CAREER: A Hybrid Local-Nonlocal Peridynamics Framework to Model Failure Across Deformations and Strain Rates

这项教师早期职业发展（Career）基金支持材料和结构断裂过程建模的基础研究。由于几种类型的加载可能导致破坏，这些问题跨越了广泛的耦合物理现象，变形，加载速率和长度尺度，其中物理测试通常是有限的和昂贵的。目前的计算方法提供了可行的方法，但在准确和健壮地执行所有考虑因素的故障模拟方面存在局限性。这项研究将通过开发新的算法来创新，通过结合现有计算技术提供的优势来克服这些限制。因此，这项研究将允许研究动态断裂，复杂的三维破坏模式，以及损伤的发生和扩展，从而加速对这些事件背后的科学的理解。这项工作的工程应用包括减轻灾害和基础设施的恶化，以及在增材制造、工具磨损和生物力学等不同领域的进步。该计划的教育部分将开发公开课程，帮助学习基础知识并传播成果。学习材料和研究将与一个面向代表性不足的本科生和研究生的拓展计划相结合，以招募、留住和培训下一代基于仿真分析的工程师。如何有效地模拟三维复杂裂缝是一个长期存在的挑战。为了克服这一挑战，本研究的主要目标是将局部经典再现核无网格方法与非局部周期动力学方法统一起来，形成混合再现核周期动力学（RKPD）框架。这种统一旨在增强非局部方法中的几个关键特征，这些特征对于跨大范围变形和变形率的复杂失效问题的有效数值分析是必要的：高精度和最佳收敛，易于集成多个物理过程，高阶精确的冲击波传播和接触力学。该框架将根据纳米二氧化硅增强环氧复合材料的实验数据进行测试和验证，该复合材料具有复杂的微观结构。此外，这些计算的发展将被纳入一个开源软件，将免费提供给科学和工程社区。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This Faculty Early Career Development (CAREER) grant supports fundamental research on modeling fracture processes in materials and structures. Due to the several types of loading that can induce failure, these problems span a broad spectrum of coupled physical phenomena, deformations, loading rates, and length scales, where physical testing is often limited and costly. Current computational methods provide viable means but have their limitations in accurately and robustly performing failure simulations across all considerations. This research will innovate by developing novel algorithms that overcome these limitations by combining the advantages offered by existing computational techniques. Consequently, this research will allow investigations of dynamic fracture, complex three-dimensional failure modes, and damage initiation and propagation, thus accelerating the understanding of the science behind these events. Engineering applications of this work include mitigation of disasters and deterioration of infrastructure, and advances in diverse areas such as additive manufacturing, tool wear, and biomechanics. The educational portion of this program will develop open courses that will aid in learning the fundamentals of the knowledge and disseminating the results. The learning material and research will be integrated with an outreach program for underrepresented undergraduate and graduate students, to recruit, retain, and train the next generation of engineers in simulation-based analysis.Effective approaches for simulating three-dimensional complex fracture has been a long-standing challenge. To overcome this challenge, the main objective of this research is to achieve a unification of the local classical reproducing kernel meshfree method and the nonlocal peridynamics method, to form the hybrid reproducing kernel peridynamics (RKPD) framework. This unification is intended to enhance several critical features in the non-local approach, necessary for effective numerical analysis of complex failure problems across a wide range of deformations and deformation rates: high accuracy and optimal convergence, ease of integration of multiple physical processes, high-order accurate shock wave propagation, and contact mechanics. The framework will be tested and validated against data obtained from experiments on a nanosilica reinforced epoxy composite, possessing a complex microstructure. Moreover, these computational developments will be incorporated into an open-source software that will be freely available to the science and engineering communities.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.