A Multicontinuum Theory for Thermal-Elastic Finite Element Analysis of Composite Materials

Structural analysis of composite materials is severely limited by the lack of constituent information. This information is generally unavailable due to the continuum hypothesis associated with the geometric scale of the problem. Micromechanics has been the traditional approach to achieving insights into constituent behavior in a composite material. However, modelling micromechanical details in a structural application is frequently impractical. In this paper, by example of linear elasticity, we suggest a viable bridge between structural analysis and micromechanics. The approach utilizes detailed finite element models of a representative volume element as a one-time preprocessor to characterize the structural stiffness of the material. This information is used to implement an analytical expression for constituent stress and strain fields (in the continuum sense) as a function of the structural fields in a conventional finite element analysis. The computational premium is minimal while the benefits and additional insights regarding constituent behavior are significant. Numerical results for constituent as well as structural fields are presented for thermal-elastic behavior of a composite plate with a hole. The results indicate dramatic differences in the constituent stress fields for a comparable structural stress caused by thermal and mechanical loads, respectively. A brief discussion of the potential extension to in-elastic analysis is also included.