A hybrid modeling combining the proper generalized decomposition approach to data-driven model learners, with application to nonlinear biphasic materials

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Abstract
Modeling soft biphasic permeable materials is a challenging issue tackled nowadays by countless researchers. The effective modeling of such materials is a corner stone in the understanding of soft biological materials and the manufacturing of effective replacements such as contact lenses, human cartilage replacements, and so on. In previous work, we modeled biphasic material mechanical behavior as a combination of an elastic solid and a pressurized fluid in a porous medium using Darcy’s equation. The modeling was simulated using the model reduction technique named proper generalized decomposition (PGD), which offers a tremendous reduction in the calculation time with respect to the classical simulation techniques, which had lead to the identification of soft materials properties. In the current work, we tackle the potential error generated by the use of linear elastic terms in the equilibrium equation. This error is modeled using both a new nonlinear term and a physically informed machine learning algorithm coupled to the PGD results. Later on, the contribution of the fluid reaction and solid reaction to the indentation force as well as the hyper parameters of the employed neural network are identified for an experimental indentation of a thick hydrogel.

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