Mathematical and Multi-Scale Foundations of Nonlocal Modeling: Research Topic 1.2 Solid Mechanics W911NF-12-R-0012-03
Abstract
The objective of the proposed research is to explore and develop connections between the new non-local models with convex-concave and the classic Griffith free energy associated with brittle fracture. The goal is to deliver rigorous rules of the choice of peridynamic horizon for control of the fidelity of peridynamic evolutions. This will provide an a-priori measure of the ability of a particular peridynamic model to reproduce solutions of classic brittle fracture peridynamic. The goal of this effort is to establish the essential theoretical foundations necessary for nonlocal models to provide reliable and predictive numerical fracture simulations for problems of brittle fracture. The approach taken here is new and is based on a mathematically rigorous development of peridynamic models with peridynamic energies. These energies are well suited to peridynamic formulations in both state, based and bond based models. The first goal is to explore and develop new nonlocal constitutive laws that provide well posed continuum models that arc useful for the accurate computation of the deformation state inside bodies undergoing brittle fracture. The PI plans to identify connections between the new non-local models and the classic Griffith free energy associated with brittle fracture. PI will explore how these new constitutive laws can be designed to rule out material interpenetration without resorting to ad-hoc fixes at thee discretization level. Second, Pl intends to develop a fundamentally sound quasi-static peridynamics for reliable modeling of quasi-static crack growth. In all cases the primary interest is to explore and rigorously determine the range of validity for peridynamic models contingent on the physical dimensions of the sample, length scale of nonlocal interaction, material properties and characteristics of the loading.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- May 22, 2017
- Source ID
- W911NF1610456
Entities
People
- Robert Lipton
Organizations
- Army Contracting Command
- Louisiana State University
- United States Army