Deformation and failure in stochastic fibrous networks: Scale, dimension and application

Abstract

There is an extensive literature on identification and analysis of representative volume elements (RVE's) in order to bound intrinsic materials properties in porous and nonporous solids. However, in such analyses there is often an implicit assumption made that solution of several large classes of linear scientific problems can be simultaneous achieved simply via a single solution of Laplace's equation for the domain. We find, however, that for an extremely technologically significant class of disordered fibrous/particular structures, the transport properties and the mechanical properties cannot simultaneously be found using a single field solution. Specifically, alterations in microstructure during loading of the material can produce different degrees of effects on mechanical load transfer and conductivity. The details of load transfer within stochastic, porous arrays are critical in understanding their likely properties, which we have shown to exhibit large variability. Nonetheless, through thoughtful use of stochastic finite element simulation, we are able to provide technologically useful guidance on material synthesis, construction, and estimations of lifetime in several key contexts. In doing so, we have addressed several mathematical issues of solution of field equations around singularities produced by phase contrast, boundary condition choice and material contrast, and geometric features inherent in fused structures. This work is a summary of some of our key findings on the subject, and suggests a roadmap for new areas of study, based both on our simulations and on our experiments on materials used in battery systems. © 2001 Trans Tech Publications.