Modelling and simulation of fibrous biological tissues via discrete homogenization methods

International audienceThanks to their geometrical organization at the cell level, soft biological tissues can be modelled from the mechanical point of view as multidimensional networks of elastic bars. The length of the bars is supposed to be small with respect to the size of the macroscopic medium. We introduce a detailed description of the overall structure accounting both for the tensions due to the bars and for the moments between pairs of bars. Using quasi-periodicity hypotheses, we apply a discrete homogenization technique, [1]. We derive a continuous homogenized mechanical law in the large transformation setting. We describe the basic principles of this approach that was first introduced in the cardiac modelling context in [2]. In a last step we present its implementation in a finite element framework. We comment some aspects of our numerical results. [1] D. Caillerie, A. Mourad, and A. Raoult, Journal of Elasticity 84(1), 33-68 (2006). Links [2] A. Mourad, Description topologique de l'architecture fibreuse et modélisation mécanique du myocarde, PhD thesis, Institut National Polytechnique, Grenoble, 2003