Non-linear Interacting Model of Fibre-Reinforced Materials with Application to the Passive Cardiac Muscle.

摘要

Non-linear models of composite materials are typically based on the principle of linear superposition, which descends directly from mixture theory. One exception in this regard is the composite based model proposed by Guo et al. (2007), where fibres and matrix were modelled separately as Neo-Hookean materials. By means of a suitable decomposition of the deformation gradient, an effective shear parameter was related to the shear deformation. In this thesis, we extended Guo's model, and proposed a model with an isotropic potential for the matrix and a general transversely isotropic potential for the fibres. The cardiac muscle can be considered as a biological composite material (consisting of myofibres and extracellular matrix) that is naturally subjected to large deformations; therefore, we chose this material as an example of application of the proposed model. We found a good agreement between the predictions of the proposed model and the available experimental data.