Modelling the Mechanical Behavior of Collagenous Materials by Considering Multiscale Effects

Abstract

Abstract Collagen is an important component of many biological tissues and plays a key role in the physiological functions of the tissue. The mechanical properties of biological tissues are important for many medical and pharmaceutical applications. For instance, to probe the interaction between a medical device and a tissue it becomes important to study the stress and deformation within the tissue under external load. Modelling the mechanics of collagenous tissues is non-trivial because of the anisotropic and hyperelastic nature of the tissue. The arrangement of the collagen within the tissue governs the directional dependence of its mechanical properties. Further, collagen mechanics is itself a strong function of the arrangement of various collagenous components (tropocollagen molecules, fibrils, fibers) at various length scales. Therefore to accurately model the mechanics of a collagenous tissue at macroscopic length scale it is necessary to consider the multiscale mechanics of collagen. In this work, we develop a multiscale-informed finite element method (multi-FEM) framework to model the mechanics of a collagenous tissue. We propose a novel exponential strain energy density function for the mechanics of collagen fibers, which shows excellent agreement with the strain energy density of a collagen fiber obtained by considering multiscale effects (molecule to fiber). Further, this exponential strain energy density is used to simulate the macroscopic mechanics of the tissue using finite element method. Using this multi-FEM framework, we systematically investigate the influence of various lower-length scale collagen properties on the macroscopic stress response of the collagenous tissue. This framework can be very useful in the development of high-fidelity computational models of collagenous tissues that can include the huge variability in the tissue properties.