In this project, the use of computational stochastic analysis is put forward in order to construct a new modeling and computational framework for nonlinear stochastic constitutive laws. Modeling the uncertainties in the constitutive behavior of nonlinear materials is a central challenge in computational mechanics and mechanics of materials. In particular, the large variability exhibited by soft biological tissues, such as vascular vessels, is a current roadblock to computational assisted surgeries, patient-specific treatments for cardiovascular diseases and wide adoption of tissue engineering approaches. In this project, the use of computational stochastic analysis is put forward in order to construct a new modeling and computational framework for nonlinear stochastic constitutive laws. The specific case of vascular constructs is purposely chosen as a prototypical application combining strong anisotropy and a high level of stochasticity. The research supported by this award will enhance the predictive capabilities of simulations involving biological materials, such as arterial and brain tissues, and will be relevant to a large class of materials, including the case of damaged composites. The interdisciplinary standpoint promoted in this effort will enable a broad exposure to students involved in various fields, such as applied mathematics and materials science, and will allow theoretical and computational aspects to be introduced through outreach activities in local high schools.
This research is focused on computational stochastic analysis for nonlinear constitutive laws. More specifically, it aims at deriving probabilistic models, a high-performance-computing environment for sampling on smooth manifolds and methodologies for the identification and validation of spatially dependent anisotropic strain energy functions. By addressing the proper mathematical randomization of nonlinear constitutive equations in close relation with calibration and validation concerns, the research supported by this award will notably advance a new information-theoretic class of stochastic methods where randomness can be accounted for from potentially multiscale experiments to coarse-scale simulations. The project will involve a set of methodological and theoretical developments, including (1) the construction of physics-based random field models and sampling algorithms for a class of polyconvex stored energy functions, and (2) the definition of methodologies for the data-poor inverse calibration and multiscale validation of the stochastic models. The novel framework will notably be used within large-scale nonlinear simulations to investigate the probability of failure of stochastic vascular constructs with patient-specific geometries.
