Effective viscoelastic behavior of cellular auxetic materials

This work is concerned with the calculation of effective, macroscopic material parameters of materials with an inhomogeneous microstructure. On the microscopic scale, the calculation of a representative volume element of the material is done taking dynamical effects into account. This makes it possible to study damping effects on the macroscopic scale. The microstructures to be analyzed are mainly composed of trusses. They are calculated with a newly developed boundary element formulation, which delivers analytical exact results. A special interest is put on microstructures which, because of their deformation mechanism, cause a negative Poisson’s ratio of a material on the macroscopic scale (auxetic materials). The calculation of adequate macroscopic material parameters is done with different optimization techniques. Beside the classical gradient-based optimization procedures, also softcomputing methods like Genetic Algorithms and Neural Networks are used. A number of numerical examples are presented where effective viscoelastic material parameters are calculated. The Genetic Algorithm turned out to deliver the most reliable results in the homogenization process, wheras the gradient-based methods may fail due to the existence of local minima in the optimization function.