Seminar Schedule – Fall 2015

Monday, December 21, 2015
Time: 3-4 PM
Place: WRW 102

Multiscale Modeling of Soft Materials: From Network to Maximal Path Advances and Microspheres

Patrick Le Tallec – Ecole Polytechnique, France

Large deformation models of structures made of soft materials such as polymers or biological tissues usually introduce macroscopic internal variables, a split of the deformation gradient or of the strain rate, and obtain the evolution laws governing the additional internal variables by postulating a specific form of dissipation within the material. This phenomenological approach is widely used, with different levels of complexity to take into account electrochemical excitations, clusterisation, ageing, crystallization and so on. It is faced with two severe challenges: a high level of arbitration in the derivation of the model, and the difficulty of handling evolutive anisotropy which occurs in damage or in phase transitions.

To overcome such limitations in polymer modelling, one tries to relate the energy densities at the continuum level with the physically motivated free energy of polymer chains. The difficulty is to pass from one chain to a network of cross-linked chains, and to relate the evolution of this network to the macroscopic deformation. The use of a microscopic network problem imposing the macroscopic deformation through a far field microscopic boundary condition is a mathematically rigorous and attractive approach, but it is practically out of reach because of its complexity and because of modeling issues (carbon fillers, strain induced crystallization, damage,…).

A simpler strategy is to reduce the microstructure to a distribution of one dimensional stress strain relations over the orientation space. Such microsphere approaches have been used successfully in the past to describe complex phenomena such as Mullins effect or strain induced crystallization. This leads to evolutive anisotropic models which respect the experimental data available at microscopic level, but up to now the different local orientations were related to the 3D deformation through a simplified affine network deformation assumption. The talk will review these approaches and explain how to go beyond the affine assumption by introducing a proper free energy to be minimized locally, the macroscopic deformation being introduced as a maximal path constraint.

For further information, please contact Dr. Stelios Kyriakides at skk@utexas.edu or (512) 471-4167.