A multicontinuum theory for structural analysis of composite material systems

The success of modern continuum mechanics in modelling problems in solid mechanics is truly remarkable. For instance, the general theories of elasticity, plasticity, and viscoeleasticity all rely on the continuum hypothesis. However, while continuum mechanics has provided a powerful means of studying the physics of deformation of composite materials, there are situations when the continuum hypothesis is simply inadequate. These problems are generally associated with inelastic behavior and are mainly attributed to the necessity to homogenize two distinctly different materials into a single continuum.

In this paper, we introduce a multicontinuum theory designed specifically for the analysis of composite material systems. The chief attribute of the theory is its ability to do structural analysis while allowing each constituent to retain its own identity. Major analytical and numerical advances in the theory originally developed by Hansen et al. [Hansen, A. C., Walker, J. L. and Donovan, R. P. (1994). A finite element formulation for composite structures based on a volume fraction mixture theory. Int. J. Engng Sci. 32, 1–17.] are presented. The utility of the theory is demonstrated by using constituent information to predict the yield surface of a unidirectional boron/aluminum composite in the course of an analysis carried out at the structural level.