This paper discusses the homogenization method to determine the effective average elastic constants of linear elasticity of general composite materials by considering their microstructure. After giving a brief theory of the homogenization method, a finite element approximation is introduced with convergence stuay and corresponding error estimate. Applying these, computer programs PREMAT and POSTMAT are developed for preprocessing and postprocessing of material characterization of composite materials. Using these programs, the homogenized elastic constants for macroscopic stress analysis are obtained for typical composite materials to show their capability. Finally, the adaptive finite element method is introduced to improve the accuracy of the finite element approximation.

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Analysis of large deformation of elastic-viscoplastic materials has been performed in this paper using the finite element method with the arbitrary Lagrangian-Eulerian description. An overstress type viscoplastic model using the internal variable approach in a rotated stress-strain space characterizes the material. Stable and efficient integration techniques for the viscoplastic relations are discussed. A linearized form in the ALE description is presented which is to be solved using iteration techniques. In particular the quasi-Newton methods have been used in this analysis. Several test problems which have been considered illustrate the effectiveness of the entire solution algorithm.

In this study, mechanical properties of three types of polymeric foams (polypropylene (PP), polystyrene (PS), and polyurethane (PU) foams) are investigated. Focus has been placed on the strain rate and temperature effects on these foams under large deformations. Selected experimental results from uniaxial compression, hydrostatic compression, and simple shear tests are presented. A phenomenological hydrodynamic elastoplastic constitutive law is developed to model these polymeric foams. Numerical implementation and validation of the constitutive model are also described.

One-point reduced integration method is studied for 4-node quadrilateral and 8-node brick elements together wih correction terms of the numerical integration rule for selective and directional reduced integration schemes for anisotropic linear elasticity. These correction terms were previously called hourglass control to the reduced integration method by Belytschko and others. In the present work the idea of existing hourglass control is carefully examined for its convergence and accuracy, and is extended to include both selective and directional reduced integration methods.