Preprint 2023-23
Stéphane P. A. Bordas, Marek Bucki, Huu Phuoc Bui, Franz Chouly, Michel Duprez, Arnaud Lejeune, Pierre-yves Rohan:
Automatic mesh refinement for soft tissue
Abstract:
Errors in biomechanical simulations arise from modelling and discretization. Discretization errors can be quantified with a posteriori error estimates. The relevance of such error estimates for practical biomechanics problems is rarely adressed. In this contribution, we propose an implementation of a posteriori error estimates targeting a user-defined quantity of interest, with the Dual Weighted Residual (DWR) technique tailored to biomechanics. We consider a general setting that encompasses three-dimensional geometries as well as model non-linearities, appearing in hyperelastic soft tissues. We take advantage of the capabilities of automatic differentiation embedded into modern finite element software, that allows to compute the error estimates generically for a large class of models and constitutive laws. First we validate our methodology using experimental measurements from silicone samples, and then illustrate its applicability for patient-specific computations of pressure ulcers on a human heel.
