Mechanics

Residual-Based Error Correction for Neural Operator Accelerated Infinite-Dimensional Bayesian Inverse Problems
Residual-based error corrector technique is proposed and applied to improve the neural operator predictions for Bayesian inference problems.
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NLMech: Implementation of Finite Difference/Meshfree Discretization of Nonlocal Fracture Models
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Peridynamics-Based Discrete Element Method (PeriDEM) Model of Granular Systems Involving Breakage of Arbitrarily Shaped Particles
Usage, manipulation, transport, delivery, and mixing of granular or particulate media, comprised of spherical or polyhedral particles, …
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Finite Element Approximation of Nonlocal Dynamic Fracture Models
In this work we estimate the convergence rate for time stepping schemes applied to nonlocal dynamic fracture modeling. Here we use the …
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Finite Element Convergence for State-Based Peridynamic Fracture Models
We establish the a priori convergence rate for finite element approximations of a class of nonlocal nonlinear fracture models. We …
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Complex Fracture Nucleation and Evolution With Nonlocal Elastodynamics
A mechanical model is introduced for predicting the initiation and evolution of complex fracture patterns without the need for a damage …
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Numerical Convergence of Finite Difference Approximations for State-Based Peridynamic Fracture Models
In this work, we study the finite difference approximation for a class of nonlocal fracture models. The nonlocal model is initially …
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Dynamic Brittle Fracture from Nonlocal Double-Well Potentials: A State-Based Model
We introduce a regularized model for free fracture propagation based on nonlocal potentials. We work within the small deformation …
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Dynamic Damage Propagation with Memory: A State-Based Model
A model for dynamic damage propagation is developed using nonlocal potentials. The model is posed using a state-based peridynamic …
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Finite Differences and Finite Elements in Nonlocal Fracture Modeling: A Priori Convergence Rates
In this chapter we present a rigorous convergence analysis of finite difference and finite element approximation of nonlinear nonlocal …
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