scholarly journals Formulation analysis and computation of an optimization-based local-to-nonlocal coupling method.

2019 ◽  
Author(s):  
Marta D'Elia ◽  
Pavel B. Bochev
Keyword(s):  
Coupling Method ◽  
Nonlocal Coupling ◽  
Formulation Analysis

scholarly journals A Quasi-nonlocal Coupling Method for Nonlocal and Local Diffusion Models

2018 ◽  
Vol 56 (3) ◽  
pp. 1386-1404 ◽  
Author(s):  
Qiang Du ◽  
Xingjie Helen Li ◽  
Jianfeng Lu ◽  
Xiaochuan Tian
Keyword(s):  
Diffusion Models ◽  
Coupling Method ◽  
Nonlocal Coupling ◽  
Local Diffusion

A quasi-nonlocal coupling method for bond-based peridynamics with classical continuum mechanics

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Feng Jiang ◽  
Yongxing Shen
Keyword(s):  
Patch Test ◽  
Continuum Mechanics ◽  
Coupling Method ◽  
Coupling Scheme ◽  
Dimensional Problem ◽  
Nonlocal Coupling ◽  
Coupling Region ◽  
Content Type ◽  
Peridynamic Model ◽  
Ghost Force

PurposeThe purpose of this paper is to propose a novel quasi-nonlocal coupling of the bond-based peridynamic model with the classical continuum mechanics model to fully take advantage of their merits and be free of ghost forces.Design/methodology/approachThis study reconstructs a total energy functional by introducing a coupling parameter that alters only the nonlocal interactions in the coupling region rather than the whole region and a modified elasticity tensor that affects the local interactions. Then, the consistency of force patch test is enforced in the coupling region to completely eliminate the ghost force in a general energy-based coupling scheme. For a one-dimensional problem, these coupling parameters are further determined through an energy patch test to preserve the energy equivalence or through an l1-regularization. And, for a two- or three-dimensional problem, depending on the existence of a solution to the discretized force patch test, they are determined through an l1-minimization or l1-regularization.FindingsOne- and two-dimensional numerical examples under affine deformation have been conducted to verify the accuracy of the quasi-nonlocal coupling method, which exhibits no ghost force. Moreover, the coupling model can reproduce almost the same deformation behaviors of points near the crack for a cracked plate under tension as that from a pure peridynamic model, the former with a rather low computational cost and an easier application of boundary conditions.Originality/valueThis work is aiming at getting over long-standing ghost force issues in the energy-based coupling scheme. The numerical results from the cracked plate problem are exhibited promising extension to dynamic problems.

The need of electron microscopy in the study of domains and domain walls in ferroelectrics

1994 ◽  
Vol 52 ◽  
pp. 550-551
Author(s):  
Wenwu Cao
Keyword(s):  
Domain Wall ◽  
Domain Walls ◽  
High Mobility ◽  
Continuum Theory ◽  
Polarization Vector ◽  
Ferroelectric Materials ◽  
Dielectric Constants ◽  
Nonlocal Coupling ◽  
Cubic Symmetry ◽  
Gradient Energy

Domain structures play a key role in determining the physical properties of ferroelectric materials. The formation of these ferroelectric domains and domain walls are determined by the intrinsic nonlinearity and the nonlocal coupling of the polarization. Analogous to soliton excitations, domain walls can have high mobility when the domain wall energy is high. The domain wall can be describes by a continuum theory owning to the long range nature of the dipole-dipole interactions in ferroelectrics. The simplest form for the Landau energy is the so called ϕ model which can be used to describe a second order phase transition from a cubic prototype,where Pi (i =1, 2, 3) are the components of polarization vector, α's are the linear and nonlinear dielectric constants. In order to take into account the nonlocal coupling, a gradient energy should be included, for cubic symmetry the gradient energy is given by,

Vibration prediction based on the coupling method of half-train model and 3D refined finite element ground model

2021 ◽  
Vol 134 ◽  
pp. 104133
Author(s):  
Bitao Wu ◽  
Yuanlai Zeng ◽  
Zhenwei Zhou ◽  
Gang Wu ◽  
Huaxi Lu
Keyword(s):  
Finite Element ◽  
Coupling Method ◽  
Ground Model ◽  
Vibration Prediction
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