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A stable extended/generalized finite element method with Lagrange multipliers and explicit damage update for distributed cracking in cohesive materials

机译:具有拉格朗日乘数的稳定扩展/广义有限元方法,以及用于在粘性材料中分布式开裂的显式损坏更新

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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. (C) 2020 Elsevier B.V. All rights reserved.
机译:开发了一种柔性,一般且稳定的混合配方,以在延长/广义有限元方法的框架内模拟粘性谷物材料中的分布式裂缝。分别在每个颗粒上离散化位移场,并且通过拉格朗日乘法器强制执行谷物之间的接口的位移和牵引场的连续性。离散拉格朗日乘法器空间的设计详细为Bilinear四边形元素,其中包含元素内的多个接口/不连续性的潜在存在。我们提供了数字证据,即设计的拉格朗日乘数空间稳定,并提供了示例,证明了该方法的鲁棒性。依靠稳定的离散化,配备有损伤的粘性区制剂,其在牵引方面表达,用于在谷物之间的界面处模拟多个裂缝的传播。损坏配方利用明确的解决方案程序,耦合了正常和切向失效模式,占不同的张力和压缩行为,并考虑了混合模式中的压缩依赖性断裂能量。该框架应用于由异构岩状材料的间接张力试验激发的复杂2D问题。 (c)2020 Elsevier B.v.保留所有权利。

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