This work lies within an overall effort to improve, as well as quantify, the uncertainty of traumatic brain injury (TBI) prediction for blast loading. Detailed finite element (FE) modeling of the human head currently provides the only viable means to quantify the mechanical response within the brain during a blast loading event. Unfortunately, the exact linkages between loading patterns, tissue mechanical response, and injury/physiological effects are still quite unknown; however, the exceedance of specified threshold values based on direct and derived measures of stress, strain, pressure, and acceleration within the brain have been shown to be useful injury criteria. The utility of these threshold values is somewhat mitigated by the fact that preliminary parametric studies focusing on varying head morphology and the material properties of FE head model components have shown significant variation in the predicted injury response, indicating that the exact relationship between model geometry, material properties, and mechanics-based injury response metrics has not yet been established.

Identifying an appropriate constitutive model form and optimal parameter values for biological tissues is an enormous challenge hindered by large epistemic uncertainties. Available experimental data sets frequently offer valuable but limited information due to the many vagaries associated with the testing of biomaterials, such as testing on different species, e.g., porcine and bovine specimens, testing with inapplicable strain rates, and having too little data. The parameters of hyperelastic, hyper-viscoelastic, and viscoelastic constitutive models, which are commonly utilized for modeling these biological tissues, can be fit to an aggregation of experimental data through a constrained optimization formulation. Specifically, this study considers fitting data from biomaterials to Ogden’s model of hyperelasticity. The goodness of fit of the optimization is limited by the appropriateness of the model forms as well as limited, and at times contradictory, data. In order to properly account for these uncertainties, a Bayesian approach is adopted for model calibration and posterior distributions are therefore produced for each model parameter.

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