A geometrically exact formulation of peridynamics

Javili, Ali; McBride, Andrew; Steinmann, Paul

doi:10.1016/j.tafmec.2020.102850

Cited by 17 publications

(9 citation statements)

References 74 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…, where dissipation occurred only as a result of the Fourier-like conduction. Furthermore, similar to our previous discussions, we elaborate on both options T and C. The dissipation inequality (22) for the case of…”

Section: Temperature Evolution Equationmentioning

confidence: 86%

“…The interaction potential of CPD is composed of three parts corresponding to one-neighbour, two-neighbour and three-neighbour interactions. The novel contribution of this work is the extension of CPD [20][21][22] to account for thermo-mechanical behaviour at finite deformation. The treatment of thermoelasticity within the framework of PD has been addressed in [23,24].…”

mentioning

confidence: 99%

See 1 more Smart Citation

Continuum-kinematics-inspired peridynamics: Thermo-mechanical problems

Javili

Ekiz

McBride

et al. 2021

Continuum Mech. Thermodyn.

View full text Add to dashboard Cite

The recently proposed continuum-kinematics-inspired peridynamics (CPD) is extended to account for thermo-mechanical coupling at large deformations. The key features of CPD are that it is geometrically exact and is built upon multi-neighbour interactions. The bond-based interactions of the original PD formalism are equivalent to one-neighbour interactions of CPD. Two-and three-neighbour interactions, however, are fundamentally different from state-based PD in that the basic elements of continuum kinematics are preserved exactly. We elaborate on thermodynamic restrictions on the interaction energies and derive thermodynamically consistent constitutive laws through a Coleman-Noll-like procedure. Notably, we show that various choices for temperature, or coldness, satisfy the dissipation inequality and provide meaningful temperature, or coldness, evolution equations together with Fourier-like conduction relations.

show abstract

Section: Temperature Evolution Equationmentioning

confidence: 86%

mentioning

confidence: 99%

Continuum-kinematics-inspired peridynamics: Thermo-mechanical problems

Javili

Ekiz

McBride

et al. 2021

Continuum Mech. Thermodyn.

View full text Add to dashboard Cite

show abstract

“…17 Due to these promising benefits, CPD has been further developed by now. [18][19][20][21][22][23][24] In most real-world problems, materials are heterogeneous. Numerous fields of applications of PD are concerned with modeling heterogeneous media, such as micro-structured materials, 6,7 functionally graded materials, [25][26][27][28] or bilayers, 29 to name a few.…”

Section: Introductionmentioning

confidence: 99%

“…CPD differs from state‐based PD, which faces issues when transferring local material models to peridynamic ones via a correspondence model — a concept that state‐based PD commonly relies on 17 . Due to these promising benefits, CPD has been further developed by now 18‐24 …”

Section: Introductionmentioning

confidence: 99%

A nonlocal interface approach to peridynamics exemplified by continuum‐kinematics‐inspired peridynamics

Laurien

Javili

Steinmann

2022

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

In this contribution, we present a novel approach on how to treat material interfaces in nonlocal models based on peridynamics (PD) and in particular continuum-kinematics-inspired peridynamics (CPD), a novel variationally consistent peridynamic formulation. Our method relies on a nonlocal interface where the material subdomains overlap. Within this region, a kinematic coupling of the two constituents is enforced. The contact is purely geometrical as interaction forces act only between points of the same material. We provide a detailed description of the computational implementation within the framework of CPD, that is in principle applicable to all formulations of PD. A variety of numerical examples for modeling bimaterial interfaces illustrate the utility of the technique for both two-dimensional and three-dimensional problems, including examples at large deformations. Our model approaches a local model when the nonlocality parameter, the horizon size, is decreased. The proposed methodology offers a viable alternative to previous approaches in PD, which are essentially imposing mixture rules for the interfacial material parameters.

show abstract

“…Silling and Lehoucq [44] tested the theory's robustness and efficiency, comparing the force densities of PD and classical elasticity theory. A considerable amount of studies using PD have been published, such as combining PD and FEM [45,46], the effect of corrosion pits on crack propagation [47], Hookean type membrane deformation under different loading conditions [48], fracture in polycrystalline materials [49], modelling of explosive loading on composite laminates [50], a geometrically exact formulation of PD [51], and plate deformations [52,53]. Besides, PD has been implemented in various applications such as flat shells under in-plane loading [54], extended non-ordinary state-based PD [55], effect of porosity on fatigue nucleation [56], crack growth modelling during fatigue [57], and higher order FGMs [58].…”

Section: Introductionmentioning

confidence: 99%

Peridynamic simulation of dynamic fracture in functionally graded materials subjected to impact load

Candaş

Öterkuş

İmrak

2021

Engineering with Computers

View full text Add to dashboard Cite

Dynamic crack propagation assessment in functionally graded materials (FGMs) with micro-cracks is accomplished using bond-based Peridynamics (PD). The dynamic fracture behaviour of various FGMs' material models is studied in Kalthoff-Winkler experiment. Dynamic crack growth predictions and associated material damage of the specimen under dynamic loading conditions are considered. The effect of micro-cracks near macro-crack tips on the toughening mechanism is evaluated in terms of crack propagation velocities. Stochastically pre-located micro-cracks are modelled to obtain the toughening effect in the material. Additionally, the velocities and time required for fracture are compared in different FGM cases. It is frankly found that if a crack propagates in the harder region of the specimen, velocities decrease and toughness increase in contrast to the softer region. Furthermore, micro-cracks around a macro-crack decelerate the crack propagation and enhance toughening mechanism in FGM body depending on gradation of material properties.

show abstract

A geometrically exact formulation of peridynamics

Cited by 17 publications

References 74 publications

Continuum-kinematics-inspired peridynamics: Thermo-mechanical problems

Continuum-kinematics-inspired peridynamics: Thermo-mechanical problems

A nonlocal interface approach to peridynamics exemplified by continuum‐kinematics‐inspired peridynamics

Peridynamic simulation of dynamic fracture in functionally graded materials subjected to impact load

Contact Info

Product

Resources

About