Variational phase-field models of fracture

本研究方案涉及裂缝的相场模型。这种方法是我与G.Francfort和J.-J.Marigo一起创建的，它基于将格里菲斯的经典理论重塑为能量最小化原理的断裂能扩散界面近似的最小化。它解决了断裂力学中的一些最大挑战：路径识别、裂纹形核和形态变化。我的研究计划的长期目标是严格构建适用于各种涉及骨折的问题的模型，它们的数学分析和数值实施，以及它们向学术界和工业界的广大公众传播。拟议的研究计划围绕三个具体的短期目标(ST1-3)进行阐述。(ST1)是基于伴随的二阶求解器的发展、分析和数值实现。(ST2)讨论了将平行时间平行化技术扩展到变分相场破裂(和其他与速率无关的过程)的方法及其实现。(ST3)涉及形核驱动力方法的数学分析和实现，以及考虑强度(基于应力的形核准则)和韧性(遵循Griffith准则的传播)的双重准则模型的推导。在会议、小型专题讨论会或研究研讨会期间举行的讨论会上，这项提案所确定的具体目标被确定为阻碍对骨折的预测性理解的主要障碍。这项研究计划将在裂缝的预测性理解和数值模拟方面取得突破性进展。它将对许多领域产生直接影响，包括：软硬生物组织的断裂；对航空航天和汽车工业至关重要的复合材料的断裂；制造技术，如激光切割玻璃和电磁切割金属；通过对冰盖断裂的预测性了解或为碳固存设计裂隙储存库来缓解气候变化的社会影响；以及材料科学，包括设计具有极端断裂性能的微结构材料。这些研究活动还有两个共同点：所有产品都将在我维护的开源软件代码vDef中实现，专家和非专家在多个行业和学术研究部门使用该代码。HQP将参与为每个组件创建文档、验证测试和教程。HQP将在垂直整合的多学科环境中接受培训。他们将参加与我正在进行的断裂力学领域的其他研究项目有关的多学科和多机构的小组会议和讨论。

This research proposal deals with phase-field models of fracture. This approach, which I created with G. Francfort and J.-J. Marigo, is based on the minimization of a diffused interface approximation of a fracture energy recasting Griffith's classical theory as an energy minimization principle. It addresses some of the biggest challenges in fracture mechanics: path identification, crack nucleation, and change of morphology. The long term objective of my research program is the rigorous construction of models applicable to a variety of problems involving fracture, their mathematical analysis and numerical implementation, and their diffusion towards a broad public in academia and industry. The proposed research program is articulated around three specific short-term objectives (ST1-3). (ST1) is the development, analysis and numerical implementation of adjoint-based second order solvers. (ST2) deals with the extension of the parareal time-parallelization technique to variational phase-field fracture (and other rate-independent processes), and its implementation. (ST3) is concerned with the mathematical analysis and implementation of the driving force approach to nucleation, and the derivation of a dual-criterion model accounting for strength (a stress-based nucleation criterion) and toughness (propagation following Griffith's criterion). The specific objectives developed in this proposal have been identified as major roadblock towards the predictive understanding of fracture in discussion sessions held during conference mini-symposia or research workshops. This research program will lead to groundbreaking advances on the predictive understanding and numerical simulation of fracture. It will have a direct impact on many fields including: the fracture of hard and soft biological tissues; fracture of composite materials, essential to the aerospace and automobile industry; manufacturing techniques such as laser cutting of glass and electromagnetic cutting of metals; mitigating the societal impact of climate change through the predictive understanding of fracture of ice sheets or the design of fractured reservoir for carbon sequestration; and materials science including the design of micro-structured materials with extreme fracture properties. These research activities share two additional aspects: All products will be implemented in the open-source software code vDef which I maintain and is used in multiple industry and academic research departments by experts and non-experts. HQP will be involved in the creation of documentation, validation tests and tutorials for each component. HQP will be trained in a vertically integrated, multi-disciplinary environment. They will participate in multi-disciplinary and multi-institutions group meetings and discussions connected with my other ongoing research projects on the field of fracture mechanics.