Inelastic mechanics: A unifying principle in biomechanics

Abstract

Many soft materials are classified as viscoelastic. They behave mechanically neither quite fluid-like nor quite solid-like - rather a bit of both. Biomaterials are often said to fall into this class. Here, we argue that this misses a crucial aspect, and that biomechanics is essentially damage mechanics, at heart. When deforming an animal cell or tissue, one can hardly avoid inducing the unfolding of protein domains, the unbinding of cytoskeletal crosslinkers, the breaking of weak sacrificial bonds, and the disruption of transient adhesions. We classify these activated structural changes as inelastic. They are often to a large degree reversible and are therefore not plastic in the proper sense, but they dissipate substantial amounts of elastic energy by structural damping. We review recent experiments involving biological materials on all scales, from single biopolymers over cells to model tissues, to illustrate the unifying power of this paradigm. A deliberately minimalistic yet phenomenologically very rich mathematical modeling framework for inelastic biomechanics is proposed. It transcends the conventional viscoelastic paradigm and suggests itself as a promising candidate for a unified description and interpretation of a wide range of experimental data. This article is part of a Special Issue entitled: Mechanobiology.

Foam rheology at large deformation

“…Since then, different soft and hard materials displayed significant softening and a striking capacity to print the history of the applied stress within their internal structure [4]. Moreover, it was recently suggested that Mullins-like softening, in materials ranging from single biopolymers over cells to model tissues, is a consequence of the presence of diverse mechanisms of energy dissipation, such as protein unfolding or sacrificial bonds [7]. While less frequent in soft materials, hardening has been recently observed in long-chain branched polymer solutions under shear [8], in granular matter [9], in foams [10], and in reconstituted networks of crosslinked, bundled, actin filaments [3] under periodic shear.…”

“…However, the common features of the remodeling processes occurring in structural networks of different nature and scale are still elusive, although valuable insight is available for polymers and biopolymers [7,11,12]. Foam has served as a model system for the study of plasticity of soft amorphous materials [13] and of its consequences such as stress relaxation [14], shear banding [15][16][17], and jamming [18].…”

Programming the mechanics of cohesive fiber networks by compression

“…The mechanisms of mechanical reinforcement are generally thought to originate from cellular activity, involving strain-dependent fiber degradation and synthesis 10,11 . However, recent studies suggest that biopolymer networks are inherently adaptive themselves, since they are held together by weak transient bonds 12,13 . Cyclic shear loading has been shown to cause reinforcement for a number of biopolymer systems [14][15][16][17] , al-though softening can occur as well 18,19 .…”

The Inelastic Hierarchy: Multiscale Biomechanics of Weak Bonds

“…Even for some less enigmatic cytoskeletal protein fibers, such as F-actin, and microtubules' structural plasticity (6) and friction-like interactions (7) have recently been shown to govern the mechanical interactions down to the molecular scale. On the other side of the hierarchy, quite remarkable similarities have been demonstrated for the inelastic mechanics of transiently crosslinked cytoskeletal networks and living cells and cell aggregates (8)(9)(10).…”

“…It is also common to all of these designs that they can adapt their stiffness to the prevailing stresses by viscoelastic stiffening and reversibly yield to imposed strains via inelastic fluidization, viz. the breaking of transient bonds (10). This dual strategy allows them to be elastically sturdy and malleable and adaptive, at the same time.…”