On the similarity of meshless discretizations of Peridynamics and Smooth-Particle Hydrodynamics
TLDR
In this article, the similarity between Peridynamics and Smooth-Particle Hydrodynamics is studied, and it is shown that the discretized equations of both methods coincide if nodal integration is used.About:
This article is published in Computers & Structures.The article was published on 2015-04-01 and is currently open access. It has received 79 citations till now. The article focuses on the topics: Peridynamics & Meshfree methods.read more
Citations
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Smoothed particle hydrodynamics (SPH) for free-surface flows: past, present and future
TL;DR: In this paper, the authors assess the recent trends in the numerical meshless method smoothed particle hydrodynamics, with particular focus on its potential use in modelling free-surface flows.
Book ChapterDOI
Phase-field modeling of fracture
TL;DR: This chapter provides an extensive overview of the literature on the so-called phase-field fracture/damage models (PFMs), particularly, for quasi-static and dynamic fracture of brittle and quasi-brittle materials, from the points of view of a computational mechanician.
Journal ArticleDOI
Numerical simulation of propagation and coalescence of flaws in rock materials under compressive loads using the extended non-ordinary state-based peridynamics
TL;DR: In this article, a four-point beam in bending with two notches as a benchmark example is firstly conducted to verify the ability, accuracy and numerical convergence of the proposed numerical method, and then the numerical samples of rock materials containing the one single pre-existing flaw with various lengths under uniaxial compression are modeled.
Journal ArticleDOI
Stability of peridynamic correspondence material models and their particle discretizations
TL;DR: In this article, a modified peridynamic correspondence material model was proposed to avoid zero-energy mode instability in a peridynamics particle code, where a term was added to the correspondence strain energy density that resists deviations from a uniform deformation.
Journal ArticleDOI
Modeling dynamic fracture of solids with a phase-field regularized cohesive zone model
Vinh Phu Nguyen,Jian-Ying Wu +1 more
TL;DR: In this article, an extension of the phase-field cohesive zone model for static fracture to dynamic fracture in brittle and quasi-brittle solids is presented, and the model performance is tested with several benchmarks for dynamic brittle and cohesive fracture.
References
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A numerical approach to the testing of the fission hypothesis.
TL;DR: A finite-size particle scheme for the numerical solution of two-and three-dimensional gas dynamical problems of astronomical interest is described and tested in this article, which is then applied to the fission problem for optically thick protostars.
Journal ArticleDOI
Reformulation of Elasticity Theory for Discontinuities and Long-Range Forces
TL;DR: In this paper, a peridynamic formulation for the basic equations of continuum mechanics is proposed, and the propagation of linear stress waves in the new theory is discussed, and wave dispersion relations are derived.
Journal ArticleDOI
Surfaces generated by moving least squares methods
Peter Lancaster,K. Salkauskas +1 more
TL;DR: In this article, an analysis of moving least squares (m.l.s.) methods for smoothing and interpolating scattered data is presented, in particular theorems concerning the smoothness of interpolants and the description of m. l.s. processes as projection methods.
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A meshfree method based on the peridynamic model of solid mechanics
TL;DR: In this article, a numerical method for solving dynamic problems within the peridynamic theory is described, and the properties of the method for modeling brittle dynamic crack growth are discussed, as well as its accuracy and numerical stability.
Journal ArticleDOI
Peridynamic States and Constitutive Modeling
TL;DR: In this article, a generalization of the original peridynamic framework for solid mechanics is proposed, which allows the response of a material at a point to depend collectively on the deformation of all bonds connected to the point.