Energy dissipation in mammalian collagen fibrils: Cyclic strain-induced damping, toughening, and strengthening

Abstract

As the fundamental structural protein in mammals, collagen transmits cyclic forces that are necessary for the mechanical function of tissues, such as bone and tendon. Although the tissue-level mechanical behavior of collagenous tissues is well understood, the response of collagen at the nanometer length scales to cyclical loading remains elusive. To address this major gap, we cyclically stretched individual reconstituted collagen fibrils, with average diameter of 145 ± 42 nm, to small and large strains in the partially hydrated conditions of 60% relative humidity. It is shown that cyclical loading results in large steady-state hysteresis that is reached immediately after the first loading cycle, followed thereafter by limited accumulation of inelastic strain and constant initial elastic modulus. Cyclic loading above 20% strain resulted in 70% increase in tensile strength, from 638 ± 98 MPa to 1091 ± 110 MPa, and 70% increase in toughness, while maintaining the ultimate tensile strain of collagen fibrils not subjected to cyclic loading. Throughout cyclic stretching, the fibrils maintained a steady-state hysteresis, yielding loss coefficients that are 5–10 times larger than those of known homogeneous materials in their modulus range, thus establishing damping of nanoscale collagen fibrils as a major component of damping in tissues.

Statement of Significance

It is shown that steady-state energy dissipation occurs in individual collagen fibrils that are the building blocks of hard and soft tissues. To date, it has been assumed that energy dissipation in tissues takes place mainly at the higher length scales of the tissue hierarchy due to interactions between collagen fibrils and fibers, and in limited extent inside collagen fibrils. It is shown that individual collagen fibrils need only a single loading cycle to assume a highly dissipative, steady-state, cyclic mechanical response. Mechanical cycling at large strains leads to 70% increase in mechanical strength and values exceeding those of engineering steels. The same cyclic loading conditions also lead to 70% increase in toughness and loss properties that are 5–10 times higher than those of engineering materials with comparable stiffness.

Introduction

Collagen serves as the hierarchical building block of structural mammalian tissues [1]. This hierarchy begins with tropocollagen molecules (1.5 nm in diameter) that assemble into collagen fibrils (10 s to 100 s of nm in diameter) having a D-band structure with 67 nm repeated spacing [2], [3], [4]. The hierarchy continues across the length scales to fascicles (bundles of fibrils with micrometer diameter) and tissues (millimeters in diameter) [5], [6], [7]. Although the bulk mechanical properties of such tissues are well described, the hierarchical underpinnings continue to be the focus of research, especially at the nanoscale [8], [9], [12]. Although molecular dynamics predictions and experimental measurements of the low strain elastic behavior of hydrated collagen fibrils [14], [15] are well established, their low and high strain response to cyclic loading remains unknown. Measurement of the dynamic response of collagen fibrils under cyclical forces, which is the focus of the current study, is important because tissues in our body experience mechanical cycling due, for instance, to cardiovascular outputs and routine movement.

The levels of strain transferred across the different hierarchies to the collagen fibrils are not definitively known, but are typically understood to span a broad distribution within a single tissue [16], [17]. Mature collagen fibrils subjected to tension in fully hydrated environment have been shown to exhibit one, or more, of the following regimes of deformation: (a) An initial, nonlinear, toe regime followed by a nonlinear “heel” regime in which micrometer and nanometer level crimps straighten [7], [13], [15], [18]; (b) an initial loading regime (often referred to as a “linear” regime) in which tropocollagen molecule uncoiling, assisted by a reduction in hydrogen bonds, takes place [19]; (c) an extended reduced stiffness regime in which molecular sliding occurs [10], [13], [20]; (d) a hardening regime in which stretching of the backbones of tropocollagen molecules, promoted by molecular cross-links, stiffens the fibril [21], [22]; and finally, (e) a softening regime in which failure occurs. Having two or more cross-links per tropocollagen molecule substantially increases hardening [21] which becomes pronounced in the presence of mature, trivalent, cross-links. This hardening behavior leads to increased modulus in the aforementioned hardening regime, which is higher than the modulus of the initial loading regime (E₁) described above [10], [22]. However, observations have varied significantly, with studies reporting rubber-like [10], linear/multi-linear [23], parabolic [24], or toe/heel/linear stress–strain curves [7], [20], which do not include all five of the aforementioned regimes of the deformation response, depending on the type and density of cross-linking [10], [18], [21], [22], [25], and partially [26], [27] or fully hydrated [10], [18], [28] conditions.

The key property that was investigated in this study is the ability of nanoscale collagen fibrils to absorb and dissipate energy in steady-state mode during cyclic loading, as quantified from mechanical loading–unloading hysteresis curves. Because energy dissipation is critical to the functions of collagenous tissues and their insertions [29], there is a pressing need to understand the hierarchical origins and extent of the hysteretic behavior of collagenous tissues, especially in the context of engineering tissues and prosthetics. At the bulk level, hysteresis can arise in collagenous tissues due to fibril sliding [11], but the contribution of the dissipative material behavior of nanoscale fibrils has not yet been quantified. An important first step in this direction has been atomic force microscope (AFM) assisted testing of hydrated bovine collagen, which showed a stress–strain behavior that is characterized by hysteresis and plastic deformation for strains exceeding 6% [18]. These results suggested the possibility of nanoscale energy absorption in collagenous tissues, and, by comparison to the non-hysteretic behavior of dry collagen tested at the same strain levels [30], indicated that hydration affects the interactions between tropocollagen molecules, possibly by modulating hydrogen bonding [31]. To address this hypothesis, we undertook the first systematic cyclical loading study of reconstituted mammalian collagen fibrils in the absence of unbound water surrounding a collagen fibril in order to quantify the amount of energy dissipation per cycle and the associated changes in key mechanical properties, such as stiffness, strength and toughness. This study was conducted with partially hydrated collagen fibrils at 60% relative humidity (RH). The absence of external water molecules focuses this study in intrafibrillar processes that affect energy dissipation inside individual collagen fibrils, rather than the exchange of water molecules between a collagen fibril and a buffer. The dissipated energy during mechanical cycling is normalized by an elastic term to yield the loss coefficient, a metric that enables a comparison amongst different materials [32], especially in the same modulus range as the collagen fibrils.

Furthermore, we quantified for the first time the effect of unloading on the recovery of the inelastic strain accrued during cyclic loading in different regimes of deformation, and the return to the mechanical behavior prior to mechanical cycling. The new insights presented in this work were made possible because of experiments at the low and the high strain regimes of the deformation of nanoscale collagen fibrils, which are controlled by some of the molecular mechanisms described above.