Multiscale Modeling of Damage in Micro-Heterogeneous Materials based on incremental variational formulations

为了优化现代工程应用，创新材料的开发至关重要。为此，越来越多的材料被使用，其特征在于独特的微观结构，例如由具有嵌入纤维的基质组成。这些微观非均匀材料的模拟需要在微观尺度上纳入高度非线性和不可逆的力学现象。在这种情况下，直接的微观-宏观过渡的方法的基础上的微观有限元计算的机械领域提供了一个合适的框架。特别感兴趣的是预测的故障初始化状态，其特征在于微观应力集中的结果，刚度降低（损坏）。因此，预期的研究项目的主要目标是开发一个材料模型的微观非均匀材料，这是能够代表在微观尺度上的损伤过程的数字。主要是，计划制定是基于离散的微观计算，需要特殊的损伤材料的法律，为个别微观组成部分。这些都必须在增量变分配方的框架内开发。随后，凸壳计划构建所产生的能量，然后导致网格独立的微观计算的解决方案。然后在数值研究中对均匀化的宏观应力和损伤量的影响进行分析。

To optimize modern engineering applications the development of innovative materials is of vital importance. For this purpose more and more materials are used that are characterized by a distinct microstructure, e.g. consisting of a matrix with embedded fibers. The simulation of these micro-heterogeneous materials requires the incorporation of the highly nonlinear and irreversible mechanical phenomena at the microscale. In this context direct micro-macro transition approaches based on microscopic Finite-Element calculations of the mechanical fields provide a suitable framework. Of particular interest is the prediction of failure-initializing states that are characterized by microscopic stress concentrations as a result of stiffness reduction (damage). Primary objective of the intended research project is therefore to develop a material model for micro-heterogeneous materials, which is able to represent the damage processes at the microscale numerically. Mainly, the planned formulation is based on discrete microscopic calculations requiring special damage material laws for the individual microscopic components. These have to be developed in the framework of incremental variational formulations. Subsequently, convex hulls are planned to be constructed for the resulting energies, which then lead to mesh-independent solutions of microscopic calculations. This has then to be analyzed in numerical studies where the influence onto homogenized macroscopic stress- and damage quantities is investigated.