Variational phase-field models of fracture

本研究建议涉及断裂的相场模型。这个方法是我和G. Francfort和J. - J. Marigo提出的能量最小化原理是基于断裂能的扩散界面近似的最小化，并将Griffith的经典理论作为能量最小化原理。它解决了断裂力学中的一些最大的挑战：路径识别，裂纹成核和形态变化。 我的研究计划的长期目标是严格构建适用于各种问题的模型，包括断裂，数学分析和数值实现，以及它们在学术界和工业界向广大公众的扩散。拟议的研究计划围绕三个具体的短期目标（ST 1 -3）进行阐述。(ST1)是开发，分析和数值实现的伴随为基础的二阶求解器。(ST2)涉及扩展的parareal时间并行技术变相场断裂（和其他率无关的过程），及其实施。(ST3)关注的是数学分析和实施的驱动力方法成核，并推导出一个双标准模型占强度（基于应力的成核标准）和韧性（传播格里菲斯的标准）。在会议小型研讨会或研究讲习班期间举行的讨论会上，本提案中制定的具体目标已被确定为对断裂预测性理解的主要障碍。这项研究计划将导致裂缝的预测理解和数值模拟的突破性进展。它将对许多领域产生直接影响，包括：硬和软生物组织的断裂;航空航天和汽车工业所必需的复合材料的断裂;玻璃激光切割和金属电磁切割等制造技术;通过对冰盖断裂的预测性了解或设计用于固碳的断裂储层来减轻气候变化的社会影响;和材料科学，包括具有极端断裂特性的微结构材料的设计。 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，并由专家和非专家在多个行业和学术研究部门使用。HQP将参与每个组件的文档、验证测试和教程的创建。HQP将在垂直整合的多学科环境中接受培训。他们将参加多学科和多机构的小组会议和讨论，与我在断裂力学领域正在进行的其他研究项目有关。

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.