CEE Seminar: Likely Instabilities in Stochastic Elastic Solids

The study of material elastic properties has traditionally used deterministic approaches, based on ensemble averages, to quantify constitutive parameters. In practice, these parameters can meaningfully take on different values corresponding to possible outcomes of the experiments. From the modelling point of view, stochastic representations accounting for data dispersion are needed to improve assessment and predictions. In this talk, I will discuss stochastic-elastic material models described by a strain-energy density where the parameters are characterized by probability distributions at a continuum level. To answer important questions, such as "what is the influence of the probabilistic parameters on the predicted elastic responses?" and "what are the possible equilibrium states and how does their stability depend on the material constitutive law?", I will consider the classic problem of the Rivlin cube, the cavitation and finite amplitude oscillations of hyperelastic spheres, and the soft elasticity of liquid crystal elastomers. These problems, for which the solution is tractable analytically, can offer significant insight into how stochastic-elastic models can be integrated into the nonlinear field theory. Similar approaches can be developed for other mechanical systems.