Computational methods for multi-scale fracture

在这个项目中，我们的目标是建立一个新的多尺度断裂机制计算框架。因此，我们计划扩展最近提出的IGA^2框架，这是对高阶连续体的概念相似的众所周知的FE^2方法的推广。在这两个尺度框架内，我们的目标是两个尺度上的相场断裂公式。首先，提出了一个脆性断裂公式，使用不同尺度上独立但热力学一致的断裂场。其次，在微观尺度上引入梯度塑性和梯度损伤模型相结合的韧性断裂公式。第三，对所提出的计算多尺度方法的渐近行为进行适当的研究将完成研究并确保正确的收敛性。为了获得有效的数值框架，提出了一种双尺度多网格公式，并结合了增强收敛的伪混合方法，从而降低了整个Newton-Raphson迭代的计算成本。这个框架，包括复杂的技术增强，将在GitHub上发布，为研究社区提供更多信息。

In this project, we aim at a novel computational framework on multiscale fracture mechanism. Therefore, we plan to extent the recently proposed IGA^2 framework, a generalization of the conceptual similar well-known FE^2 method towards higher-order continua. Within this two-scale framework, we aim at a phase-field fracture formulation on both scales. First, a brittle fracture formulation is proposed, using independent, but thermodynamically consistent fracture fields on the different scales. Second, a ductile fracture formulation combining gradient plasticity and gradient damage models will be introduced on the micro-scale. Third, suitable investigations on the asymptotic behavior of the proposed computational multi-scale method will accomplish the investigation and ensure a correct convergence. To obtain an efficient numerical framework, a two-scale multi-grid formulation is proposed, combined with a pseudo mixed approach for enhanced convergens and thus, reduced computational cost throughout the Newton-Raphson iteration. This framework, including sophisticated technical enhancements, will be published on GitHub to provide additional information for the research community.