In Search of a Perfect Micromechanics Model for Multiphase Materials: High-Fidelity Generalized Method of Cells
Marek-Jerzy Pindera
Applied Mechanics Program
Civil Engineering Department
University of Virginia, Charlottesville, VA 22904
Date: Friday, November 15, 2002
Time: 3:30 p.m.
Place: 110 Othmer Hall
A number of micromechanics-based models have been proposed in the literature for the elastic and inelastic response of multiphase materials. These range from the simple, and very efficiently, but highly inaccurate rule-of-mixtures type models to highly accurate but very inefficient finite-element based homogenization techniques. These models will be first briefly reviewed, and their capabilities and shortcomings highlighted in order to motivate my (obviously subjective) definition of a perfect micromechanics model. Relative to this definition, the Generalized Method of Cells is an intermediate model that is quite accurate at the macro-level but not always accurate at the micro-level. The reason lies in the absence of so-called shear coupling which provides the required bridge between macroscopically applied normal stresses and the microscopic shear stresses necessary for an accurate estimate of microlevel field quantities. In order to overcome this deficiency, a new micromechanics model has been developed recently for the response of multiphase materials with arbitrary periodic microstructures, named High-Fidelity Generalized Method of Cells in part because it employs the same sub-volume discretization as the original Generalized Method of Cells. The model’s analytical framework is based on the homogenization technique, but the method of solution for the local displacement and stress fields borrows concepts previously employed in constructing the Higher-Order Theory for Functionally Graded Materials, in contrast with the typical finite-element based solution strategies. Resulting closed-form macroscopic constitutive equations valid for both uniaxial and multiaxial loading of periodic materials with elastic and inelastic constitutive phases, obtained from the developed approach, can be incorporated into structural analysis computer codes. The model makes possible accurate simulation of the average stress-strain response of heterogeneous materials such as ceramic, metal, and polymeric matrix composites employed in the aerospace, electronic and biomedical industries. In addition to the excellent predictive capability of the macroscopic response, the model also predicts the internal or micro-level stress and strain fields with very good accuracy in both elastic and inelastic regions, which justifies the chosen name. This predictive capability is demonstrated through comparison with elasticity and plasticity analytical solutions and finite-element results for axisymmetric, axial shear, and transverse loading. Furthermore, a recently developed reformulation strategy has increased the model’s efficiency and ease of implementation, thereby bringing it a step closer to a perfect micromechanics model.
