A multi-scale approach to model arterial tissue

Felipe Figueredo Rocha¹; Pablo Javier Blanco²; Raúl Feijóo¹; Pablo Javier Sánchez³; Alfredo Edmundo Huespe⁴

¹ National Laboratory for Scientific Computing - LNCC and INCT-MACC; ² National Laboratory for Scientific Computing - LNCC and INCT-MACC; ³ CIMEC-UNL-CONICET and GIMNI-UTN-FRSF; ⁴ CIMEC-UNL-CONICET

doi:10.20906/CPS/CILAMCE2015-0241

Resumo

To gain insight on the onset and progress of some cardiovascular diseases, as well as to propose adequate treatments, a detailed characterization of the mechanical behaviour of the arterial wall is required. The classical constitutive modelling approach based purely on phenomenological laws fails in representing the micromechanical phenomena, which dominates important aspects such as rupture and remodelling of these tissues. In turn, the multi-scale constitutive modelling raises as a more rational alternative allowing to consider the microscopic details and interactions of the basic unit blocks of the biological tissues, such as the existence of the collagen fibres, pores, etc. In this paper, we review a constitutive multi-scale theory based on the existence of Representative Volume Element (RVE) in the finite strain regime, which is presented in a variational formulation framework. The homogenisation of the displacement and deformation gradient as well the virtual power equivalence between macro- and micro-scales through an extended version of the Hill-Mandel principle, are assumed as fundamental hypotheses of the model. As a result, we obtain the homogenisation of the macro-scale stress and the RVE equilibrium problem. The constitutive tangent operator is used to analyse the loss of stability of the macroscopic material response. This allows us to model macroscopic crack nucleation induced, for instance, by strain localization phenomena due to microscopic shear bands, damage or any other possible microscopic failure mechanism. In this context, preliminary results are discussed on the light of the present theoretical framework

Palavras-chave: Multiscale Modelling; Representative Volume Element; Finite Strain; Variational Formulations ; Failure