Viscoelastic fracture of biological composites

Abstract

Soft constituent materials endow biological composites, such as bone, dentin and nacre, with viscoelastic properties that may play an important role in their remarkable fracture resistance. In this paper we calculate the scaling properties of the quasi-static energy release rate and the viscoelastic contribution to the fracture energy of various biological composites, using both perturbative and non-perturbative approaches. We consider coarse-grained descriptions of three types of anisotropic structures: (i) Liquid-crystal-like composites (ii) Stratified composites (iii) Staggered composites, for different crack orientations. In addition, we briefly discuss the implications of anisotropy for fracture criteria. Our analysis highlights the dominant lengthscales and scaling properties of viscoelastic fracture of biological composites. It may be useful for evaluating crack velocity toughening effects and structure-dissipation relations in these materials.

Mode I fracture of a biopolymer gel: Rate-dependent dissipation and large deformations disentangled

“…Following [7], we estimate the bulk dissipation for a stationnary crack (for 180 which time derivatives can be replaced by space derivatives, i.e. V ∂t = ∂r)…”

“…In [7], η is an effective material viscosity. d c is the microscopic length scale where the linear theory 185 fails, which is actually the lengthscale d measured in our experiment.…”

“…Second, the fracture mechanics of these materials is made particularly complex by the interplay of large deformations [3] and viscoelastic processes [4]. 10 Fracture of soft materials has been widely studied both theoretically [5,6,7] and experimentally [8,1,9,10,11]. Large efforts were made to measure the rate dependency of the energy release rate [1,10,11] and to model it using either viscoelastic models [6,5] or microscopic damage models [4].…”

Velocity jump in the crack propagation induced on a semi-crystalline polymer sheet by constant-speed stretching

“…Tough polymers could even replace glass and metal used in automobiles to reduce their weight, which should greatly contribute to the reduction of energy consumption. For developing tough polymers, one of the relevant issues is the velocity-dependent properties of fracture and, in fact, this issue has been explored for various forms of polymers, which include adhesive [1][2][3][4][5], laminar [6] and viscoelastic polymers [7,8], weakly cross-linked gels [9,10], biopolymer gels [11], and biological composites [12].…”

Visco- and plastoelastic fracture of nanoporous polymer sheets

“…Accordingly, active studies have been performed on mechanical and fracture mechanical properties, focusing on an important parameter for cellular solids, the volume fraction of the matrix material φ [1]. However, studies on velocity dependent properties of their fracture are relatively limited, compared with intensive studies that have been performed on other materials such as adhesive [6][7][8][9][10], laminar [11], viscoelastic [12,13], weakly cross-linked [14,15], biopolymer gel [16], and biological composite [17] materials, including recent active experimental [18][19][20], numerical [21,22], and theoretical [23,24] studies on the velocity jump in crack propagation in elastomers.…”