PI proposes to develop finite-strain constitutive models for semi-crystalline polymers, such as polyethylene and polypropylene. These are multi-phase material systems consisting of a "soft" phase that provides elasticity to the system in intimate contact with a "hard" phase that is responsible for plastic deformation at large strains. They exhibit structure on two different length scales, ranging from the nanometer scale, at which the constituent polymer chains order themselves into "lamellar" structures, to the micrometer scale, where either randomly oriented "lamellar grains," or "spherulitic grains" are observed. Because these polymers are among the most commonly used in many applications, including in the packaging, fluid distribution, automotive and toy industries, there is great interest in manipulating their structure to optimize their mechanical response. Improvements in their mechanical properties are expected to have a positive impact on the environment. The methodology to be developed will make use of variational "linear comparison" homogenization techniques, and will account for: (i) the strongly nonlinear response of the constituent phases, (ii) the dual microstructure at the "grain" and "polycrystal" levels, (iii) coupled elasto-viscoplastic constitutive behavior, and (iv) finite deformations. The work will involve close collaborations with the experimental group of Jean-Yves Cavaille at the INSA de Lyon (France). Efforts will be made to recruit a top-level minority graduate student, who will benefit from the PI's on-going international collaborations. The PI is writing a book that aims to make recent progress in nonlinear homogenization---including the present work on polymeric systems---available to a larger audience.
