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

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.