Measure-valued and weak solutions to the nonlinear peridynamic model in nonlocal elastodynamics

DOI10.1088/0951-7715/28/1/285zbMath1312.35163OpenAlexW2034468614MaRDI QIDQ5497060

Etienne Emmrich, Dimitri Puhst

Publication date: 2 February 2015

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/c374e28d89bc90b2f4e5876d9a0f138605e60fca

zbMATH Keywords

measure-value and weak solutionsnonlinear peridynamic model

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Second-order nonlinear hyperbolic equations (35L70) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Existence of solutions of dynamical problems in solid mechanics (74H20) PDEs in connection with mechanics of deformable solids (35Q74) Integro-partial differential equations (35R09)

Related Items (13)

Visco-elastodynamics at large strains Eulerian ⋮ A short note on modeling damage in peridynamics ⋮ On weak solutions for a nonlocal model with nonlocal damping term ⋮ Regularity and convergence results for nonlocal peridynamic equations with truncated tensor kernels ⋮ A Framework for Nonlocal, Nonlinear Initial Value Problems ⋮ A Numerical Framework for Nonlinear Peridynamics on Two-Dimensional Manifolds Based on Implicit P-(EC)\(^{ {\boldsymbol k}}\) Schemes ⋮ Leading-order nonlocal kinetic energy in peridynamics for consistent energetics and wave dispersion ⋮ Bond-based peridynamics does not converge to hyperelasticity as the horizon goes to zero ⋮ A class of elliptic equations involving nonlocal integrodifferential operators with sign-changing weight functions ⋮ Wellposedness of a nonlinear peridynamic model ⋮ Global existence and blow-up for the fractional \(p\)-Laplacian with logarithmic nonlinearity ⋮ On solvability of nonlinear integro-differential equation ⋮ The solvability of a strongly-coupled nonlocal system of equations

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