Depth-dependent strain fields of articular cartilage under rolling load by the optimized digital image correlation technique

It is significant to investigate the depth-dependent mechanical behaviors of articular cartilage under rolling load since considerable rolling occurs for cartilage joint in activities of daily living. In this study, the rolling experiments of articular cartilage were conducted by applying an optimized digital image correlation (DIC) technique for the first time and the depth-dependent normal strain and shear strain of cartilage were analyzed. It is found that the normal strain and shear strain values of different layers increase firstly and then decrease with rolling time, and they increase with increasing compressive strains. The normal strain and shear strain values decrease along cartilage depth with constant compressive strain. The normal strain values of different normalized depth decrease with increasing rolling rates. The shear strain values of superficial layer and middle layer decrease; however there are no major changes for the shear strain values of deep layer with increasing rolling rates. The normal strain values with different rolling time increase with increasing rolling numbers and the 30.6% increase in initial normal strain is observed from 1st to 99th cycle. The fitting relationship of the normal strain and normalized depth was obtained considering the effects of compressive strain and rolling rate and the fitting curves agree with the experimental results for cartilage very well.     

Depth-dependent normal strain of articular cartilage under sliding load by the optimized digital image correlation technique

The sliding experiments of articular cartilage were conducted by applying an optimized digital image correlation (DIC) technique and the depth-dependent normal strain and friction force were analyzed for cartilage. It is found that the friction forces of cartilage increase firstly and then decrease slowly with the slide of slider and increase with increasing compressive strain. The normal strain values of different layers increase obviously with sliding time with compressive strain of 35.2%. The normal strain values of superficial layer and middle layer appear in an increasing trend however little change of normal strain in deep layer is observed with sliding time with compressive strains of 18.9% and 11.2%. The depth-dependent normal strain values decrease along depth direction with constant compressive strain and the normal strain values of different normalized depth increase with increasing compressive strain. The friction forces and depth-dependent normal strain values of cartilage decrease slightly with increasing sliding rates. It is noted that the first sliding friction forces are the largest and then the friction forces decrease with increasing sliding numbers. The normal strain value increases with increasing sliding numbers and the increasing amplitude of normal strain during the former two sliding is significant. The fitting relationship of normal strain and normalized depth was obtained considering the effects of compressive strain and sliding rate and the fitting curves agree with the experimental data for cartilage with different compressive levels and sliding rates very well.     

Stress relaxation behavior of nano-hydroxyapatite reinforced poly(vinyl alcohol) gel composites as biomaterial

Nano-hydroxyapatite reinforced poly(vinyl alcohol) (nano-HA/PVA) gel composites has been proposed as a promising biomaterial to replace diseased or damaged articular cartilage. In this paper, the stress relaxation mechanism of nano-HA/PVA gel composites was investigated. The various influence factors on the stress relaxation behavior of the composites were also evaluated. The results showed that the relaxation mechanism of the composites was mainly determined by the synergistic effect of two stress relaxation mechanisms analogous to those of the natural articular cartilage and the polymer. The relaxation rate of the composites increased with the rise of strain ratio, but it declined with the relaxation time. Under the given strain ratio, the relaxation rate of the composite presented a trend of rising first and then falling with the increasing amount of nano-HA content. Contrarily, the normalized equilibrium relaxation modulus of the composites decreased first and then presented increasing trend with the rise of nano-HA content. Furthermore, the normalized equilibrium relaxation modulus of the composites decreased with the rise of strain.     

Biomechanical properties of single chondrocytes and chondrons determined by micromanipulation and finite-element modelling

A chondrocyte and its surrounding pericellular matrix (PCM) are defined as a chondron. Single chondrocytes and chondrons isolated from bovine articular cartilage were compressed by micromanipulation between two parallel surfaces in order to investigate their biomechanical properties and to discover the mechanical significance of the PCM. The force imposed on the cells was measured directly during compression to various deformations and then holding. When the nominal strain at the end of compression was 50 per cent, force relaxation showed that the cells were viscoelastic, but this viscoelasticity was generally insignificant when the nominal strain was 30 per cent or lower. The viscoelastic behaviour might be due to the mechanical response of the cell cytoskeleton and/or nucleus at higher deformations. A finite-element analysis was applied to simulate the experimental force-displacement/time data and to obtain mechanical property parameters of the chondrocytes and chondrons. Because of the large strains in the cells, a nonlinear elastic model was used for simulations of compression to 30 per cent nominal strain and a nonlinear viscoelastic model for 50 per cent. The elastic model yielded a Young''s modulus of 14 ± 1 kPa (mean ± s.e.) for chondrocytes and 19 ± 2 kPa for chondrons, respectively. The viscoelastic model generated an instantaneous elastic modulus of 21 ± 3 and 27 ± 4 kPa, a long-term modulus of 9.3 ± 0.8 and 12 ± 1 kPa and an apparent viscosity of 2.8 ± 0.5 and 3.4 ± 0.6 kPa s for chondrocytes and chondrons, respectively. It was concluded that chondrons were generally stiffer and showed less viscoelastic behaviour than chondrocytes, and that the PCM significantly influenced the mechanical properties of the cells.     

A formulation to model the nonlinear viscoelastic properties of the vascular tissue

Nearly all soft tissues, including the vascular tissue, present a certain degree of viscoelastic material response, which becomes apparent performing multiple relaxation tests over a wide range of strain levels and plotting the resulting stress relaxation curves, nonlinear viscoelasticity of the tissue. Changes in relaxation rate at each strain may occur at multiple strain levels. A constitutive formulation considering the particular features of the vascular tissue, such as anisotropy, together with these nonlinear viscoelastic phenomena is here presented and used to fit stress?Cstretch curves from experimental relaxation tests. This constitutive model was used to fit several data set of in vitro experimental stress relaxation tests performed on ovine and porcine aorta. The good fitting of the experimental data shows the capability of the model to reproduce the viscoelastic response of the vascular tissue.     

Mechanical Properties of Graphene Foam and Graphene Foam—Tissue Composites

Graphene foam (GF), a 3‐dimensional derivative of graphene, has received much attention recently for applications in tissue engineering due to its unique mechanical, electrical, and thermal properties. Although GF is an appealing material for cartilage tissue engineering, the mechanical properties of GF‐tissue composites under dynamic compressive loads have not yet been reported. The objective of this study is to measure the elastic and viscoelastic properties of GF and GF‐tissue composites under unconfined compression when quasi‐static and dynamic loads are applied at strain magnitudes below 20%. The mechanical tests demonstrate a 46% increase in the elastic modulus and a 29% increase in the equilibrium modulus after 28‐days of cell culture as compared to GF soaked in tissue culture medium for 24 h. There is no significant difference in the amount of stress relaxation, however, the phase shift demonstrates a significant increase between pure GF and GF that has been soaked in tissue culture medium for 24 h. Furthermore, the authors have shown that ATDC5 chondrocyte progenitor cells are viable on graphene foam and have identified the cellular contribution to the mechanical strength and viscoelastic properties of GF‐tissue composites, with important implications for cartilage tissue engineering.

     

Viscoelastic analysis of a polyurethane thermosetting resin under relaxation and at constant compression strain rate

The evolution of the viscoelastic behaviour of a polyurethane resin was investigated on the basis of uniaxial compression tests in stress relaxation and at constant strain rate. Both methods were applied to PUR specimens whose curing cycle was interrupted at different steps. The experimental data were precisely modelled in terms of a three-parameter constitutive equation whose general form was derived from the Kohlrausch relaxation law. The viscoelastic behaviour was followed during the cross-linking process and during the final cooling ramp. A close correlation was found between the degree for cross-linking and the elastic modulus increase during the curing period. Furthermore, it was stated that the evolution of the viscoelastic parameters during the cooling phase describes in a quantitative way the construction of the glassy behaviour and that it controls the development of internal stresses in PUR mouldings.     

The influence of hygrothermal conditions on the damage processes in quasi-isotropic carbon/epoxy laminates

The effects of hygrothermal conditions on damage development in quasi-isotropic carbon-fiber/epoxy laminates are described. First, monotonic and loading/unloading tensile tests were conducted on dry and wet specimens at ambient and high temperatures to compare the stress/strain response and damage development. The changes in the Young's modulus and Poisson's ratio were obtained experimentally from the monotonic tensile tests. The critical stresses for transverse cracking and delamination for the above three conditions are compared. The delamination area is measured by using scanning acoustic microscopy (SAM) at various loads to discuss the effects of delamination on the nonlinear stress/strain behavior. Next, the stress distributions under tensile load including hygrothermal residual stresses are computed by a finite-element code and their effects on damage initiation are discussed. Finally, a simple model for the prediction of the Young's modulus of a delaminated specimen is proposed. It is found that moisture increases the critical stresses for transverse cracking and delamination by reducing the residual stresses while high temperature decreases the critical stresses in spite of relaxation of the residual stresses. The results of the finite-element analysis provide some explanations for the onset of transverse cracking and delamination. The Young's modulus predicted by the present model agrees with experimental results better than that predicted by conventional models.     

Viscoelastic properties of mineralized alginate hydrogel beads

Alginate hydrogels have applications in biomedicine, ranging from delivery of cells and growth factors to wound management aids. However, they are mechanically soft and have shown little potential for the use in bone tissue engineering. Here, the viscoelastic properties of alginate hydrogel beads mineralized with calcium phosphate, both by a counter-diffusion (CD) and an enzymatic approach, are characterized by a micro-manipulation technique and mathematical modeling. Fabricated hydrogel materials have low mineral content (below 3?% of the total hydrogel mass, which corresponds to mineral content of up to 60?% of the dry mass) and low dry mass content (<5?%). For all samples compression and hold (relaxation after compression) data was collected and analyzed. The apparent Young's modulus of the mineralized beads was estimated by the Hertz model (compression data) and was shown to increase up to threefold upon mineralization. The enzymatically mineralized beads showed higher apparent Young's modulus compared to the ones mineralized by CD, even though the mineral content of the former was lower. Full compression-relaxation force-time profiles were analyzed using viscoelastic model. From this analysis, infinite and instantaneous Young's moduli were determined. Similarly, enzymatic mineralized beads, showed higher instantaneous and infinite Young's modulus, even if the degree of mineralization is lower then that achieved for CD method. This leads to the conclusion that both the degree of mineralization and the spatial distribution of mineral are important for the mechanical performance of the composite beads, which is in analogy to highly structured mineralized tissues found in many organisms.     

Relaxation behavior of neat and particulate filled polypropylene in uniaxial and multiaxial compression

The recently developed confined compression test was used to measure the viscoelastic bulk and shear relaxation moduli of neat, glass bead and talc filled polypropylene. In this paper further modifications of the test are introduced and a criterion for the assessment of the quality of experimental data is suggested. As expected, shear as well as the bulk relaxation moduli were found to increase with the addition of particles. In order to determine the pressure sensitivity of the material, unconfined compression tests were also performed and compared with the confined tests through interconversion of the measured moduli. In agreement with earlier results on other polymers, it turned out that the relaxation response is significantly retarded at higher confinement levels. It is shown that the effect of filler particles on the long-term behavior depends on the specific uniaxial or multiaxial stress state. Poisson’s ratio was calculated by interconversion from the bulk and shear relaxation modulus; these results show that with a single test in the confined configuration, a complete viscoelastic characterization of the material can be obtained.     

加载速率对关节软骨变形特性影响的研究

通过对不同加载速率下关节软骨变形特性的研究,探讨关节软骨在异常应力下的损伤机制。在UMT-2多功能试验机上开展三种加载速率下关节软骨的压缩试验,并建立相应的有限元模型。在线性加载下,关节软骨的弹性模量随应变经历了先急剧下降后缓慢增加的变化;有限元模拟的应变与试验测定的应变的偏差低于0.025;当加载速率为0.01MPa/s和0.0067MPa/s时,软骨弹性模量和孔隙压力的差异较小,但与加载速率0.02MPa/s对应的弹性模量和孔隙压力的差异较为显著。加载速率对软骨变形和孔隙压力有着显著影响,但当加载速率低于某一值时,软骨变形对加载速率的依赖性降低,其研究结果有助于深入理解在异常应力速率下关节软骨的损伤机制。     

Stress states and nonlinear mechanical behavior associated with nanoindentation testing of polymers

Interest in determining material properties on the nanoscale has promoted use of nanoindentation testing as a measurement technique. Classical elasticity solution of indentation geometry has provided values of the mechanical properties for linear elastic materials. Recent attempts to apply this test technique to polymers have given indications of time dependent response in the early relaxation period. There is corresponding interest in the possibility of obtaining their nonlinear viscoelastic behavior. As a preliminary to analytical study providing a basis for such testing, the first part of this paper examines the initial stress and strain condition in the vicinity of the indenter. Data from recent tests on poly(vinyl acetate) material at load levels typical of current testing indicate that stress magnitudes in the nonlinear and possibly plastic-like range are present near the specimen surface. The second part of this study pursues the examination of how the heavily nonlinear region may be characterized for polymers in analogy with the treatment utilized for metals and other elastic-plastic materials. As an example, analysis of data on PVAc indicates that its behavior in nanoindentation should in several respects correspond to materials exhibiting a relatively low value of the ratio of elastic modulus to yield stress.     

Application of ANSYS to the stress relaxation of articular cartilage in unconfined compression

The purpose of this paper is to establish a poroelastic model of cartilage for stress relaxation using the new elements in ANSYS version 12. Articular cartilage was modeled as a fluid-saturated solid because of its high water content and biphasic property. The biphasic theory for cartilage, which is capable of investigating the essential mechanical features of articular cartilage, was developed by Mow et al. (1980). In order to calibrate the material properties of the tissue-engineered cartilage, which is now emerging as a potential alternative treatment of osteoarthritis, the capacity of commercial software for modeling the cartilage needs to be verified. The aim of this research is to evaluate the porous elements available in ANSYS software and to promote the expanded application of the finite element method for analyzing soft tissues. By creating cartilage models using the fluid–solid coupling finite element analysis of porous media, ANSYS has been used in this paper to demonstrate the unconfined compressive behaviors of articular cartilage during stress relaxation. Furthermore, the validation of the fluid–solid coupling finite element model by ANSYS software ensures that the results of the present study are consistent with the analytical results of the linear Kuei, Lai, and Mow (KLM) biphasic theory.     

Structure and mechanical properties of corn kernels: a hybrid composite material

The mechanical properties of corn kernels were evaluated at three levels of kernel structure, varying in the proportions of horny endosperm, and six levels of moisture content in the range of 6 to 34% (wet basis) under a compression mode of loading. The observed values of ultimate stress, modulus of elasticity, modulus of toughness and modulus of resilience varied from 8 to 82 MPa, 20 to 480 MPa, 0.8 to 4.4 MJ m^–3 and 0.2 to 0.8 MJ m^–3, respectively, within the experimental range. Each of these properties decreased in magnitude as the moisture content increased. The microscopic study revealed that the resistance of kernels to fracture was predominantly influenced by the kernel structure. The size of cracks increased with increasing strain or decreasing proportion of the horny endosperm in the kernels. The viscoelastic behaviour of the kernels was determined at two levels of kernel structure, five levels of kernel moisture (12 to 34%) with three deformation rates (1.27, 5.08 and 12.7 mm min^–1) by means of stress relaxation tests. The analysis of the test data suggested that the hybrid composite kernels were hydrorheologically simple materials.     

Characterization of Complex Modulus of Viscoelastic Materials Subject to Static Compression

In this paper, a procedure to estimate complex modulus of incompressibleviscoelastic materials from stiffness measurements as functions offrequency under heavy compressive pre-strain is presented together withsome results for a typical viscoelastic material. Two existing methodsare discussed which enable predictions of the complex modulus based onthe measurements as functions of frequency and pre-strain. A new moreefficient formula is proposed which obtains the modulus by combining thefrequency effects at a reference pre-strain and the pre-strain effectsat a chosen frequency, i.e., dynamic effects. This formula reflects thetrend of dynamic modulus with the static compression under theassumption that the relaxation function is dependent on the staticcompression. The relaxation function can be transformed into frequency-dependent functions, which are modified to represent the pre-strain effect at a chosen frequency.Dynamic properties of a viscoelastic material were obtained at agiven strain amplitude from 1 to 180 Hz under nine levels of compressivepre-strain and performances of the formulas are comparatively discussed.     

Aluminum Melt Foam Processing for Light-Weight Structures

Aluminum foam was prepared by two routes, namely, gas injection technique and by the decomposition of TiH₂ blowing agent. The foam structure can be largely controlled by the amount of degassing agent and duration of foaming. The heterogeneity in cell structure could be explained on the basis of foam stability, drainage in the cell walls, and heat transfer during quenching. The variation in cell size and drainage is negligible when the holding time is around 120 s at 750°C. The constant strain rate compression tests indicate that the Young's modulus, plateau stress, and energy absorption capacity increases with relative density of the foam, while the densification strain reduces with increase in relative density.     

Viscoelastic modelling and strain-rate behaviour of plasticized poly(vinyl chloride)

The effect of four different types of plasticizers and four strain-rates on the tensile behaviour of poly(vinyl chloride) (PVC) has been studied. di(2-ethylhexyl phthalate), benzyl butyl phthalate, epoxidized soyabean oil and chloroparaffin were mixed at different ratios and were used as plasticizers in concentration levels of up to 77% of the PVC weight. The plasticized and unplasticized PVC were processed into sheets by compression moulding. Tensile tests were conducted at different strain rates. It was found that tensile modulus increases with increasing strain rate while it decreases with increasing plasticizer concentration. The rate of variation of tensile modulus either as a function of strain rate and/or the plasticizer concentration was, in all cases, dependent on the mixing ratio of the different types of plasticizers. Assuming the material to be a linearly viscoelastic one, a simple viscoelastic model along with a least-squares-based computer procedure was applied which enabled us to fit the experimentally obtained curves with the respective theoretical predictions as well as to study the strain-rate effect on the relaxation spectrum, H(), of the material under consideration.     

Impact testing to determine the mechanical properties of articular cartilage in isolation and on bone

The biomechanical response of cartilage to impact loads, both in isolation and in situ on its bone substrate, has been little studied despite the common occurrence of osteoarthritis subsequent to cartilage injury. An instrumented drop tower was used to apply controlled impact loads of different energies to explants of bovine articular cartilage. Results were compared with a conventional slow stress-strain test. The effects of the underlying bone were investigated by progressively shortening a core of bone removed with the cartilage, and by gluing cartilage samples to substrates of different moduli. The maximum dynamic modulus of isolated samples of bovine articular cartilage, at strain rates between 1100 and 1500 s⁻¹, was approximately two orders of magnitude larger than the quasistatic modulus and varied non-linearly with applied stress. When attached to a substrate of higher modulus, increasing the thickness of the substrate increased the effective modulus of the combination until a steady value was achieved. A lower modulus substrate reduced the effective modulus of the combination. Severe impacts resulted in damage to the bone rather than to the cartilage. The modulus of cartilage rises rapidly and non-linearly with strain rate, giving the tissue a remarkable ability to withstand impact loads. The presence of cartilage attenuated the peak force experienced by the bone and spread the impact loading period over a longer time.     

An evaluation of human articular cartilage on femoral head

In this study, we investigated stress relaxation behavior of the human articular cartilage on femoral head. Articular cartilage is a white dense connective tissue that covers the bone ends within diarthrodial joints and works as a weight-transmitting and energy-absorbing material. Human articular cartilage on femoral head was used as test material. Relaxation tests were carried out by using the indentation technique via Instron Universal Testing Machine. Test materials were investigated in an isotonic salt solution at 37 °C. To keep the temperature constant, two vessels being in each other were utilized. Thus, hot water was circulated in the outer vessel and isotonic salt solution was kept in the inner vessel. Experimental results showed that there is a remarkable difference between normal and degenerated cartilage for the same age and sex. It was observed that the relaxation percent of normal cartilage as a function of relaxation time is much higher than that of degenerated cartilage.