Abstract A flexible, general and stable mixed formulation is developed to model distributed cracking in cohesive grain-based materials in the framework of the extended/generalized finite element method. The displacement field is discretized on each grain separately, and the continuity of the displacement and traction fields across the interfaces between grains is enforced by Lagrange multipliers. The design of the discrete Lagrange multiplier space is detailed for bilinear quadrangular elements with the potential presence of multiple interfaces/discontinuities within an element. We give numerical evidence that the designed Lagrange multiplier space is stable and provide examples demonstrating the robustness of the method. Relying on the stable discretization, a cohesive zone formulation equipped with a damage constitutive formulation expressed in terms of the traction is used to model propagation of multiple cracks at the interfaces between grains. The damage formulation makes use of an explicit solution procedure, couples the normal and tangential failure modes, accounts for different tension and compression behaviours and takes into account a compression-dependent fracture energy in mixed mode. The framework is applied to complex 2D problems inspired by indirect tension tests of heterogeneous rock-like materials.

中文翻译：

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一种具有拉格朗日乘子和显式损伤更新的稳定扩展/广义有限元方法，用于粘性材料中的分布式裂纹

摘要 在扩展/广义有限元方法的框架内，开发了一种灵活、通用且稳定的混合公式来模拟粘性颗粒基材料中的分布开裂。位移场在每个晶粒上分别离散化，并且通过拉格朗日乘子加强晶粒间界面上位移场和牵引力场的连续性。离散拉格朗日乘子空间的设计针对双线性四边形元素进行了详细说明，其中一个元素内可能存在多个界面/不连续性。我们给出了设计的拉格朗日乘子空间稳定的数值证据，并提供了证明该方法稳健性的示例。依靠稳定的离散化，内聚区公式配备了以牵引力表示的损伤本构公式，用于模拟晶粒间界面处多个裂纹的扩展。损伤公式使用显式求解程序，耦合法向和切向破坏模式，考虑不同的拉伸和压缩行为，并考虑混合模式下与压缩相关的断裂能。该框架适用于受非均质类岩石材料的间接张力测试启发的复杂二维问题。考虑了不同的拉伸和压缩行为，并考虑了混合模式下与压缩相关的断裂能。该框架适用于受非均质类岩石材料的间接张力测试启发的复杂二维问题。考虑了不同的拉伸和压缩行为，并考虑了混合模式下与压缩相关的断裂能。该框架适用于受非均质类岩石材料的间接张力测试启发的复杂二维问题。