Survey of existence results in nonlinear peridynamics in comparison with local elastodynamics

DOI10.1515/cmam-2015-0020zbMath1327.74003OpenAlexW2395151902MaRDI QIDQ500843

Dimitri Puhst, Etienne Emmrich

Publication date: 5 October 2015

Published in: Computational Methods in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/cmam-2015-0020

zbMATH Keywords

generalized solutionsexistencenonlinear elastodynamicsGalerkin approximationperidynamicsnonlocal models

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Nonlinear differential equations in abstract spaces (34G20) Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids (74-02) Weak solutions to PDEs (35D30) Existence of solutions of dynamical problems in solid mechanics (74H20) Second-order quasilinear hyperbolic equations (35L72)

Related Items (11)

Visco-elastodynamics at large strains Eulerian ⋮ Dispersive effects in two- and three-dimensional peridynamics ⋮ Convergence of a full discretization for a second-order nonlinear elastodynamic equation in isotropic and anisotropic Orlicz spaces ⋮ A Numerical Framework for Nonlinear Peridynamics on Two-Dimensional Manifolds Based on Implicit P-(EC)\(^{ {\boldsymbol k}}\) Schemes ⋮ An asymptotically compatible approach for Neumann-type boundary condition on nonlocal problems ⋮ Peridynamics review ⋮ Wellposedness of a nonlinear peridynamic model ⋮ Numerical methods for the nonlocal wave equation of the peridynamics ⋮ Quasistatic elastoplasticity via Peridynamics: existence and localization ⋮ An asymptotically compatible approach for Neumann-type boundary condition on nonlocal problems ⋮ A fast-convolution based space-time Chebyshev spectral method for peridynamic models

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