A peridynamic model for plasticity: Micro-inertia based flow rule, entropy equivalence and localization residuals

Rahaman, Md. Masiur; Roy, Pranab; Roy, Debasish; Reddy, J. N.

doi:10.1016/j.cma.2017.07.034

Cited by 35 publications

(10 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Statebased material models are distinguished as ordinary and non-ordinary models. For ordinary state-based PD, the following material models are available: Elastic brittle [14,[33][34][35], Plasticity [36][37][38], Composite [39], Eulerian fluid [40], position-aware linear solid (PALS) [41], and Viscoelastic [42][43][44][45]. For non-ordinary state-based PD the correspondence model [14,46], the beam\plate model [47], and a model for cementitious composites [48] are available.…”

Section: Materials Models For Pdmentioning

confidence: 99%

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

Diehl¹,

Lipton²,

Wick³

et al. 2021

Preprint

View full text Add to dashboard Cite

Computational modeling of the initiation and propagation of complex fracture is central to the discipline of engineering fracture mechanics. This review focuses on two promising approaches: phase-field (PF) and peridynamic (PD) models applied to this class of problems. The basic concepts consisting of constitutive models, failure criteria, discretization schemes, and numerical analysis are briefly summarized for both models. Validation against experimental data is essential for all computational methods to demonstrate predictive accuracy. To that end, The Sandia Fracture Challenge and similar experimental data sets where both models could be benchmarked against are showcased. Emphasis is made to converge on common metrics for the evaluation of these two fracture modeling approaches. Both PD and PF models are assessed in terms of their computational effort and predictive capabilities with their relative advantages and challenges are summarized.

show abstract

Section: Materials Models For Pdmentioning

confidence: 99%

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

Diehl¹,

Lipton²,

Wick³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…where Δ l dis,e IM is the elastic part of the incremental distortional stretch calculated using Equations (15) and (26). Given the incremental distortion energy at each load step, the total distortion energy is the summation as…”

Section: Nonlocal Yield Function and Yield Criterionmentioning

confidence: 99%

“…The basic idea was to construct displacement fields for each lattice point using the least square technique and the strain field was then obtained to develop the plasticity model. Plasticity has also been developed for other discontinuous lattice‐like models, such as discrete element method 22,23 and peridynamics 24‐27 …”

Section: Introductionmentioning

confidence: 99%

A nonlocal lattice particle model for J2 plasticity

Wei

Chen

Liu

2020

Numerical Meth Engineering

View full text Add to dashboard Cite

Summary In virtue of their intrinsic integro‐differential formulation of underlying physical behavior of materials, discontinuous computational methods are more beneficial over continuum‐mechanics‐based approaches for materials failure modeling and simulation. However, application of most discontinuous methods is limited to elastic/brittle materials, which is partially due to their formulations are based on force and displacement rather than stress and strain measures as are the cases for continuous approaches. In this article, we formulate a nonlocal maximum distortion energy criterion in the framework of a lattice particle model for modeling of elastoplastic materials. Similar to the maximum distortion energy criterion in continuum mechanics, the basic idea is to decompose the energy of a discrete material point into dilatational and distortional components, and plastic yielding of bonds associated with this material point is assumed to occur only when the distortional component reaches a critical value. However, the formulated yield criterion is nonlocal since the energy of a material point depends on the deformation of all the bonds associated with this material point. Formulation of equivalent strain hardening rules for the nonlocal yield model was also developed. Compared to theoretical and numerical solutions of several benchmark problems, the proposed formulation can accurately predict both the stress‐strain curves and the deformation fields under monotonic loading and cyclic loading with different strain hardening cases.

show abstract

“…However, the range of PD applications is broad and not limited to fracture mechanics. Various applications and extensions of PD other than those dealing exclusively with material failure include quasi-static problems [16][17][18][19][20], coupled problems [21][22][23], multiscale modeling [24][25][26][27][28][29][30], structural mechanics [31][32][33][34][35], constitutive models [36][37][38][39][40][41][42][43][44], plasticity [45,46], biomechanics [47,48] and wave dispersion [49][50][51][52][53][54][55]. For an extensive study of the balance laws, applications, and implementations, see [56], and for a brief description of PD together with a review of its applications and related studies in different fields to date, see the review [57].…”

Section: Introductionmentioning

confidence: 99%