A multiscale simulation method for the determination of mechanical properties of semi-crystalline polymers is presented. First, a four-phase model of crystallization of semi-crystalline polymers is introduced, which is based on the crystallization model of Strobl. From this, a simulation on the nanoscale is derived, which models the formation of lamellae and spherulites during the cooling of the polymer by using a cellular automaton. In the solidified state, mechanical properties are assigned to the formed phases and thus the mechanical behavior of the nanoscale is determined by a finite element (FE) simulation. At this scale, simulations can only be performed up to a simulation range of a few square micrometers. Therefore, the dependence of the mechanical properties on the degree of crystallization is determined by means of homogenization. At the microscale, the cooling of the polymer is simulated by a cellular automaton according to evolution equations. In combination with the mechanical properties determined by homogenization, the mechanical behavior of a macroscopic component can be predicted.

A decisive disadvantage of high dimensional optimization problems is the large number of parameters which make the identification process difficult. Many of this are reflected in the mathematical properties of the objective function used for parameter identification. Ideally, the objective function has a simple, paraboloid-like form with a single minimum whose location corresponds to the desired parameter set. Instead, unfavorable "landscape forms" occur, for example "bumpy" areas with several local minima. In literature, the dominant methods are attempt to simplify high-dimensional functions, or to research new, mostly stochastic optimization methods. This article examines a way to obtain information about the landscape of the objective function underlying an optimization problem. A path search algorithm based on the Dijkstra algorithm is presented. The purpose of the algorithm is to find the approximately deepest path between two local minima, which allows to obtain information about the characteristics of the objective function. It is tested on the Himmelblau and Rastrigin function and allows to examine the landscape between two local minima with respect to their topographic characteristics.

A cross-scale homogenization approach for multi-phase materials is to calculate an effective material stiffness in the smaller scale for the multiple states. These detailed results are used to identify a calculation rule for the effective material stiffness in the larger scale. The calculation of the stiffness matrix using ABAQUS for 3D finite elements was already described by [1]. This can be transferred to the calculation of the 2D stiffness matrix in R 3×3 without much effort. However, some 2D elements in ABAQUS require the specification of a matrix in R 4×4. In this article, the methods for calculating this type of stiffness matrix in 2D are presented.

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A typical property of filled rubber material, known as Mullins effect, is that prestraining leads to a reduction of stresses at strain levels smaller than the maximum strain in the loading history. This softening is related to the direction of the prestrain and therefore induces a material anisotropy. The microstructural process responsible for this effect is still subject of discussion. Here, a mechanism based on the self-organization of weak physical links is proposed. The central idea states that these links organize into a pattern of different linkage densities leading to the observed properties. The theory is tested by a simulation program. In the simulation, several typical rubber properties can be reproduced, while clearly observing self-organization of the model elements.