Multiscale Elastic Models of Collagen Bio-structures: From Cross-Linked Molecules to Soft Tissues

Abstract

Mechanics of collagen bio-structures at different scales (nano, micro, and macro) is addressed, aiming to describe multiscale mechanisms affecting the constitutive response of soft collagen-rich tissues. Single-scale elastic models of collagen molecules, fibrils, and crimped fibers are presented and integrated by means of consistent inter-scale relationships and homogenization arguments. In this way, a unique modeling framework based on a structural multiscale approach is obtained, which allows to analyze the macroscale mechanical behavior of soft collagenous tissues. It accounts for the dominant mechanisms at lower scales without introducing phenomenological descriptions. Comparisons between numerical results obtained via present model and the available experimental data in the case of tendons and aortic walls prove present multiscale approach to be effective in capturing the deep link between histology and mechanics, opening to the possibility of developing patient-specific diagnostic and clinical tools.