Multi-scale modelling of rubber-like materials and soft tissues: an appraisal

Abstract

We survey, in a partial way, multi-scale approaches for the modelling of rubber-like and soft tissues and compare them with classical macroscopic phenomenological models. Our aim is to show how it is possible to obtain practical mathematical models for the mechanical behaviour of these materials incorporating mesoscopic (network scale) information. Multi-scale approaches are crucial for the theoretical comprehension and prediction of the complex mechanical response of these materials. Moreover, such models are fundamental in the perspective of the design, through manipulation at the micro-and nano-scales, of new polymeric and bioinspired materials with exceptional macroscopic properties.

Computationally Informed Design of a Multi-Axial Actuated Microfluidic Chip Device

“…The obtained material characterization and model fitting is in perfect agreement with similar studies in the literature 57 – 60 that analogously recognized the 2-parameter hyperelastic Ogden model as the most appropriate and computationally handy model for generalized theories of rubber-like materials.…”

Continuum Constitutive Modeling for Isotropic Hyperelastic Materials

“…The established models have been thoroughly reviewed and evaluated by Boyce and Arruda (2000) [1], Steinmann, Hossain, and Possart (2012) [2], and Hossain and Steinmann (2013) [3]. Current multiscale approaches for modeling rubber-like materials and soft tissues have been briefly reviewed and compared with classical macroscopic phenomenological models by Puglisi and Saccomandi (2016) [4].…”

Rivlin's legacy in continuum mechanics and applied mathematics

“…The solutions of the canonical boundary value problems obtained by Rivlin form the basis of many of the developments of the theory (e.g. [3]). Today, many branches of physics and engineering science use the theory of nonlinear elasticity initiated by Rivlin.…”