Nonlinear micromechanical formulation of the high fidelity generalized method of cells

Abstract

a b s t r a c tThe recent High Fidelity Generalized Method of Cells (HFGMC) micromechnical modeling framework of multiphase composites is formulated in a new form which facilitates its computational efficiency that allows an effective multiscale material-structural analysis. Towards this goal, incremental and total formulations of the governing equations are derived. A new stress update computational method is established to solve for the nonlinear material constituents along with the micromechanical equations. The method is well-suited for multiaxial finite increments of applied average stress or strain fields. Explicit matrix form of the HFGMC model is presented which allows an immediate and convenient computer implementation of the offered method. In particular, the offered derivations provide for the residual field vector (error) in its incremental and total forms along with an explicit expression for the Jacobian matrix. This enables the efficient iterative computational implementation of the HFGMC as a stand alone. Furthermore, the new formulation of the HFGMC is used to generate a nested local-global nonlinear finite element analysis of composite materials and structures. Applications are presented to demonstrate the efficiency of the proposed approach. These include the behavior of multiphase composites with nonlinearly elastic, elastoplastic and viscoplastic constituents.

The effect of anisotropic damage evolution on the behavior of ductile and brittle matrix composites

“…This micromechanics model has been reviewed by Aboudi (2004) and more recently has been shown by Haj-Ali and Aboudi (2009) to provide excellent prediction for (undamaged) nonlinear and inelastic matrix composites by extensive comparisons with finite element solutions. In addition, this micromechanics model has been coupled by these authors to a finite element software to investigate the response of metal matrix composite structures.…”

Micromechanics Modeling of Composites Subjected to Multiaxial Progressive Damage in the Constituents

“…More recently, Haj-Ali and Aboudi [25] formulated the HFGMC model in a new form that facilitates its computational efficiency. To this end, the explicit matrix form of the HFGMC model was presented, which allowed an immediate and convenient computer implementation of the model.…”

Micromechanical Analysis for Two-Phase Copper-Silver Composites under Large Deformations

“…A detailed review of this class of nonlinear micromechanical methods can be found in [1][2][3], among several others. In addition, the prediction of the local deformation process of periodic alternate multiphase materials requires the detailed description of the spacial description of the soft and hard phases subject to different kinds of loading [4]. Hence, the formation of constitutive equations that govern the large deformations of composite materials, which consist of elasto-viscoplastic phases, is necessary for the modeling and analysis of their deformation behavior.…”