Macro-Micro Uncoupled Homogenization Procedure for Microscopic Nonlinear Behavior Analysis of Composites

Abstract

For easy and practical simulation of microscopic nonlinear mechanical behavior of composite materials, new homogenization analysis procedure named macro-micro uncoupled method is proposed. In this procedure, microscopic simulation of material strength test is carried out first, then nonlinear homogenized material properties are obtained. Both the homogenization method and RVE (Representative Volume Element) approach are shown for this microscopic simulation. Macroscopic nonlinear behavior of a structure made of composite materials can be analyzed by only referring the pre-calculated homogenized material nonlinearity. As an example, microscopic fracture propagation for textile composite materials and microscopic large deformation for porous elastic materials are analyzed.

A New Estimation Method of Coke Strength by Numerical Multiscale Analysis

“…9,10) One of the merits of the homogenization method is strict dynamics theory and the method can reflect the correlations between macro and micro scale. 3) To analyze the microscopic fracture of composite materials such as coke, the correlations must be taken into consideration.…”

Acceleration of material‐dominated calculations via phase‐space simplicial subdivision and interpolation

“…A number of enhancements and extensions of the present approach immediately suggest themselves. Thus, considerable synergism may be expected from the combination of the proposed scheme with database approaches [15][16][17][18][19][20][21][22][23][24][25][26], where the information from each traversed simplex are added 'on the fly' to a database for subsequent use, should the same simplex be traversed again. Although this archiving introduces additional overhead and complexity, the benefits can greatly outweigh the cost, especially for large computational models.…”

“…A general class of acceleration methods for material-dominated calculations, known as database methods, consists of precalculating and storing the material or sub-grid model over the range of states or processes expected to arise during the simulation (cf., e.g., [15][16][17][18][19][20][21][22]). However, these methods may become unwieldy when the phase space of the material is of high dimensionality or when the full range of states and processes is difficult to bound a priori.…”

Homogenization Methods and Multiscale Modeling: Nonlinear Problems

“…Constructing effective constitutive laws without prior knowledge on their form is, however, possible, but in some restricted cases. A second class of techniques is based on the construction of a numerical, material map between effective stress and strains (Terada and Kikuchi, 1995;Takano et al, 1996;Temizer and Wriggers, 2007;Yvonnet et al, 2009Yvonnet et al, , 2013Clément et al, 2012;Tran et al, 2011), which can be applied, for example, in the case of hyperelastic materials or for linear viscoelasticity, as described in the following. A third class of methodologies, valid for viscoplastic materials at small strains, uses preliminary computations to construct a basis for anelastic modes (TFA and NTFA techniques).…”