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

该学院早期职业发展（CAREER）资助支持材料和结构断裂过程建模的基础研究。由于几种类型的负载，可以引起故障，这些问题跨越了耦合的物理现象，变形，加载速率和长度尺度，其中物理测试往往是有限的和昂贵的范围。目前的计算方法提供了可行的手段，但在所有考虑因素中准确和鲁棒地执行故障模拟方面有其局限性。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，这项研究将允许调查动态断裂，复杂的三维失效模式，以及损伤的启动和传播，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，以及增材制造、工具磨损和生物力学等不同领域的进展。该计划的教育部分将开发开放课程，以帮助学习知识的基础知识和传播结果。学习材料和研究将与针对代表性不足的本科生和研究生的推广计划相结合，以招募，保留和培训下一代基于模拟分析的工程师。模拟三维复杂断裂的有效方法一直是一个长期的挑战。为了克服这一挑战，本研究的主要目标是实现局部经典再生核无网格方法和非局部再生核方法的统一，形成混合再生核再生核方法（RKPD）框架。这种统一的目的是提高几个关键功能的非局部方法，有效的数值分析复杂的故障问题在广泛的变形和变形率：高精度和最佳收敛，易于集成的多个物理过程，高阶精确的冲击波传播，接触力学。该框架将进行测试和验证对纳米二氧化硅增强环氧树脂复合材料，具有复杂的微观结构的实验获得的数据。此外，这些计算发展将被纳入一个开源软件，将免费提供给科学和工程界。这个奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

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.