The relationship between mechanical properties and ballistic penetration depth in a viscoelastic gel.

The fundamental material response of a viscoelastic material when impacted by a ballistic projectile has important implication for the defense, law enforcement, and medical communities particularly for the evaluation of protective systems. In this paper, we systematically vary the modulus and toughness of a synthetic polymer gel to determine their respective influence on the velocity-dependent penetration of a spherical projectile. The polymer gels were characterized using tensile, compression, and rheological testing taking special care to address the unique challenges associated with obtaining high fidelity mechanical data on highly conformal materials. The depth of penetration data was accurately described using the elastic Froude number for viscoelastic gels ranging in Young's modulus from ~60 to 630 kPa. The minimum velocity of penetration was determined to scale with the gel toughness divided by the gel modulus, a qualitative estimate for the zone of deformation size scale upon impact. We anticipate that this work will provide insight into the critical material factors that control ballistic penetration behavior in soft materials and aid in the design and development of new ballistic testing media.

Interfacial optimization of fiber-reinforced hydrogel composites for soft fibrous tissue applications.

Meniscal tears are the most common orthopedic injuries to the human body, yet the current treatment of choice is a partial meniscectomy, which is known to lead to joint degeneration and osteoarthritis. As a result, there is a significant clinical need to develop materials capable of restoring function to the meniscus following an injury. Fiber-reinforced hydrogel composites are particularly suited for replicating the mechanical function of native fibrous tissues due to their ability to mimic the native anisotropic property distribution present. A critical issue with these materials, however, is the potential for the fiber-matrix interfacial properties to severely limit composite performance. In this work, the interfacial properties of an ultra-high-molecular-weight polyethylene (UHMWPE) fiber-reinforced poly(vinyl alcohol) (PVA) hydrogel are studied. A novel chemical grafting technique, confirmed using X-ray photoelectron spectroscopy, is used to improve UHMWPE-PVA interfacial adhesion. Interfacial shear strength is quantified using fiber pull-out tests. Results indicate significantly improved fiber-hydrogel interfacial adhesion after chemical grafting, where chemically grafted samples have an interfacial shear strength of 256.4±64.3kPa compared to 11.5±2.9kPa for untreated samples. Additionally, scanning electron microscopy of fiber surfaces after fiber pull-out reveal cohesive failure within the hydrogel matrix for treated fiber samples, indicating that the UHMWPE-PVA interface has been successfully optimized. Lastly, inter-fiber spacing is observed to have a significant effect on interfacial adhesion. Fibers spaced further apart have significantly higher interfacial shear strengths, which is critical to consider when optimizing composite design. The results in this study are applicable in developing similar chemical grafting techniques and optimizing fiber-matrix interfacial properties for other hydrogel-based composite systems.

Tunable mechanical behavior of synthetic organogels as biofidelic tissue simulants.

Solvent-swollen polymer gels can be utilized as mechanical simulants of biological tissues to evaluate protective systems and assess injury mechanisms. However, a key challenge in this application of synthetic materials is mimicking the rate-dependent mechanical response of complex biological tissues. Here, we characterize the mechanical behavior of tissue simulant gel candidates comprising a chemically crosslinked polydimethylsiloxane (PDMS) network loaded with a non-reactive PDMS solvent, and compare this response with that of tissue from murine heart and liver under comparable loading conditions. We first survey the rheological properties of a library of tissue simulant candidates to investigate the effects of solvent loading percentage, reactive functional group stoichiometry, and solvent molecular weight. We then quantify the impact resistance, energy dissipation capacities, and energy dissipation rates via impact indentation for the tissue simulant candidates, as well as for the murine heart and liver. We demonstrate that by tuning these variables the silicone gels can be engineered to match the impact response of biological tissues. These experiments inform the design principles required for synthetic polymer gels that are optimized to predict the response of specific biological tissues to impact loading, providing insight for further tuning of this gel system to match the impact response of other "soft tissues".

Micro- and nanomechanical analysis of articular cartilage by indentation-type atomic force microscopy: validation with a gel-microfiber composite.

As documented previously, articular cartilage exhibits a scale-dependent dynamic stiffness when probed by indentation-type atomic force microscopy (IT-AFM). In this study, a micrometer-size spherical tip revealed an unimodal stiffness distribution (which we refer to as microstiffness), whereas probing articular cartilage with a nanometer-size pyramidal tip resulted in a bimodal nanostiffness distribution. We concluded that indentation of the cartilage's soft proteoglycan (PG) gel gave rise to the lower nanostiffness peak, whereas deformation of its collagen fibrils yielded the higher nanostiffness peak. To test our hypothesis, we produced a gel-microfiber composite consisting of a chondroitin sulfate-containing agarose gel and a fibrillar poly(ethylene glycol)-terephthalate/poly(butylene)-terephthalate block copolymer. In striking analogy to articular cartilage, the microstiffness distribution of the synthetic composite was unimodal, whereas its nanostiffness exhibited a bimodal distribution. Also, similar to the case with cartilage, addition of the negatively charged chondroitin sulfate rendered the gel-microfiber composite's water content responsive to salt. When the ionic strength of the surrounding buffer solution increased from 0.15 to 2 M NaCl, the cartilage's microstiffness increased by 21%, whereas that of the synthetic biomaterial went up by 31%. When the nanostiffness was measured after the ionic strength was raised by the same amount, the cartilage's lower peak increased by 28%, whereas that of the synthetic biomaterial went up by 34%. Of interest, the higher peak values remained unchanged for both materials. Taken together, these results demonstrate that the nanoscale lower peak is a measure of the soft PG gel, and the nanoscale higher peak measures collagen fibril stiffness. In contrast, the micrometer-scale measurements fail to resolve separate stiffness values for the PG and collagen fibril moieties. Therefore, we propose to use nanostiffness as a new biomarker to analyze structure-function relationships in normal, diseased, and engineered cartilage.

Mechanical characterization of soft viscoelastic gels via indentation and optimization-based inverse finite element analysis.

Polymer gels are widely accepted as candidate materials for tissue engineering, drug delivery, and orthopedic load-bearing applications. In addition, their mechanical and physical properties can be tailored to meet a wide range of design requirements. For soft gels whose elastic modulus is in the kPa range, mechanical characterization by bulk mechanical testing methods presents challenges, for example, in sample preparation, fixture design, gripping, and/or load measurement accuracy. Nanoindentation, however, has advantages when characterizing the mechanical properties of soft materials. This study was aimed at investigating the application of an inverse finite element analysis technique to identify material parameters of polymer gels via nanoindentation creep testing, optimization, and finite element simulation. Nanoindentation experiments were conducted using a rigid circular flat punch, and then simulated using the commercial software ABAQUS. The optimization (error minimization) procedure was integrated in the parameter determination process using a Matlab shell program, which makes this approach readily adaptable to other test geometries and material models. The finite element results compare well with a derived analytical viscoelastic solution for a rigid circular flat punch on a Kelvin-Voigt half-space.

A buckling-based metrology for measuring the elastic moduli of polymeric thin films.

As technology continues towards smaller, thinner and lighter devices, more stringent demands are placed on thin polymer films as diffusion barriers, dielectric coatings, electronic packaging and so on. Therefore, there is a growing need for testing platforms to rapidly determine the mechanical properties of thin polymer films and coatings. We introduce here an elegant, efficient measurement method that yields the elastic moduli of nanoscale polymer films in a rapid and quantitative manner without the need for expensive equipment or material-specific modelling. The technique exploits a buckling instability that occurs in bilayers consisting of a stiff, thin film coated onto a relatively soft, thick substrate. Using the spacing of these highly periodic wrinkles, we calculate the film's elastic modulus by applying well-established buckling mechanics. We successfully apply this new measurement platform to several systems displaying a wide range of thicknessess (nanometre to micrometre) and moduli (MPa to GPa).

Dynamic elastic modulus of porcine articular cartilage determined at two different levels of tissue organization by indentation-type atomic force microscopy.

Cartilage stiffness was measured ex vivo at the micrometer and nanometer scales to explore structure-mechanical property relationships at smaller scales than has been done previously. A method was developed to measure the dynamic elastic modulus, |E(*)|, in compression by indentation-type atomic force microscopy (IT AFM). Spherical indenter tips (radius = approximately 2.5 microm) and sharp pyramidal tips (radius = approximately 20 nm) were employed to probe micrometer-scale and nanometer-scale response, respectively. |E(*)| values were obtained at 3 Hz from 1024 unloading response curves recorded at a given location on subsurface cartilage from porcine femoral condyles. With the microsphere tips, the average modulus was approximately 2.6 MPa, in agreement with available millimeter-scale data, whereas with the sharp pyramidal tips, it was typically 100-fold lower. In contrast to cartilage, measurements made on agarose gels, a much more molecularly amorphous biomaterial, resulted in the same average modulus for both indentation tips. From results of AFM imaging of cartilage, the micrometer-scale spherical tips resolved no fine structure except some chondrocytes, whereas the nanometer-scale pyramidal tips resolved individual collagen fibers and their 67-nm axial repeat distance. These results suggest that the spherical AFM tip is large enough to measure the aggregate dynamic elastic modulus of cartilage, whereas the sharp AFM tip depicts the elastic properties of its fine structure. Additional measurements of cartilage stiffness following enzyme action revealed that elastase digestion of the collagen moiety lowered the modulus at the micrometer scale. In contrast, digestion of the proteoglycans moiety by cathepsin D had little effect on |E(*)| at the micrometer scale, but yielded a clear stiffening at the nanometer scale. Thus, cartilage compressive stiffness is different at the nanometer scale compared to the overall structural stiffness measured at the micrometer and larger scales because of the fine nanometer-scale structure, and enzyme-induced structural changes can affect this scale-dependent stiffness differently.

Review of Instrumented Indentation.

Instrumented indentation, also known as depth-sensing indentation or nanoindentation, is increasingly being used to probe the mechanical response of materials from metals and ceramics to polymeric and biological materials. The additional levels of control, sensitivity, and data acquisition offered by instrumented indentation systems have resulted in numerous advances in materials science, particularly regarding fundamental mechanisms of mechanical behavior at micrometer and even sub-micrometer length scales. Continued improvements of instrumented indentation testing towards absolute quantification of a wide range of material properties and behavior will require advances in instrument calibration, measurement protocols, and analysis tools and techniques. In this paper, an overview of instrumented indentation is given with regard to current instrument technology and analysis methods. Research efforts at the National Institute of Standards and Technology (NIST) aimed at improving the related measurement science are discussed.