Force flux and the peridynamic stress tensor

DOI10.1016/j.jmps.2007.08.004zbMath1171.74319OpenAlexW2007393042MaRDI QIDQ731037

Richard B. Lehoucq, Stewart A. Silling

Publication date: 1 October 2009

Published in: Journal of the Mechanics and Physics of Solids (Search for Journal in Brave)

Full work available at URL: https://www.osti.gov/biblio/1720351

zbMATH Keywords

flux stress peridynamics elastic material

Mathematics Subject Classification ID

Generalities, axiomatics, foundations of continuum mechanics of solids (74A99)

Related Items

Dynamic problems for metamaterials: review of existing models and ideas for further research, Determination of material properties of a linearly elastic peridynamic material, From statistical mechanics to nonlocal theory, Discretized peridynamics for brittle and ductile solids, A peridynamic model for the nonlinear static analysis of truss and tensegrity structures, Anisotropic peridynamics for homogenized microstructured materials, Imposition of local boundary conditions in peridynamics without a fictitious layer and unphysical stress concentrations, A nonlocal nonlinear stiffened shell theory with stiffeners modeled as geometrically-exact beams, A new method based on Taylor expansion and nearest-node strategy to impose Dirichlet and Neumann boundary conditions in ordinary state-based peridynamics, Three-dimensional hydraulic fracturing modeling based on peridynamics, Stability of Nonlocal Dirichlet Integrals and Implications for Peridynamic Correspondence Material Modeling, Static and dynamic Green's functions in peridynamics, A note on Eringen's moment balances, A posteriori error analysis of finite element method for linear nonlocal diffusion and peridynamic models, An electromechanical micropolar peridynamic model, Discretized peridynamics for linear elastic solids, An improved stabilized peridynamic correspondence material model for the crack propagation of nearly incompressible hyperelastic materials, Edelen's dissipation potentials and the visco-plasticity of particulate media, Non-local gradients in bounded domains motivated by continuum mechanics: fundamental theorem of calculus and embeddings, Multiscale dynamics of heterogeneous media in the peridynamic formulation, Nonlocal gradient operators with a nonspherical interaction neighborhood and their applications, Thermoelastic response of laminated plates considering interfacial conditions and cracks based on peridynamics, A bond-based peridynamics modeling of polymeric material fracture under finite deformation, The peridynamic stress tensors and the non‐local to local passage, Moving interfaces in peridynamic diffusion models and the influence of discontinuous initial conditions: numerical stability and convergence, Bond-based peridynamics does not converge to hyperelasticity as the horizon goes to zero, Objectivity of state-based peridynamic models for elasticity, On solvability of one singular equation of peridynamics, Computational homogenization in linear elasticity of peristatic periodic structure composites, Attenuation of waves in a viscoelastic peridynamic medium, Peridynamics review, Variational principles and generalized Hill’s bounds in micromechanics of linear peridynamic random structure composites, An obstacle problem for nonlocal equations in perforated domains, An axisymmetric ordinary state-based peridynamic model for linear elastic solids, On nonlocal geometrically exact shell theory and modeling fracture in shell structures, Superposition-based coupling of peridynamics and finite element method, Particle Method Modeling of Nonlocal Multiresolution Continua, At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: An underestimated and still topical contribution of Gabrio Piola, Implementing peridynamics within a molecular dynamics code, A fully coupled porous flow and geomechanics model for fluid driven cracks: a peridynamics approach, A novel linear elastic constitutive model for continuum-kinematics-inspired peridynamics, A variational rod model with a singular nonlocal potential, The peridynamic formulation for transient heat conduction, A unified interpretation of stress in molecular systems, A meshfree unification: reproducing kernel peridynamics, Convergence, adaptive refinement, and scaling in 1D peridynamics, Nonlocal problems in perforated domains, Hyperelasticity as a \(\Gamma\)-limit of peridynamics when the horizon goes to zero, Convergence of peridynamics to classical elasticity theory, On the equivalence of the two foundational formulations for atomistic flux in inhomogeneous transport processes, A constructive peridynamic kernel for elasticity, Robust a posteriori stress analysis for quadrature collocation approximations of nonlocal models via nonlocal gradients, Multiscale analysis of linear evolution equations with applications to nonlocal models for heterogeneous media, On the prescription of boundary conditions for nonlocal Poisson's and peridynamics models, A constitutive model for a linearly elastic peridynamic body

Cites Work