Abstract
Motivated by problems arising in biophysics in which elastic structures and materials interact with a solvent fluid, we introduce approaches for modeling such systems. At the length scales characterized by soft materials, thermal fluctuations of the fluid environment play a significant physical role. Thus, we present a continuum description of the mechanics that takes into account the fluid-structure hydrodynamic coupling and use results from the theory of stochastic analysis to incorporate random
fields that appropriately capture the effects of thermal fluctuations. We then discuss a numerical discretization of the resulting system of partial differential equations based on spectral and finite difference methods, demonstrating that it yields results consistent with principles from statistical mechanics. We plan to use similar methodology in future work to study the rheology of fluids and soft materials.
