A Multiscale Implementation Based on Adaptive Mesh Refinement for the Nonlocal Peridynamics Model in One Dimension

DOI10.1137/15M1010300zbMath1381.74214MaRDI QIDQ2806412

Qiang Du, Max D. Gunzburger, John Burkardt, Feifei Xu

Publication date: 18 May 2016

Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)

zbMATH Keywords

finite element methodsmultiscale methodsperidynamicssolid mechanicsnonlocal modelsdiscontinuous displacements

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Theories of fracture and damage (74A45) Fredholm integral equations (45B05) Integral equations with kernels of Cauchy type (45E05) Generalities, axiomatics, foundations of continuum mechanics of solids (74A99) PDEs in connection with mechanics of deformable solids (35Q74)

Related Items

Numerical methods for nonlocal and fractional models, An \(hp\)-Galerkin method with fast solution for linear peridynamic models in one dimension, A fast discontinuous Galerkin method for a bond-based linear peridynamic model discretized on a locally refined composite mesh, Peridynamics review, A reproducing kernel enhanced approach for peridynamic solutions, A cookbook for approximating Euclidean balls and for quadrature rules in finite element methods for nonlocal problems, Nonlocal convection-diffusion problems on bounded domains and finite-range jump processes, A multiscale method for nonlocal mechanics and diffusion and for the approximation of discontinuous functions

Cites Work

• Unnamed Item
• Nonlocal constrained value problems for a linear peridynamic Navier equation
• Non-ordinary state-based peridynamic analysis of stationary crack problems
• The morphing method as a flexible tool for adaptive local/non-local simulation of static fracture
• Continuous and discontinuous finite element methods for a peridynamics model of mechanics
• Peridynamic modeling of membranes and fibers
• Convergence of peridynamics to classical elasticity theory
• Reformulation of elasticity theory for discontinuities and long-range forces
• Peridynamic states and constitutive modeling
• On the well-posedness of the linear peridynamic model and its convergence towards the Navier equation of linear elasticity
• A Convergent Adaptive Finite Element Algorithm for Nonlocal Diffusion and Peridynamic Models
• Coupling of nonlocal and local continuum models by the Arlequin approach
• Asymptotically Compatible Schemes and Applications to Robust Discretization of Nonlocal Models
• Nonconforming Discontinuous Galerkin Methods for Nonlocal Variational Problems
• Mathematical and Numerical Analysis of Linear Peridynamic Models with Nonlocal Boundary Conditions
• A Nonlocal Vector Calculus with Application to Nonlocal Boundary Value Problems
• Handbook of Peridynamic Modeling
• Peridynamics as an Upscaling of Molecular Dynamics
• On the use of isoparametric finite elements in linear fracture mechanics
• Representation of singularities with isoparametric finite elements
• A Convergent Adaptive Algorithm for Poisson’s Equation
• Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints
• A NONLOCAL VECTOR CALCULUS, NONLOCAL VOLUME-CONSTRAINED PROBLEMS, AND NONLOCAL BALANCE LAWS
• A posteriori error analysis of finite element method for linear nonlocal diffusion and peridynamic models
• Peridynamic State-Based Models and the Embedded-Atom Model
• Analysis and Comparison of Different Approximations to Nonlocal Diffusion and Linear Peridynamic Equations
• The bond-based peridynamic system with Dirichlet-type volume constraint