A Simple Circular Cell Method for Multilevel Finite Element Analysis

Abstract

A simple multiscale analysis framework for heterogeneous solids based on a computational homogenization technique is presented. The macroscopic strain is linked kinematically to the boundary displacement of a circular or spherical representative volume which contains the microscopic information of the material. The macroscopic stress is obtained from the energy principle between the macroscopic scale and the microscopic scale. This new method is applied to several standard examples to show its accuracy and consistency of the method proposed.

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

“…[279] concludes that the smaller surface-to-volume ratio associated with a spherical RVE yields less influence of the boundary resulting in a better convergence to the effective material behavior as the size of the RVE increases, see also Ref. [280]. The size of the RVE has been also examined in the context of the granular media by Meier et al [281] where the discrete element method is used to evaluate the size of the RVE.…”

Concurrent multiscale modeling of three dimensional crack and dislocation propagation

“…The rest of the domain is the coarse scale region X cs where the system is described through a usual continuum formulation. 1 The number of atoms in sub-domain X fs is denoted by n fs . The outer boundary of X cs is denoted by @X cs with @X cs ¼ @X cs…”

“…The idea of the Cauchy-Born rule is to compute the material properties and stresses from the same potential used in the fine scale domain X fs . In other words at every point of the continuum model, we have 1 In this paper, the superscripts fs and cs denote the fine scale and coarse scale, respectively.…”

“…In these methods, different length and time scales are correlated to keep both accuracy and efficiency. Moreover, whereas the current computational power is capable of solving several billions of degrees of freedom, the multiscale methods are not only capable of solving problems which are impossible to solve with the current computational power; but also they are useful to solve the problems with noticeably reduced sizes to save the cost, energy, computational power and human resources to implement sophisticated parallel software and run huge simulations [1,2].…”

A hierarchical multi-scale approach to mechanical characterization of heat affected zone in welded connections

“…Multiscale methods can be categorized into hierarchical, semi-concurrent and concurrent methods [28]. Please refer to the manuscripts by Talebi et al [29,30] for the detailed description of the methods. In hierarchical multiscale methods, information are passed from the lower scale to the higher scale only, usually using, the conventional method of computational homogenization.…”