Anelastic reorganisation of fibre-reinforced biological tissues

• Published in: Computing and visualization in science Vol. 20; no. 3-6; pp. 95 - 109
• Main Authors: Di Stefano, Salvatore, Carfagna, Melania, Knodel, Markus M., Hashlamoun, Kotaybah, Federico, Salvatore, Grillo, Alfio
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2019; Springer Nature B.V
• Subjects: Algorithms; Anelasticity; Anisotropy; Calculus of Variations and Optimal Control; Optimization; Computational Mathematics and Numerical Analysis; Computer Applications in Chemistry; Deformation; Distortion; Evolution; Fiber reinforced materials; Mathematics; Mathematics and Statistics; Microcracks; Numerical Analysis; Reinforcing fibers; Soft tissues; Special Issue CS Symposium 2016; Visualization; Anelastic distortions; Fibre-reinforcement; Anisotropic media; Biological tissues
• DOI: 10.1007/s00791-019-00313-1
• ISSN: 1432-9360

In this work, we contribute to the study of the structural reorganisation of biological tissues in response to mechanical stimuli. We specialise our investigation to a class of hydrated soft tissues, whose internal structure features reinforcing fibres. These are oriented statistically within the tissue, and their pattern of orientation is such that, at each material point, the tissue is anisotropic. From its natural, stress-free state, the tissue can be distorted anelastically into a global reference configuration, and then deformed under the action of external mechanical loads. The anelastic distortions are responsible for changing irreversibly the internal structure of the tissue, which, in the present context, occurs through both the rearrangement of the bonds among the tissue cells and the deformation-driven reorientation of the fibres. The anelastic strains, in addition, are assumed to model the onset and evolution of microcracks in the tissue, which may be triggered by the mechanical loads applied to the tissue in the case of traumatic events, or diseases. For our purposes, we formulate an anisotropic model of remodelling and we consider a fully isotropic model of structural reorganisation for comparison, with the aim to study if, how, and to what extent the evolution of anelastic distortions is influenced by the tissue’s anisotropy.