Thermodynamical Topology Optimization For Consideration of Dissipative Material Properties

拓扑优化方法确定部件的几何形状，从而提供最大的阻力，例如，在给定的外部载荷下的变形。有不同的方法，其中大多数都有数学或启发式的背景。在拟议的研究项目中，将对材料建模领域的方法进行调整和扩展，以便除了拓扑优化之外，甚至可以考虑复杂的材料属性，例如非弹性应变率。这使得在优化过程中能够准确地考虑混凝土材料的性能，其特征通常是底层微结构的变化。这样，充分挖掘了材料的潜力，不仅从宏观结构性能方面进行了优化，而且还从微观材料性能方面进行了优化。由于微观结构的变化是耗散过程，本研究比较了两种不同的建模方法，并对结果进行了比较。一种方法使保守能量加耗散能量贡献最小化；另一种方法使耗散最大化。因此，这两种方法都考虑了优化过程中微结构演化的耗散效应。然而，哪种方法更好还不能在预见中确定，将在本研究项目中进行检验。

The method of topology optimization determines the geometry of a component so that it provides maximum resistance, for example, to deformations at given external loads. There are different approaches, most of which have a mathematical or heuristic background. In the proposed research project, a method from the field of material modeling will be adapted and extended such that, in addition to topology optimization, even complex material properties, as e.g. inelastic strain rates, can be considered. This makes it possible to accurately consider the concrete material behavior, which is usually characterized by changes in the underlying microstructure, already during the optimization process. In this way, the potential of the material is fully exploited, and the optimization is carried out not only in terms of macroscopic structural properties but also in terms of microscopic material properties. Since the changes in the microstructure are dissipative processes, the proposed research project compares two different modeling methods and compares the results. One method minimizes conservative plus dissipative energy contributions; the other method maximizes dissipation. Both methods thus take into account the dissipative effects of the evolution of microstructures during optimization. However, which method is the "better" is not determinable in the foresight and will be examined in this research project.