Fracture processes in quasi-brittle materials are governed by the strain localization phenomenon, which involves the formation of localized damage zones and cohesive cracks. In this work, we present numerical tools to model strain localization from the onset of localized damage to the formation and propagation of multiple intersecting cracks. Two main ingredients are used for this purpose: (i) a microplane model to describe the initial anisotropic damage phase; (ii) the strong discontinuity method to introduce cracks as strong discontinuities in the damaged continuum using the Embedded Finite Element Method (E-FEM). Here, we formulate the microplane microdamage model within a thermodynamic framework by means of simple constitutive laws on each microplane. In order to describe intersecting cracks, we extend the standard E-FEM to accommodate two strong discontinuities. The coupling between the microplane microdamage model with the strong discontinuity model is achieved using a transition method based on the energy equivalence between both models. Exploiting the anisotropic description provided by the microplane model, transition criteria are formulated based on the quantities defined on each microplane. The proposed methodologies are illustrated using several elementary test cases involving both simple and complex stress-strain states.

准脆性材料的断裂过程受应变局部化现象的支配，该现象涉及局部损伤区和粘结裂纹的形成。在这项工作中，我们提供了数值工具来建模从局部破坏的开始到多个相交裂纹的形成和传播的应变局部化。为此，使用了两种主要成分：（i）用于描述初始各向异性破坏阶段的微平面模型；（ii）使用嵌入有限元法（E-FEM）在破坏的连续体中引入裂纹作为强不连续性的强不连续性方法。在这里，我们通过在每个微平面上的简单本构定律在热力学框架内制定微平面微损伤模型。为了描述相交的裂缝，我们扩展了标准E-FEM，以适应两个强烈的不连续性。使用基于两个模型之间能量等效性的过渡方法，可以实现微平面微损伤模型与强不连续模型之间的耦合。利用微平面模型提供的各向异性描述，基于每个微平面上定义的数量来制定过渡标准。使用涉及简单应力状态和复杂应力应变状态的几个基本测试用例说明了所提出的方法。过渡标准是根据每个微平面上定义的数量制定的。使用涉及简单应力状态和复杂应力应变状态的几个基本测试用例说明了所提出的方法。过渡标准是根据每个微平面上定义的数量制定的。使用涉及简单应力状态和复杂应力应变状态的几个基本测试用例说明了所提出的方法。