Scale effects on the macroscopic properties and the onset of failure in microstructured materials

A critical aspect in the design of composite and microstructured materials involves the prediction of their macroscopic behavior and ultimate failure, based upon information about their underlying microstructures. The traditional approach to these problems, usually involving classic continuum theories, ignores the characteristic microstructural length scale, and its role in determining the overall material behavior and failure. As a result, these classic continuum theories are not realistic when applied to complex heterogeneous materials, and consequently, there is a need to develop improved theories to aid in the microstructural design of these advanced materials. Incorporating microstructure related scale information in improved continuum theories will provide realistic predictions for the material behavior, and a better understanding of the failure mechanisms involved. A prerequisite to developing appropriate continuum theories, however, is a comprehensive study of the problems related to behavior, instability, and scale in materials with microstructure.;An investigation into the influence of scale on the overall behavior, the stability, and the failure of materials with periodic microstructures is to be presented. Attention is focused on rate-independent, nonlinear elastic and elastoplastic materials, which are subjected to general finite macroscopic deformations. Initially, consideration is given to planar lattice models, which serve as idealizations for more complicated microstructured materials. Here, the influence of scale on the macroscopic properties and the onset of failure in these materials are explored, as well as the sensitivity of these scale effects to imperfections in the material microstructure. Of further interest is the range of validity for the classic continuum theory predictions, which is established by comparing the local and global instability modes. Subsequently, the investigation is extended to include a similar study of cellular materials. Here, attention is focused on the influence of scale on the onset of failure, and the role of scale in determining the ultimate failure mechanism in aluminum honeycombs. Results are presented which illustrate the more typical scale related mechanical phenomena in the materials considered. The presentation is then concluded with a detailed discussion of these results and suggestions for future research.