Computational homogenization of brittle fracture

脆性断裂的计算均质化

• 批准号: 426323259
• 负责人: Professor Dr. Matti Schneider
• 金额: --
• 依托单位: Arbeitsgruppe Ingenieurmathematik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2019
• 资助国家: 德国
• 起止时间: 2018-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/426323259?language=en
• 关键词: Computational; homogenization; brittle; fracture

For modelling materials with complex microstructure multiscale methods are especially important, i.e. to get hands on material properties which are difficult to determine for anisotropic materials. For hardening material behavior, multiscale methods have reached a high level of maturity and sophistication, both in the mean field context and for computational homogenization.The goal of the proposal is to develop simulation technology to computationally homogenize a special class of brittle fracture models. Building upon recent mathematical results on the periodic and stochastic homogenization of the Francfort-Marigo model, which is often approximated by phase field damage models in mechanics, the (anisotropic) parameters of an effective phase field damage models shall be determined by simulations on complex microstructures. In contrast to methods published so far, the proposed methodology ensures a proper scale transition independent of the applied boundary conditions, because the existence of a representative elementary volume is (mathematically) ensured.The effective (anisotropic) critical energy release rate is computed, for prescribed normal, by the fracture surface (through the microstructure) of minimal area. Using an idea of G. Strang the non-convex minimal surface problem can be transformed into a convex program with unique minimal value. In analogy to segmentation methods used in image processing, performing algorithms are to be identified, enabling the computational homogenization of the Francfort-Marigo model for heterogeneous materials of industrial complexity.To demonstrate the power of the proposed technique, the method shall be implemented in the commercial finite element code Abaqus, and enhanced to work for complex parts.The objectives of the proposed project are:- computation of the fracture surface and the effective critical energy release rate for - complex microstructures based on digital volume images - complex synthetic microstructures - materials with locally isotropic and anisotropic material behavior- fast and robust macroscopic solution of an anisotropic phase field damage modelIn case of approval the project will provide insights for users of phase field damage models, which form of the anisotropic phase field model needs to be assumed and how the associated parameters can be robustly and efficiently computed numerically, provided the corresponding parameters on the microscopic scale are available.

对于具有复杂微观结构的材料建模，多尺度方法尤其重要，即掌握各向异性材料难以确定的材料特性。对于硬化材料行为，多尺度方法在平均场环境和计算均质化方面都达到了高度的成熟度和复杂性。该提案的目标是开发模拟技术，以计算均质化一类特殊的脆性断裂模型。基于最近关于 Francfort-Marigo 模型的周期性和随机均质化的数学结果（通常由力学中的相场损伤模型来近似），有效相场损伤模型的（各向异性）参数应通过对复杂微观结构的模拟来确定。与迄今为止发布的方法相比，所提出的方法确保了独立于所应用的边界条件的适当的尺度转换，因为（在数学上）确保了代表性基本体积的存在。对于规定的法线，通过最小面积的断裂表面（通过微观结构）计算有效（各向异性）临界能量释放率。利用G. Strang的思想，非凸极小曲面问题可以转化为具有唯一极小值的凸规划。与图像处理中使用的分割方法类似，将确定执行算法，从而实现工业复杂性异质材料的 Francfort-Marigo 模型的计算均质化。为了证明所提出技术的强大功能，该方法应在商业有限元代码 Abaqus 中实现，并增强以适用于复杂零件。该项目的目标是：- 断裂表面的计算 以及有效临界能量释放率 - 基于数字体图像的复杂微观结构 - 复杂的合成微观结构 - 具有局部各向同性和各向异性材料行为的材料 - 各向异性相场损伤模型的快速稳健的宏观解如果获得批准，该项目将为相场损伤模型的用户提供见解，需要假设哪种形式的各向异性相场模型以及如何计算相关参数 如果微观尺度上的相应参数可用，则可以稳健且有效地进行数值计算。