A morphing approach to couple state-based peridynamics with classical continuum mechanics

Abstract

Please cite this article as: F. Han, G. Lubineau, Y. Azdoud, A. Askari, A morphing approach to couple state-based peridynamics with classical continuum mechanics, Comput. Methods Appl. Mech. Engrg. (2015), http://dx.doi. org/10.1016/j.cma.2015.12.024 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. AbstractA local/nonlocal coupling technique called the morphing method is developed to couple classical continuum mechanics with state-based peridynamics. State-based peridynamics, which enables the description of cracks that appear and propagate spontaneously, is applied to the key domain of a structure, where damage and fracture are considered to have non-negligible effects. In the rest of the structure, classical continuum mechanics is used to reduce computational costs and to simultaneously satisfy solution accuracy and boundary conditions. Both models are glued by the proposed morphing method in the transition region. The morphing method creates a balance between the stiffness tensors of classical continuum mechanics and the weighted coefficients of state-based peridynamics through the equivalent energy density of both models. Linearization of state-based peridynamics is derived by Taylor approximations based on vector operations. The discrete formulation of coupled models is also described. Two-dimensional numerical examples illustrate the validity and accuracy of the proposed technique. It is shown that the morphing method, originally developed for bond-based peridynamics, can be successfully extended to state-based peridynamics through the original developments presented here.

Numerical convergence of nonlinear nonlocal continuum models to local elastodynamics

“…Our results and analysis support a combined local-nonlocal approach to the numerical solution of these problems. This type of numerical approach is the focus of many recent investigations, see other works, [39][40][41][42][43][44][45][46] where the use of nonlocal models and local models is applied to different subdomains of the computational domain. These approaches are promising in that they reduce the computational cost of the numerical simulation.…”

Numerical Simulations of the Ice Load of a Ship Navigating in Level Ice Using Peridynamics

“…It can also be considered as a length-scale parameter which gives peridynamics a "non-local" character. The size of the horizon changes depending on the nature of the problem [Bobaru, Yang, Alves et al (2009); Freimanis and Paeglitis (2017); Han, Lubineau, Yan et al (2016)]. For three-dimensional analysis the most common are cubic lattices with uniform spacing in all directions, and the horizon may be chosen according to convergence, since for any value of δ, the parameters in the peridynamic material model can be chosen to match the measured Young's modulus of the material, and physical behaviour can be accurately represented.…”

An implicit dual‐based approach to couple peridynamics with classical continuum mechanics

“…Furthermore, Seleson et al present the force‐based coupling method using nonlocal weights composed of blending functions; they also generalize this coupling approach to couple PD and higher‐order gradient models of any order. Moreover, the morphing method is proposed by Lubineau et al to construct a single unified balance equation between BPD and CCM models; after that, this morphing‐based coupling method has been successfully used to study the failure simulation of materials and is further developed by Han et al to couple the OSPD and CCM models. Apart from the coupling between PD and CCM, Tong and Li propose the multiscale coupling of molecular dynamics and PD, Fan and Li propose a hybrid model of PD and smoothed particle hydrodynamics to simulate soil fragmentation, Shojaei et al propose a coupling of PD with a meshless method, and Han et al propose an adaptive coupling between damage mechanics and PD to objectively simulate all the steps that lead to material failure.…”

“…Theoretically speaking, the coupling of PD and CCM should be achieved with simplicity and effectivity, for which there are three reasons . First, both PD and CCM are continuum theories, and the derivations of the constitutive parameters are based on the strain energy density . Second, nonlocal PD models can be generally connected to local CCM counterparts through a limiting process; in other words, the PD models for an elastic material can reproduce the classical local models as the length scale goes to zero, which is mathematically addressed by Silling and Lehoucq .…”

“…It should be noted that the efficiency and accuracy of the SNS‐FEM have been demonstrated by acoustic analyses, electromagnetic analyses, transient heat transfer analyses, and stochastic analyses . Therefore, the SNS‐FEM is chosen to couple OSPD to reduce the computational cost on one hand and make this implicit DB‐CA much stable and accurate on the other, which is also a difference from the recent implicit coupling method where the traditional FEM is used. As with many researchers working on the coupling method of PD and CCM, the main purpose of this paper is to provide a viable and convenient numerical coupling method for engineers, which takes full advantage of the generality of PD and the computational efficiency of CCM to solve the engineering crack problems; thus, more emphasis is placed on the formula derivation and algorithm details relevant to the software implementation in the following parts.…”