Hybrid Micro-Macro Modeling of Evolving Microstructures in Finite Plasticity

材料在有限弹塑性应变作用下的发展各向异性和尺寸效应的建模是当前研究的一个重要挑战，对工业应用具有重要意义，例如成形过程的模拟。多尺度方法通过模型固有尺度桥接技术来解释材料的微观结构演变，为定量描述这些效应提供了一个重要的视角。这些技术在最近发展的基于能量最小化的增量均匀化和弛豫方法中的应用，为单晶和多晶的塑性微结构分析提供了一个重要的新视角。然而，迄今为止开发的许多规模桥接技术对计算的要求非常高，只能有限地适用于大规模计算。需要建立基于多尺度的本构模型，使其在大规模计算中具有预测性和可操作性。为此，我们研究了一类混合微观宏观模型，它将纯宏观模型的成分与完整的两尺度模型的成分“混合”在一起。这些混合模型的特点是宏观塑性模型与微观塑性模型的耦合，微观塑性模型以一种简化的方式描述了晶粒重取向等关键的微观结构机制。这种耦合是由特定的均质化假设控制的连接假设提供的，这些假设定义了基于微观模型所描述的微观机制的宏观模型的有效结构各向异性张量的演化。该研究的中心目标是开发计算效率高的多晶塑性微观宏观场景，这些场景解释了基于织构和位错结构的各向异性的演变，以及广义内变量的长度尺度相关平衡方程的尺寸效应。

The modeling of developing anisotropies and size effects in materials undergoing finite elastic-plastic strains is an important challenge of current research with high importance for industrial applications, e.g. for simulations of forming processes. A crucial perspective towards the quantitative description of these effects is provided by multiscale approaches which account for the microstructure evolution of the material by modelinherent scale bridging techniques. The rootage of these techniques in recently developed energy-minimization-based incremental homogenization and relaxation methods provides an important new perspective for the analysis of plastic microstructures in single crystals and polycrystals. However, many of the scale bridging techniques developed so far are computationally extremely demanding and only of restricted applicability to largescale computations. There is a need for the construction of multiscale-based constitutive models which are predictive and handleable in large-scale computations. To this end, we investigate a class of hybrid micro-macro models, which ’mix’ ingredients of a purely macroscopic modeling with those of full two-scale models. These hybrid models are characterized by the coupling of a macroscopic plasticity model with a microscopic plasticity model, where the latter describes in a simplified manner a key microstructural mechanism such as grain reorientation. The coupling is provided by a linking hypothesis governed by specific homogenization assumptions, which define the evolution of effective structural anisotropy tensors of the macro model based on the micro-mechanism described by the micro model. The central goal of the research is the development of computationally efficient micro–macro scenarios for polycrystalline plasticity, which account for the evolution of texture– and dislocation–structure–based anisotropies as well as for size effects by length-scale-dependent balance equations for generalized internal variables.