition/construction of boundary conditions on the RVE as well as the consistent linearization of the macroscopic constitutive equations are discussed in this contribution. Furthermore, remarks concerning stability problems on both scales as well as their interactions are given and representative numerical examples for elasto-plastic microstructures are discussed.

No abstract

No abstract