In this contribution we investigate the application of phase-field fracture models on non-linear multiscale computational homogenization schemes. In particular, we introduce different phase-fields on a two-scale problem and develop a thermodynamically consistent model. This allows on the one hand for the prediction of local micro-fracture patterns, which effectively acts as an anisotropic damage model on the macroscale. On the other and, the macro-fracture phase-field model allows to predict complex fracture pattern with regard to local microstructures. Both phase-fields are introduced in a common framework, such that a joint consistent linearization for the Newton-Raphson iteration can be developed. Finally, the limits of both models as well as the applicability are shown in different numerical examples.

翻译：本文研究了相场断裂模型在非线性多尺度计算均匀化方案中的应用。具体而言，我们在双尺度问题中引入了不同的相场，并建立了热力学一致模型。该模型一方面能够预测局部微观断裂模式，在宏观尺度上有效表现为各向异性损伤模型；另一方面，宏观断裂相场模型能够根据局部微观结构预测复杂断裂模式。两种相场均在一个统一框架中引入，从而可以开发适用于牛顿-拉夫逊迭代的联合一致线性化。最后，通过不同的数值算例展示了两种模型的局限性及其适用性。