Nonlocal Theories for Free Crack Propagation in Brittle Materials

Explore the fundamentals of nonlocal theories for free crack propagation in brittle materials in this comprehensive lecture. Delve into the dynamic fracture of brittle solids, examining the connection between large and small length scales. Discover a new class of multi-scale models for solving free crack propagation problems using the peridynamic formulation. Learn about short-range forces between material points, mesoscopic dynamics, and the upscaling process to identify macroscopic dynamics. Investigate the relationship between nonlocal short-range forces and dynamic free crack evolution in brittle media. Examine physical and mathematical underpinnings of nonlocal fracture modeling, including concepts such as weak convergence, compactness, and Gamma-convergence. Explore computational modeling challenges, cohesive dynamics in peridynamic formulation, and the dependence of dynamics on horizon size. Gain insights into multiscale models, finite horizon models, and free process zone models for a comprehensive understanding of nonlocal theories in brittle material fracture.

Intro
Outline of Course
Dynamic fracture of Brittle Solids
Dynamic fracture of Ceramic Solids
Classic theory of Dynamic Fracture Mechanics The theory of dynamic fracture is based on the notion
Continuum fracture modeling: top down approach
A classic modeling approach
On modeling multiple cracks: top down approach
Phase field methods: top down
Nonlocal dynamic models-peridynamics
Nonlocal models: bottom up approaches
Lattice models: bottom up approaches
Nonlocal dynamics as a multi-scale model
Computational Modeling Challenges: Predict the
Computational Challenge: Predict the
The Challenge - quantitative modeling of complex fracture and residual strength
Dynamics for a family of nonlocal models: a multscale model
Cohesive-dynamics in Peridynamic Formulation: Background: A general nonlinear-nonlocal formulation
Peridynamics simulation for Cohesive Evolution Different material phases
Multiscale model parameterized by length scale of non- local interaction E
Same small strain behavior for each
Cohesive Energy, Kinetic, Energy
Study the dependence of dynamics with respect to horizion size
Finite horizon model free process zone model: Collection of neighborhoods containing softening behavior