Shearlet approximation of brittle fracture evolutions (C03* [A10])

脆性断裂演化的剪切波近似 (C03* [A10])

• 批准号: 316125039
• 金额: --
• 依托单位: Lehrstuhl für Angewandte Numerische Analysis und Optimierung und Data Analysis (M15)
• 依托单位国家: 德国
• 项目类别: CRC/Transregios
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2019-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/316125039?language=en
• 关键词: Shearlet; approximation; brittle; fracture; evolutions

A brittle material, subjected to a force, first deforms itself elastically, then it breaks without any intermediate phase. A model of brittle fractures was proposed by Francfort and Marigo, where the material displacement is typically a smooth function except on a relatively smooth jump set determining the fracture. This approach has the advantage not to require a pre-defined crack path, but has the drawback that any mesh discretization is a geometrical bias. Differently from finite elements, shearlets are frames with rotation invariance and optimal nonlinear approximation properties for the class of typical solutions of the brittle fracture model. The main goal of the project is the robust numerical simulation of brittle fractures, implementing a provably convergent and geometrically unbiased adaptive frame scheme based on shearlet discretizations.

脆性材料在受到力的作用下，首先发生弹性变形，然后在没有任何中间相的情况下断裂。 Francfort 和 Marigo 提出了脆性断裂模型，其中材料位移通常是一个平滑函数，除了确定断裂的相对平滑的跳跃集之外。这种方法的优点是不需要预定义的裂纹路径，但缺点是任何网格离散化都是几何偏差。与有限元不同，剪切波是具有旋转不变性和脆性断裂模型典型解类的最佳非线性逼近性质的框架。该项目的主要目标是对脆性断裂进行稳健的数值模拟，实现基于剪切波离散化的可证明收敛且几何无偏的自适应框架方案。