Deformation micromechanisms of collagen fibrils under uniaxial tension

Abstract

Collagen, an essential building block of connective tissues, possesses useful mechanical properties due to its hierarchical structure. However, little is known about the mechanical properties of collagen fibril, an intermediate structure between the collagen molecule and connective tissue. Here, we report the results of systematic molecular dynamics simulations to probe the mechanical response of initially unflawed finite size collagen fibrils subjected to uniaxial tension. The observed deformation mechanisms, associated with rupture and sliding of tropocollagen molecules, are strongly influenced by fibril length, width and cross-linking density. Fibrils containing more than approximately 10 molecules along their length and across their width behave as representative volume elements and exhibit brittle fracture. Shorter fibrils experience a more graceful ductile-like failure. An analytical model is constructed and the results of the molecular modelling are used to find curve-fitted expressions for yield stress, yield strain and fracture strain as functions of fibril structural parameters. Our results for the first time elucidate the size dependence of mechanical failure properties of collagen fibrils. The associated molecular deformation mechanisms allow the full power of traditional material and structural engineering theory to be applied to our understanding of the normal and pathological mechanical behaviours of collagenous tissues under load.

Anisotropic microsphere-based approach to damage in soft fibered tissue

“…The discretization and associated peaks may be considered as lacking accuracy. However, in a recent work, Tang et al (2010) presented some results realting to the deformation of collagen fibrils under uniaxial tension where, as the fibril stretched, it started to fail showing a behavior very similar to that presented in this section, demonstrating that a finite number of fibrils in each fiber bundle could lead to a more realistic behavior of fibers than that achieved by an ideally perfect integration scheme for an affine scenario.…”

“…In this context, some authors have proposed continuum damage models for only one component of the material (fibers or matrix), applied to transversally anisotropic soft tissues following the approach of Simo (1987) (Natali et al, 2005;Balzani et al, 2006;Calvo et al, 2007;Ehret and Itskov, 2009;Peña and Doblaré, 2009), or that of Göktepe and Miehe (2005) and Dal and Kaliske (2009) in connection the microsphere framework for failure of rubber-like materials. Other models for the failure of fibrils (see e.g Buehler (2008); Tang et al (2010)) use molecular simulations to provides a more detailed insight into the failure process of collagen fibrils, which is basically due to the rupture of the cross-links between the tropocollagen molecules that compose the fibril. In the framework of cytoskeletal and polymers networks, Head et al (2003) presented a different regime of elastic response (affine and non affine) depending of the quality and density of the filament links, leading to an affine response under an unlinked scenario.…”

A study of the mechanical behaviour of the human aortic artery by means of non-linear finite element models

“…A reactive mesoscopic model was presented in [18], where tropocollagen molecules are described as a collection of particles interacting according to multibody potentials (see also [23]). Based on these molecular simulations, a multiscale, plasticity based, constitutive model was presented in [24]. Another plasticity based model has been presented in [25], where viscoplastic sliding of collagen fibrils is associated with the irreversible degradation of the proteoglycan bridges between them.…”

“…The two dimensional Hodge-Petruska model Following [18] and [24], a two dimensional Hodge-Petruska arrangement [84] has been considered to reproduce the staggered structure of the tropocollagen molecules inside a fibril. In this model, see Fig.…”

“…3.11a we compare our results with those presented in [18], where molecular dynamics (MD) simulations were made using a short chain of collagen molecules. Further MD simulations were performed in [24] increasing the size of the fibril until it behaved as a representative volume element. Results presented in [24] show a subtle increase in the yield strength (see Fig.…”