A Coupling Strategy for Nonlocal and Local Models With Applications

Explore a comprehensive lecture on coupling strategies for nonlocal and local models, focusing on applications in nonlocal elasticity. Delve into the increasing use of nonlocal models in science and engineering, their advantages in capturing complex effects, and the computational challenges they present. Learn about an optimization-based method for coupling nonlocal and local problems, including its formulation, well-posedness, and implementation using Sandia's agile software components toolkit. Examine numerical results for nonlocal diffusion in three dimensions and discover applications in coupling static peridynamics with classical elasticity. Cover topics such as nonlocal vector calculus, model problems, solution uniqueness, coupling error, convergence analysis, and various numerical tests including crack simulations and tensile bar experiments.

Intro
NONLOCAL MODELS
NONLOCAL vs LOCAL
WHAT ABOUT COUPLING?
OUTLINE
NONLOCAL VECTOR CALCULUS
MODEL PROBLEMS - Dirichlet VC and BC
IS THE SOLUTION UNIQUE?
THE COUPLING ERROR
ASSUMPTIONS, LEMMAS AND TOOLS
THE ALGORITHM
CONVERGENCE ANALYSIS
NUMERICAL TESTS
MODEL PROBLEMS - mixed VC and BC
THE DISCRETIZATION - 3D
SOLUTION WITH A CRACK
THE PERIDYNAMIC MODEL
THE LOCAL MODEL
THE COUPLING STRATEGY
THE GEOMETRY
THE PATCH TEST
CRACK TEST
TENSILE BAR - WITH CRACK
LOTS OF THINGS TO DO!