Rauter, Natalie

For the numerical simulation of short fiber-reinforced composites and the correct analysis of the deformation, information about the plastic behavior and its spatial distribution is essential. When using purely deterministic modeling approaches information of the probabilistic microstructure is not included in the simulation process. One possible approach for the integration of stochastic information is the use of random fields, which requires information about the correlation structure of all material input parameters. In this study the correlation structure for finite strain elasto-plastic material behavior of short fiber-reinforced composites is analyzed. This approach combines the use of already established procedures for linear-elastic material behavior with a homogenization method for plasticity. The obtained results reveal a complex correlation structure, which is approximated with triangle and exponential correlation functions influenced by the window size. Due to the dependence of the hyperelastic and plastic material parameters on the fiber mass fraction, the strain-energy density function coefficients are cross-correlated with the yield strength of the composite. With this knowledge at hand, in a subsequent work numerical simulations of tensile tests are conducted that cover the elastic and plastic domain and include spatially distributed material properties.

The present work provides a profound analytical and numerical analysis of the material properties of SFRC on the mesoscale as well as the resulting correlation structure taking into account the probabilistic characteristics of the fiber geometry. This is done by calculating the engineering constants using the analytical framework given by Tandon and Weng as well as Halpin and Tsai. The input parameters like fiber length, diameter and orientation are chosen with respect to their probability density function. It is shown, that they are significantly influenced by the fiber length, the fiber orientation and the fiber volume fraction. The verification of the analytically obtained values is done on a numerical basis. Therefore, a two-dimensional microstructure is generated and transferred to a numerical model. The advantage of this procedure is, that there are several fibers with different geometrical properties placed in a preset area. The results of the numerical analysis meet the analytically obtained conclusions. Furthermore, the results of the numerical simulations are independent of the assumption of a plane strain and plane stress state, respectively. Finally, the correlation structure of the elasticity tensor is investigated. Not only the symmetry properties of the elasticity tensor characterize the correlation structure, but also the overall transversely-isotropic material behavior is confirmed. In contrast to the influencing parameters, the correlation functions vary for a plane strain and a plane stress state.