Concurrent coupling of peridynamics and classical elasticity for elastodynamic problems

Wang, Xiaonan; Kulkarni, Shank S.; Tabarraei, Alireza

doi:10.1016/j.cma.2018.09.019

Cited by 66 publications

(20 citation statements)

References 64 publications

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“…Macek et al [Macek and Silling (2007); ; Liu and Hong (2012); Seleson, Beneddine and Prudhomme (2013); Lubineau, Azdoud, Han et al (2012); Han and Lubineau (2012); Shojaei, Mudric, Zaccariotto et al (2016); Shojaei, Mossaiby, Zaccariotto et al (2018); Fang, Liu, Fu et al (2019); Wang, Kulkarni and Tabarraei (2019)] proposed to couple peridynamics with classical continuum mechanics for reducing the computational cost. Macek et al [Macek and Silling (2007)] and Kilic et al ] coupled peridynamics with classical continuum mechanics by satisfying kinematic compatibility over an overlap zone where both peridynamics and classical continuum mechanics co-exist.…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Local/Nonlocal Continuum Mechanics Modeling and Simulation of Fracture in Brittle Materials

Wang

Han

Lubineau

2019

Computer Modeling in Engineering &Amp; Sciences

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Classical continuum mechanics which leads to a local continuum model, encounters challenges when the discontinuity appears, while peridynamics that falls into the category of nonlocal continuum mechanics suffers from a high computational cost. A hybrid model coupling classical continuum mechanics with peridynamics can avoid both disadvantages. This paper describes the hybrid model and its adaptive coupling approach which dynamically updates the coupling domains according to crack propagations for brittle materials. Then this hybrid local/nonlocal continuum model is applied to fracture simulation. Some numerical examples like a plate with a hole, Brazilian disk, notched plate and beam, are performed for verification and validation. In addition, a peridynamic software is introduced, which was recently developed for the simulation of the hybrid local/nonlocal continuum model.

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Section: Introductionmentioning

confidence: 99%

A Hybrid Local/Nonlocal Continuum Mechanics Modeling and Simulation of Fracture in Brittle Materials

Wang

Han

Lubineau

2019

Computer Modeling in Engineering &Amp; Sciences

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“…PD has experienced prolific growth as an area of research, with a significant number of contributions in multiple disciplines. Various applications and extensions of PD not dealing exclusively with material failure include quasi-static problems [18][19][20][21][22], coupled problems [23][24][25][26][27], multiscale modeling [28][29][30][31][32][33][34][35], structural mechanics [36][37][38][39][40], constitutive models [41][42][43][44][45][46][47][48], biomechanics [49,50], and wave dispersion [51][52][53][54][55][56][57]. For an extensive study of the balance laws, applications, and implementations, see [58].…”

Section: Introductionmentioning

confidence: 99%

The computational framework for continuum-kinematics-inspired peridynamics

et al. 2020

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Peridynamics (PD) is a non-local continuum formulation. The original version of PD was restricted to bond-based interactions. Bond-based PD is geometrically exact and its kinematics are similar to classical continuum mechanics (CCM). However, it cannot capture the Poisson effect correctly. This shortcoming was addressed via state-based PD, but the kinematics are not accurately preserved. Continuum-kinematics-inspired peridynamics (CPD) provides a geometrically exact framework whose underlying kinematics coincide with that of CCM and captures the Poisson effect correctly. In CPD, one distinguishes between one-, two- and three-neighbour interactions. One-neighbour interactions are equivalent to the bond-based interactions of the original PD formalism. However, two- and three-neighbour interactions are fundamentally different from state-based interactions as the basic elements of continuum kinematics are preserved precisely. The objective of this contribution is to elaborate on computational aspects of CPD and present detailed derivations that are essential for its implementation. Key features of the resulting computational CPD are elucidated via a series of numerical examples. These include three-dimensional problems at large deformations. The proposed strategy is robust and the quadratic rate of convergence associated with the Newton–Raphson scheme is observed.

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“…It provides a robust and powerful tool for modeling complex problems and systems and has become a prevalent tool in a wide range of industries and applications . FEM has the flexibility to be coupled with other numerical techniques such as molecular dynamics, peridynamics, and meshless methods . Due to its reliable and robust formulation, we use FEM to study the damping properties on polymer composites.…”

Section: Finite Element Modelmentioning

confidence: 99%

A Stochastic Analysis of the Damping Property of Filled Elastomers

Kulkarni

Tabarraei

2018

Macro Theory & Simulations

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Finite elements modeling is used to investigate the damping property of Polymer composites consisting of a viscoelastic matrix and randomly dispersed elastic particles. The impact of vibration frequency, inclusions size and volume fraction on the damping capability of polymer composites are studied. It is shown that analytical micromechanics methods give accurate predictions only when inclusions volume fraction is small. The results show that loading frequency and inclusions volume fraction significantly impact the damping capability of polymer composites. The effect of domain boundary conditions on the simulation results is studied by conducting finite element modelings on representative volume elements (RVEs) which are subjected to periodic or mixed boundary conditions. The modeling results indicate that both boundary conditions lead to similar predictions for damping. Sensitivity analyses are conducted to assess how material properties influence the damping property. The sensitivity analyses show that an increase in the stiffness of the composite matrix leads to a reduction in the damping capability of polymer composites. In contrast, an increase in the stiffness of inclusions results in an increase in the damping capability of polymer composites. Moreover, the damping properties are improved if the relaxation time of the viscoelastic matrix is increased.

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Concurrent coupling of peridynamics and classical elasticity for elastodynamic problems

Cited by 66 publications

References 64 publications

A Hybrid Local/Nonlocal Continuum Mechanics Modeling and Simulation of Fracture in Brittle Materials

A Hybrid Local/Nonlocal Continuum Mechanics Modeling and Simulation of Fracture in Brittle Materials

The computational framework for continuum-kinematics-inspired peridynamics

A Stochastic Analysis of the Damping Property of Filled Elastomers

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