Computational modelling of the mechanical behaviour of protein-based hydrogels

Protein-based hydrogels have been extensively studied in the field of biomaterials given their ability to mimic living tissues and their special resemblance to the extracellular matrix. Despite this, the methods used for the control of mechanical properties of hydrogels are very limited, focusing mainly on their elasticity, with an often unrealistic characterization of mechanical properties such as extensibility, stiffness and viscoelasticity. Being able to control these properties is essential for the development of new biomaterials, since it has been demonstrated that mechanical properties affect cell behaviour and biological processes. To better understand the mechanical behaviour of these biopolymers, a computational model is here developed to characterize the mechanical behaviour of two different protein-based hydrogels. Strain-stress tests and stress-relaxation tests are evaluated computationally and compared to the results obtained experimentally in a previous work. To achieve this goal the Finite Element Method is used, combining hyperelastic and viscoelastic models. Different hyperelastic constitutive models (Mooney-Rivlin, Neo-Hookean, first and third order Ogden, and Yeoh) are proposed to estimate the mechanical properties of the protein-based hydrogels by least-square fitting of the in-vitro uniaxial test results. Among these models, the first order Ogden model with a viscoelastic model defined in Prony parameters better reproduces the strain-stress response and the change of stiffness with strain observed in the in-vitro tests.