A meshfree unification: reproducing kernel peridynamics
From MaRDI portal
Publication:2512477
DOI10.1007/s00466-013-0969-xzbMath1398.74452OpenAlexW2161215684MaRDI QIDQ2512477
John T. Foster, Wing Kam Liu, Miguel A. Bessa, Ted Beltytschko
Publication date: 7 August 2014
Published in: Computational Mechanics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00466-013-0969-x
reproducing kernelmoving least squaresmeshfree methodsstate-based peridynamicsstrong form discretizationweak form discretization
Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)
Related Items
A non-local heat transport model in solids with discontinuities via Lagrangian particle method, A Petrov-Galerkin method for nonlocal convection-dominated diffusion problems, A meshfree method for bending and failure in non-ordinary peridynamic shells, A Review of Nonlocality in Computational Contact Mechanics, Enriched reproducing kernel particle method for fractional advection-diffusion equation, Temporal stability of collocation, Petrov-Galerkin, and other non-symmetric methods in elastodynamics and an energy conserving time integration, An efficient nesting sub-domain gradient smoothing integration algorithm with quadratic exactness for Galerkin meshfree methods, The total and updated Lagrangian formulations of state-based peridynamics, A comparative review of peridynamics and phase-field models for engineering fracture mechanics, An asymptotically compatible probabilistic collocation method for randomly heterogeneous nonlocal problems, An isogeometric enriched quasi-convex meshfree formulation with application to material interface modeling, Stability of Nonlocal Dirichlet Integrals and Implications for Peridynamic Correspondence Material Modeling, Dual-Support Smoothed Particle Hydrodynamics for Elastic Mechanics, Construction of a peridynamic model for viscous flow, An inherently consistent reproducing kernel gradient smoothing framework toward efficient Galerkin meshfree formulation with explicit quadrature, A smoothed variable horizon peridynamics and its application to the fracture parameters evaluation, A gradient reproducing kernel based stabilized collocation method for the static and dynamic problems of thin elastic beams and plates, On differences and comparisons of peridynamic differential operators and nonlocal differential operators, Possible causes of numerical oscillations in non-ordinary state-based peridynamics and a bond-associated higher-order stabilized model, Nonconforming Discontinuous Galerkin Methods for Nonlocal Variational Problems, A meshfree peridynamic model for brittle fracture in randomly heterogeneous materials, Peridynamic differential operator and its applications, Peridynamic operator method, A class of mesh-free algorithms for some problems arising in finance and machine learning, Mathematics of smoothed particle hydrodynamics: a study via nonlocal Stokes equations, Meshless numerical solution for nonlocal integral differentiation equation with application in peridynamics, Isogeometric convolution hierarchical deep-learning neural network: isogeometric analysis with versatile adaptivity, A Numerical Framework for Nonlinear Peridynamics on Two-Dimensional Manifolds Based on Implicit P-(EC)\(^{ {\boldsymbol k}}\) Schemes, Convolution hierarchical deep-learning neural networks (C-HiDeNN): finite elements, isogeometric analysis, tensor decomposition, and beyond, Convolution hierarchical deep-learning neural network (C-HiDeNN) with graphics processing unit (GPU) acceleration, Application of the Method of Peridynamics to the Simulation of Hydraulic Fracturing Process, An asymptotically compatible approach for Neumann-type boundary condition on nonlocal problems, Asymptotically Compatible SPH-Like Particle Discretizations of One Dimensional Linear Advection Models, Peridynamics review, The generation of non-ordinary state-based peridynamics by the weak form of the peridynamic method, Localized radial basis functions-based pseudo-spectral method (LRBF-PSM) for nonlocal diffusion problems, A stabilized non-ordinary state-based peridynamics for the nonlocal ductile material failure analysis in metal machining process, Upper bound shakedown analysis with the nodal natural element method, Symmetric global partition polynomials for reproducing kernel elements, Kinematic constraints in the state-based peridynamics with mixed local/nonlocal gradient approximations, Nonlocal diffusion and peridynamic models with Neumann type constraints and their numerical approximations, A mesh-grading material point method and its parallelization for problems with localized extreme deformation, Mesh-free error integration in arbitrary dimensions: a numerical study of discrepancy functions, An accurate and efficient numerical method for solving linear peridynamic models, Nonlocal matching boundary conditions for non-ordinary peridynamics with correspondence material model, A reproducing kernel enhanced approach for peridynamic solutions, Peridynamic least squares minimization, Peridynamic Petrov-Galerkin method: a generalization of the peridynamic theory of correspondence materials, A FETI approach to domain decomposition for meshfree discretizations of nonlocal problems, An effective way to control numerical instability of a nonordinary state-based peridynamic elastic model, Analytical expression of RKPM shape functions, Particle Method Modeling of Nonlocal Multiresolution Continua, A peridynamics-SPH coupling approach to simulate soil fragmentation induced by shock waves, Mollified finite element approximants of arbitrary order and smoothness, An efficient meshfree gradient smoothing collocation method (GSCM) using reproducing kernel approximation, An asymptotically compatible treatment of traction loading in linearly elastic peridynamic fracture, Modified reproducing kernel method for singularly perturbed boundary value problems with a delay, Peridynamic analysis of dynamic fracture: influence of peridynamic horizon, dimensionality and specimen size, An asymptotically compatible approach for Neumann-type boundary condition on nonlocal problems, Integral approximations to classical diffusion and smoothed particle hydrodynamics, Simulating quasi-brittle failures including damage-induced softening based on the mechanism of stress redistribution, On the consistency between nearest-neighbor peridynamic discretizations and discretized classical elasticity models, A framework for data-driven analysis of materials under uncertainty: countering the curse of dimensionality, Stability of peridynamic correspondence material models and their particle discretizations, Numerical experiments on the convergence properties of state-based peridynamic laws and influence functions in two-dimensional problems, Robust a posteriori stress analysis for quadrature collocation approximations of nonlocal models via nonlocal gradients, A two-field state-based peridynamic theory for thermal contact problems, Two-dimensional continuum modelling granular column collapse by non-local peridynamics in a mesh-free method with rheology, A higher-order stress point method for non-ordinary state-based peridynamics, A novel kinematic-constraint-inspired non-ordinary state-based peridynamics, Bond-based peridynamics, a survey prospecting nonlocal theories of fluid-dynamics, Temporally stabilized peridynamics methods for shocks in solids
Cites Work
- Unnamed Item
- Unnamed Item
- Isogeometric collocation for elastostatics and explicit dynamics
- Differentiation by integration using orthogonal polynomials, a survey
- Advances in multiple scale kernel particle methods
- Imposing essential boundary conditions in mesh-free methods
- Force flux and the peridynamic stress tensor
- Extrinsic meshfree approximation using asymptotic expansion for interfacial discontinuity of derivative
- Meshless methods: a review and computer implementation aspects
- Convergence of peridynamics to classical elasticity theory
- Synchronized reproducing kernel interpolant via multiple wavelet expansion
- Generalizing the finite element method: Diffuse approximation and diffuse elements
- A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method
- Moving least-square reproducing kernel methods. I: Methodology and convergence
- Meshless methods: An overview and recent developments
- Generalized multiple scale reproducing kernel particle methods
- Reformulation of elasticity theory for discontinuities and long-range forces
- A stabilized least-squares radial point collocation method (LS-RPCM) for adaptive analysis
- Peridynamic states and constitutive modeling
- A non-ordinary state-based peridynamic method to model solid material deformation and fracture
- An approach for incorporating classical continuum damage models in state-based peridynamics
- Extra-dof-free and linearly independent enrichments in GFEM
- Error analysis of collocation method based on reproducing kernel approximation
- Mathematical and Numerical Analysis of Linear Peridynamic Models with Nonlocal Boundary Conditions
- ISOGEOMETRIC COLLOCATION METHODS
- Meshfree Particle Methods
- Subdomain radial basis collocation method for fracture mechanics
- Generation of Finite Difference Formulas on Arbitrarily Spaced Grids
- Weighted radial basis collocation method for boundary value problems
- Reproducing kernel enhanced local radial basis collocation method
- Smoothed particle hydrodynamics: theory and application to non-spherical stars
- Element‐free Galerkin methods
- A FINITE POINT METHOD IN COMPUTATIONAL MECHANICS. APPLICATIONS TO CONVECTIVE TRANSPORT AND FLUID FLOW
- A point interpolation meshless method based on radial basis functions
- Reproducing kernel particle methods for structural dynamics
- Reproducing kernel particle methods
- Dispersion and stability properties of radial basis collocation method for elastodynamics
- Viscoplasticity using peridynamics
- Maximum principle and convergence analysis for the meshfree point collocation method
- Meshfree Methods