Abstract
Nonlocal peridynamic theory for materials modeling
Qiang Du
Columbia University
We discuss mathematical and computational issues related to some nonlocal
balance laws and in particular the peridynamic theory for materials models.
A vector calculus for nonlocal operators is presented which provides a
rigorous fundation to pose abstract nonlocal balance laws with reduced
regularity requirements. We address some basic mathematical and computational
issues and explore the connections with local models. We also discuss
questions concerning finite dimensional approximations of such nonlocal
models, such as convergence, conditioning, a priori and a posteriori error
analysis and adaptive methods.
balance laws and in particular the peridynamic theory for materials models.
A vector calculus for nonlocal operators is presented which provides a
rigorous fundation to pose abstract nonlocal balance laws with reduced
regularity requirements. We address some basic mathematical and computational
issues and explore the connections with local models. We also discuss
questions concerning finite dimensional approximations of such nonlocal
models, such as convergence, conditioning, a priori and a posteriori error
analysis and adaptive methods.