Mathematical and computational aspects of solid mechanics

断裂是一种普遍存在的现象，具有重大的经济、技术和社会影响。其预测性的理解影响到许多学科，包括制造，材料设计，医疗保健，以及预测和减缓气候变化的影响。拟议的Tier-1加拿大研究主席的数学和计算方面的固体力学研究计划的重点是变分相场模型的断裂，共同创建的被提名人。这种方法已经证明了它的能力，预测裂纹成核和演变沿着复杂的路径，而没有任何先验假设所需的经典模型。它适用于在广泛的材料和situation.The第一个目标是开发和实施新一代的裂缝模拟算法的裂缝演化的定量预测。为了充分利用现有的高性能计算资源，并允许对大规模现实问题进行数值模拟，需要这些。次要目标是研究逆问题，即，通过规定边界变形、诱导材料特性变化或施加电场、磁场或温度场来控制断裂扩展。这样的问题有直接的应用程序的制造技术和极端断裂properties.The第三个目标的材料的系统设计的变分相场模型的范围扩展到活组织的断裂。具体应用包括研究天然材料和人造材料之间的相互作用，如植入物和假体，以及受老化和各种刺激的活组织断裂特性的长期演变。该计划的最终目标旨在减少断裂力学知识与其应用之间的差距。这将通过多学科合作和研究生教育，通过组织研究讲习班和专业发展课程来实现。此外，作为该项目一部分开发的所有模型和算法将在一个强大的和有良好记录的软件包中实施，该软件包根据开源许可证发布。

Fracture is a ubiquitous phenomenon with significant economic, technological, and societal impacts. Its predictive understanding affects many disciplines, including manufacturing, materials design, healthcare, and prediction and mitigation of the effects of climate change.The proposed Tier-1 Canada Research Chair on mathematical and computational aspects of solid mechanics research program focuses on variational phase-field models of fracture, co-created by the nominee. This approach has demonstrated its ability to predict crack nucleation and evolution along complex paths without any of the a priori assumptions required by classical models. It is applicable to the quantitative prediction of fracture evolution in a broad range of materials and situations.The first objective is the development and implementation of a new generation of algorithms for fracture simulation. These are needed in order to fully leverage existing high-performance computing resources, and allow the numerical simulation of large-scale real-life problems.The secondary objective is the study of inverse problems, i.e., controlling fracture propagation by prescribing boundary deformations, inducing changes in materials properties, or applying electrical, magnetic, or temperature fields. Such problems have direct applications to manufacturing techniques and to the systematic design of materials with extreme fracture properties.The third objective aims at extending the reach of variational phase-field models to the fracture of live tissue. Specific applications include the study of interactions between natural and made made materials such as implants and prostheses, as well as the long term evolution of fracture properties of live tissues subject to aging and diverse stimuli.The final objective of this program aims at reducing the gap between knowledge and its use in fracture mechanics. This will be achieved through multidisciplinary collaborations and graduate education, through the organization of research workshops and professional development courses. Furthermore, all models and algorithm developed as part of this project will be implemented in a robust and well-documented software package released under an open-source license.