Nonlinear time-dependent mechanical behavior of mammalian collagen fibrils.

The viscoelastic mechanical behavior of collagenous tissues has been studied extensively at the macroscale, yet a thorough quantitative understanding of the time-dependent mechanics of the basic building blocks of tissues, the collagen fibrils, is still missing. In order to address this knowledge gap, stress relaxation and creep tests at various stress (5-35 MPa) and strain (5-20%) levels were performed with individual collagen fibrils (average diameter of fully hydrated fibrils: 253 ± 21 nm) in phosphate buffered saline (PBS). The experimental results showed that the time-dependent mechanical behavior of fully hydrated individual collagen fibrils reconstituted from Type I calf skin collagen, is described by strain-dependent stress relaxation and stress-dependent creep functions in both the heel-toe and the linear regimes of deformation in monotonic stress-strain curves. The adaptive quasilinear viscoelastic (QLV) model, originally developed to capture the nonlinear viscoelastic response of collagenous tissues, provided a very good description of the nonlinear stress relaxation and creep behavior of the collagen fibrils. On the other hand, the nonlinear superposition (NSP) model fitted well the creep but not the stress relaxation data. The time constants and rates extracted from the adaptive QLV and the NSP models, respectively, pointed to a faster rate for stress relaxation than creep. This nonlinear viscoelastic behavior of individual collagen fibrils agrees with prior studies of macroscale collagenous tissues, thus demonstrating consistent time-dependent behavior across length scales and tissue hierarchies. STATEMENT OF SIGNIFICANCE: Pure stress relaxation and creep experiments were conducted for the first time with fully hydrated individual collagen fibrils. It is shown that collagen nanofibrils have a nonlinear time-dependent behavior which agrees with prior studies on macroscale collagenous tissues, thus demonstrating consistent time-dependent behavior across length scales and tissue hierarchies. This new insight into the non-linear viscoelastic behavior of the building blocks of mammalian collagenous tissues may serve as the foundation for improved macroscale tissue models that capture the mechanical behavior across length scales.

Strain rate induced toughening of individual collagen fibrils.

The nonlinear mechanical behavior of individual nanoscale collagen fibrils is governed by molecular stretching and sliding that result in a viscous response, which is still not fully understood. Toward this goal, the in vitro mechanical behavior of individual reconstituted mammalian collagen fibrils was quantified in a broad range of strain-rates, spanning roughly six orders of magnitude, from 10-4 to 35 s-1. It is shown that the nonlinear mechanical response is strain rate sensitive with the tangent modulus in the linear deformation regime increasing monotonically from 214 ± 8 to 358 ± 11 MPa. More pronounced is the effect of the strain rate on the ultimate tensile strength that is found to increase monotonically by a factor of four, from 42 ± 6 to 160 ± 14 MPa. Importantly, fibril strengthening takes place without a reduction in ductility, which results in equivalently large increase in toughness with the increasing strain rate. This experimental strain rate dependent mechanical response is captured well by a structural constitutive model that incorporates the salient features of the collagen microstructure via a process of gradual recruitment of kinked tropocollagen molecules, thus giving rise to the initial "toe-heel" mechanical behavior, followed by molecular stretching and sustained intermolecular slip that is initiated at a strain rate dependent stress threshold. The model shows that the fraction of tropocollagen molecules undergoing straightening increases continuously during loading, whereas molecular sliding is initiated after a small fibril strain (1%-2%) and progressively increases with applied strain.

Microscale Creep and Stress Relaxation Experiments with Individual Collagen Fibrils.

Nanoscale macromolecular biological structures exhibit time-dependent behavior, yet a quantitative understanding of their time-dependent mechanical behavior remains elusive, largely due to experimental challenges in attaining sufficient spatial and temporal resolution and control of stress or strain in conditions that guarantee their molecular integrity. To address this gap, an experimental methodology was developed to conduct creep and stress relaxation experiments with individual mammalian collagen fibrils. An image-based edge detection method implemented with high magnification optical microscopy and combined with closed-loop proportional-integral-derivative (PID) control was implemented and calibrated to apply constant force or stretch ratio values to individual collagen fibrils via a Microelectromechanical Systems (MEMS) device. This experimental methodology allowed for real-time control of uniaxial tensile stress or strain with 27 nm displacement resolution. The overall experimental system was tuned to apply step inputs with rise times below 0.5 s, less than 2.5% overshoot, and steady-state error less than 0.5%. Three individual collagen fibrils with diameters 101-121 nm were subjected to creep and stress relaxation tests in the range 4-20% engineering strain, under partially hydrated conditions. The collagen fibrils demonstrated non-linear viscoelastic behavior that was described well by the adaptive quasi-linear viscoelastic model. The results of this study demonstrate for the first time that mammalian collagen fibrils, the building blocks of connective tissues, exhibit nonlinear viscoelastic behavior in their partially hydrated state.

Nanofibrillar Si Helices for Low-Stress, High-Capacity Li+ Anodes with Large Affine Deformations.

We report on the chemical lithiation of long microscale helices composed of densely packed amorphous silicon (aSi) nanofibrils, fabricated by glancing angle deposition (GLAD) through e-beam evaporation. In situ electron microscopy and companion finite element modeling demonstrate that the nanofibrillar structure of the aSi helices allows for 2 orders of magnitude faster effective rates for Li diffusion ( D0 = 10-10 cm2/s) compared to solid aSi nanowires, while also averting fragmentation during lithiation. More importantly, it is shown that specific helical geometries can accommodate large, lithium-induced, volumetric expansions without shape distortion. A major advantage of the helical nanostructures is that the compressive force generated due to lithiation-induced expansion is an order of magnitude smaller than in straight nanocolumns that permanently buckle during lithiation. Thus, GLAD-fabricated films composed of dense periodic microscale helices with properly designed coil geometries are highly suitable for robust, high-capacity Li+ anodes.

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

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 ±â€¯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 ±â€¯98 MPa to 1091 ±â€¯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.

Strong and tough mineralized PLGA nanofibers for tendon-to-bone scaffolds.

Engineering complex tissues such as the tendon-to-bone insertion sites require a strong and tough biomimetic material system that incorporates both mineralized and unmineralized tissues with different strengths and stiffnesses. However, increasing strength without degrading toughness is a fundamental challenge in materials science. Here, we demonstrate a promising nanofibrous polymer-hydroxyapatite system, in which, a continuous fibrous network must function as a scaffold for both mineralized and unmineralized tissues. It is shown that the high toughness of this material system could be maintained without compromising on the strength with the addition of hydroxyapatite mineral. Individual electrospun poly (lactide-co-glycolide) (PLGA) nanofibers demonstrated outstanding strain-hardening behavior and ductility when stretched uniaxially, even in the presence of surface mineralization. This highly desirable hardening behavior which results in simultaneous nanofiber strengthening and toughening was shown to depend on the initial cross-sectional morphology of the PLGA nanofibers. For pristine PLGA nanofibers, it was shown that ellipsoidal cross-sections provide the largest increase in fiber strength by almost 200% compared to bulk PLGA. This exceptional strength accompanied by 100% elongation was shown to be retained for thin and strongly bonded conformal mineral coatings, which were preserved on the nanofiber surface even for such very large extensions.

Novel method for mechanical characterization of polymeric nanofibers.

A novel method to perform nanoscale mechanical characterization of highly deformable nanofibers has been developed. A microelectromechanical system (MEMS) test platform with an on-chip leaf-spring load cell that was tuned with the aid of a focused ion beam was built for fiber gripping and force measurement and it was actuated with an external piezoelectric transducer. Submicron scale tensile tests were performed in ambient conditions under an optical microscope. Engineering stresses and strains were obtained directly from images of the MEMS platform, by extracting the relative rigid body displacements of the device components by digital image correlation. The accuracy in determining displacements by this optical method was shown to be better than 50 nm. In the application of this method, the mechanical behavior of electrospun polyacrylonitrite nanofibers with diameters ranging from 300 to 600 nm was investigated. The stress-strain curves demonstrated an apparent elastic-perfectly plastic behavior with elastic modulus of 7.6+/-1.5 GPa and large irreversible strains that exceeded 220%. The large fiber stretch ratios were the result of a cascade of periodic necks that formed during cold drawing of the nanofibers.