A variational multiscale immersed meshfree method for heterogeneous materials
Journal
Computational Mechanics
Journal Volume
67
Journal Issue
4
Start Page
1059
End Page
1097
ISSN
01787675
14320924
Date Issued
2021
Author(s)
Abstract
We introduce an immersed meshfree formulation for modeling heterogeneous materials with flexible non-body-fitted discretizations, approximations, and quadrature rules. The interfacial compatibility condition is imposed by a volumetric constraint, which avoids a tedious contour integral for complex material geometry. The proposed immersed approach is formulated under a variational multiscale based formulation, termed the variational multiscale immersed method (VMIM). Under this framework, the solution approximation on either the foreground or the background can be decoupled into coarse-scale and fine-scale in the variational equations, where the fine-scale approximation represents a correction to the residual of the coarse-scale equations. The resulting fine-scale solution leads to a residual-based stabilization in the VMIM discrete equations. The employment of reproducing kernel (RK) approximation for the coarse- and fine-scale variables allows arbitrary order of continuity in the approximation, which is particularly advantageous for modeling heterogeneous materials. The effectiveness of VMIM is demonstrated with several numerical examples, showing accuracy, stability, and discretization efficiency of the proposed method.
Subjects
Heterogeneous Material
Reproducing Kernel Particle Method
Variational Multiscale Immersed Method
Volumetric Constraint
Computational Methods
Mechanical Engineering
Complex Materials
Discrete Equations
Heterogeneous Materials
Interfacial Compatibility
Reproducing Kernel
Variational Equations
Variational Multiscale
Volumetric Constraints
Numerical Methods
Publisher
Springer Science and Business Media Deutschland GmbH
Type
journal article