Peridynamic theory of solid mechanics
Publisher Summary The classical theory of solid mechanics is based on the assumption of a
continuous distribution of mass within a body and all internal forces are contact forces that …
continuous distribution of mass within a body and all internal forces are contact forces that …
Review on nonlocal continuum mechanics: physics, material applicability, and mathematics
The classical continuum mechanics assumes that a material is a composition of an infinite
number of particles each of which is a point that can only move and interact with its nearest …
number of particles each of which is a point that can only move and interact with its nearest …
A meshfree method based on the peridynamic model of solid mechanics
SA Silling, E Askari - Computers & structures, 2005 - Elsevier
An alternative theory of solid mechanics, known as the peridynamic theory, formulates
problems in terms of integral equations rather than partial differential equations. This theory …
problems in terms of integral equations rather than partial differential equations. This theory …
Peridynamic states and constitutive modeling
SA Silling, M Epton, O Weckner, J Xu, E Askari - Journal of elasticity, 2007 - Springer
A generalization of the original peridynamic framework for solid mechanics is proposed. This
generalization permits the response of a material at a point to depend collectively on the …
generalization permits the response of a material at a point to depend collectively on the …
Analysis and approximation of nonlocal diffusion problems with volume constraints
A recently developed nonlocal vector calculus is exploited to provide a variational analysis
for a general class of nonlocal diffusion problems described by a linear integral equation on …
for a general class of nonlocal diffusion problems described by a linear integral equation on …
Peridynamics via finite element analysis
RW Macek, SA Silling - Finite elements in analysis and design, 2007 - Elsevier
Peridynamics is a recently developed theory of solid mechanics that replaces the partial
differential equations of the classical continuum theory with integral equations. Since the …
differential equations of the classical continuum theory with integral equations. Since the …
nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications
Physics-informed neural networks (PINNs) are effective in solving inverse problems based
on differential and integro-differential equations with sparse, noisy, unstructured, and multi …
on differential and integro-differential equations with sparse, noisy, unstructured, and multi …
Convergence, adaptive refinement, and scaling in 1D peridynamics
We introduce here adaptive refinement algorithms for the non‐local method peridynamics,
which was proposed in (J. Mech. Phys. Solids 2000; 48: 175–209) as a reformulation of …
which was proposed in (J. Mech. Phys. Solids 2000; 48: 175–209) as a reformulation of …
Peridynamic model for dynamic fracture in unidirectional fiber-reinforced composites
We propose a computational method for a homogenized peridynamics description of fiber-
reinforced composites and we use it to simulate dynamic brittle fracture and damage in …
reinforced composites and we use it to simulate dynamic brittle fracture and damage in …
Peridynamic modeling of membranes and fibers
The peridynamic theory of continuum mechanics allows damage, fracture, and long-range
forces to be treated as natural components of the deformation of a material. In this paper, the …
forces to be treated as natural components of the deformation of a material. In this paper, the …