The anisotropic and region-dependent mechanical response of wrap-around tendons under tensile, compressive and combined multiaxial loads.

The present work reports on the multiaxial region and orientation-dependent mechanical properties of two porcine wrap-around tendons under tensile, compressive and combined loads based on an extensive study with n=175 samples. The results provide a detailed dataset of the anisotropic tensile and compressive longitudinal properties and document a pronounced tension-compression asymmetry. Motivated by the physiological loading conditions of these tendons, which include transversal compression at bony abutments in addition to longitudinal tension, we systematically investigated the change in axial tension when the tendon is compressed transversally along one or both perpendicular directions. The results reveal that the transversal compression can increase axial tension (proximal-distal direction) in both cases to orders of 30%, yet by a larger amount in the first case (transversal compression in anterior-posterior direction), which seems to be more relevant for wrap-around tendons in-vivo. These quantitative measurements are in line with earlier findings on auxetic properties of tendon tissue, but show for the first time the influence of this property on the stress response of the tendon, and may thus reveal an important functional principle within these essential elements of force transmission in the body. STATEMENT OF SIGNIFICANCE: The work reports for the first time on multiaxial region and orientation-dependent mechanical properties of wrap-around tendons under various loads. The results indicate that differences in the mechanical properties exist between zones that are predominantly in a uniaxial tensile state and those that experience complex load states. The observed counterintuitive increase of the axial tension upon lateral compression points at auxetic properties of the tendon tissue which may be pivotal for the function of the tendon as an element of the musculoskeletal system. It suggests that the tendon's performance in transmitting forces is not diminished but enhanced when the action line is deflected by a bony pulley around which the tendon wraps, representing an important functional principle of tendon tissue.

Structural Integrity Assessment of an NEPE Propellant Grain Considering the Tension-Compression Asymmetry in Its Mechanical Property.

In order to investigate the effect of tension-compression asymmetry of propellant mechanical properties on the structural integrity of a Nitrate Ester Plasticized Polyether (NEPE) propellant grain, the unified constitutive equations under tension and compression were established, a new method for grain structural integrity assessment was proposed and the structural integrity of the NEPE propellant grain under the combined axial and transverse overloads was evaluated. The results indicate that the mechanical state of the NEPE propellant grain is in the coexistence of tension and compression under the combined axial and transverse overloads, and the tension and compression regions in the propellant grain is independent of the propellant constitutive behavior. The tension-compression asymmetry of the propellant mechanical properties has a certain impact on its mechanical response. The maximum equivalent stress and strain considering the tension-compression asymmetry falls between that obtained through the tension and compression constitutive model, and is the same as damage coefficient. The safety factor of the NEPE propellant grain considering the tension-compression asymmetry of its mechanical properties is larger than that non-considering, and the traditional method of structural integrity assessment is conservative.

Experimental dataset on the in-plane tensile, shear, and compressive properties of a carbon-epoxy twill woven composite.

This data article presents experimental data on the in-plane mechanical behavior of a carbon-epoxy twill woven composite. Properties under tension, shear, and compression are measured and reported, which include force vs. stroke curves, stress vs. strain curves, in-plane on-axis and off-axis moduli, in-plane shear modulus, tensile and compressive strengths, post-peak residual stress under compression, and on-axis and off-axis Poisson ratios. Laminate plates of the composite were ordered from a commercial vendor and specimens of desired dimensions were cut using a waterjet cutter. Tests were conducted in accordance with ASTM standards D3039 and D6641, under on-axis and off-axis tension, and under on-axis compression. The data represents a complete set of in-plane mechanical properties for the composite and can be used directly as lamina level input to numerical FEA models and design analyses with woven composite laminates. It can also serve as benchmark for the calibration and validation of these models. It can be used to calculate properties for other off-axis configurations using transformation equations. Since the data is intended to be a lamina level input, it can be used to determine and model the in-plane behavior of any laminate layup with this composite. The data also serves to demonstrate the marked anisotropy and tension compression asymmetry exhibited by woven composites.

Dataset for centrifuge modelling of laterally monotonic loaded monopiles in saturated dense sand.

The presented dataset was collected in seven centrifuge tests, specifically designed for modelling the lateral response of offshore monopiles in dense sand. Two model piles with outer diameter D = 50 mm were loaded laterally at 100 × g. The embedding depths were 3D, 5D, 7D and 9D, with load eccentricity of 5, 10 and 15. Fibre Bragg gratings (FBGs) were used to measure the tensile and compressive strains of the monopiles. The raw data obtained from different sensors during the tests and the analysed data (e.g. soil reaction, pile deflection) are included in separate editable files, enabling future reuse and development of the experimental results.

Atomic investigations on the tension-compression asymmetry of AlxFeNiCrCu (x = 0.5, 1.0, 1.5, 2.0) high-entropy alloy nanowires.

The tension and compression of high-entropy alloy (HEA) nanowires (NWs) are remarkably asymmetric, but the micro mechanism is still unclear. In this research, the tension-compression asymmetry of AlxFeNiCrCu HEA NWs (x = 0.5, 1.0, 1.5, 2.0) was quantitatively characterized via molecular dynamics simulations, focusing on the influences of the NW diameter, the Al content, the crystalline orientation, and the temperature, which are significant for applying HEAs in nanotechnology. The increased NW diameter improves the energy required for stacking faults nucleating, thus strengthening AlFeNiCrCu HEA NWs. A few twins during stretching weaken the strengthening effects, thereby decreasing the tension-compression asymmetry. The increased Al content raises the tension-compression asymmetry by promoting the face-centered cubic to body-centered cubic phase transition during stretching. The tension along the [001] crystalline orientation is stronger than the compression, while the [110] and [111] crystalline orientations are entirely the opposite, and the tension-compression asymmetry along the [111] crystalline orientation is the minimum. The diversities in the tension-compression asymmetry depend on the deformation mechanism. Compressing along the [001] crystalline orientation and stretching along the [110] crystalline orientation induces twinning. Deformation along the [111] crystalline orientation only leaves stacking faults in the NWs. Therefore, the tension and compression along the [111] crystalline orientation exhibit minimal asymmetry. As the temperature rises, the tension-compression asymmetry along the [001] and [111] crystalline orientations increases, while that along the [110] crystalline orientation decreases.

On multiscale tension-compression asymmetry in skeletal muscle.

Skeletal muscle tissue shows a clear asymmetry with regard to the passive stresses under tensile and compressive deformation, referred to as tension-compression asymmetry (TCA). The present study is the first one reporting on TCA at different length scales, associated with muscle tissue and muscle fibres, respectively. This allows for the first time the comparison of TCA between the tissue and one of its individual components, and thus to identify the length scale at which this phenomenon originates. Not only the passive stress-stretch characteristics were recorded, but also the volume changes during the axial tension and compression experiments. The study reveals clear differences in the characteristics of TCA between fibres and tissue. At tissue level TCA increases non-linearly with increasing deformation and the ratio of tensile to compressive stresses at the same magnitude of strain reaches a value of approximately 130 at 13.5% deformation. At fibre level instead it initially drops to a value of 6 and then rises again to a TCA of 14. At a deformation of 13.5%, the tensile stress is about 6 times higher. Thus, TCA is about 22 times more expressed at tissue than fibre scale. Moreover, the analysis of volume changes revealed little compressibility at tissue scale whereas at fibre level, especially under compressive stress, the volume decreases significantly. The data collected in this study suggests that the extracellular matrix has a distinct role in amplifying the TCA, and leads to more incompressible tissue behaviour. STATEMENT OF SIGNIFICANCE: This article analyses and compares for the first time the tension-compression asymmetry (TCA) displayed by skeletal muscle at tissue and fibre scale. In addition, the volume changes of tissue and fibre specimens with application of passive tensile and compressive loads are studied. The study identifies a key role of the extracellular matrix in establishing the mechanical response of skeletal muscle tissue: It contributes significantly to the passive stress, it is responsible for the major part of tissue-scale TCA and, most probably, prevents/balances the volume changes of muscle fibres during deformation. These new results thus shed light on the origin of TCA and provide new information to be used in microstructure-based approaches to model and simulate skeletal muscle tissue.

Effect of Tension-Compression Asymmetry Response on the Bending of Prismatic Martensitic SMA Beams: Analytical and Experimental Study.

This paper aims to analytically derive bending equations, as well as semi-analytically predict the deflection of prismatic SMA beams in the martensite phase. To this end, we are required to employ a simplified one-dimensional parametric model considering asymmetric response in tension and compression for martensitic beams. The model takes into account the different material parameters in martensite twined and detwinned phases as well as elastic modulus depending on the progress of the detwinning process. In addition, the model considers the diverse slope of loading and unloading in martensite detwinned phases favored by tension and compression. To acquire general bending equations, we first solve the pure bending problem of a prismatic SMA beam. Three different phases are assumed in the unloading procedure and the effect of neutral fiber distance from the centerline is also considered during this stage. Then according to the pure bending solution and employing semi-analytical methods, general bending equations of an SMA beam are derived. Polynomial approximation functions are utilized to obtain the beam deflection-length relationship. To validate the attained analytical expressions, several three- and four-point bending tests were conducted for rectangular and circular SMA beams. Experimental data confirm the reasonable accuracy of the analytical results. This work may be envisaged to go deep enough in investigating the response of SMA beams under an arbitrary transverse loading and stress distribution during loading and unloading, as well as findings may be applicable to a good prediction of bending behavior.

Tension-compression asymmetry in the mechanical response of hydrogels.

Two factors play the key role in application of hydrogels as biomedical implants (for example, for replacement of damaged intervertebral discs and repair of spinal cord injuries): their stiffness and strength (measured in tensile tests) and mechanical integrity (estimated under uniaxial compression). Observations show a pronounced difference between the responses of hydrogels under tension and compression (the Young's moduli can differ by two orders of magnitude), which is conventionally referred to as the tension-compression asymmetry (TCA). A constitutive model is developed for the mechanical behavior of hydrogels, where TCA is described within the viscoplasticity theory (plastic flow is treated as sliding of junctions between chains with respect to their reference positions). The governing equations involve five material constants with transparent physical meaning. These quantities are found by fitting stress-strain diagrams under tension and compression on a number of pristine and nanocomposite hydrogels with various kinds of chemical and physical bonds between chains. Good agreement is demonstrated between the experimental data and results of simulation. The influence of volume fraction of nanoparticles, concentration of cross-links, and topology of a polymer network on material parameters is analyzed numerically.

Investigating the passive mechanical behaviour of skeletal muscle fibres: Micromechanical experiments and Bayesian hierarchical modelling.

Characterisation of the skeletal muscle's passive properties is a challenging task since its structure is dominated by a highly complex and hierarchical arrangement of fibrous components at different scales. The present work focuses on the micromechanical characterisation of skeletal muscle fibres, which consist of myofibrils, by realising three different deformation states, namely, axial tension, axial compression, and transversal compression. To the best of the authors' knowledge, the present study provides a novel comprehensive data set representing of different deformation states. These data allow for a better understanding of muscle fibre load transfer mechanisms and can be used for meaningful modelling approaches. As the present study shows, axial tension and compression experiments reveal a strong tension-compression asymmetry at fibre level. In comparison to the tissue level, this asymmetric behaviour is more pronounced at the fibre scale, elucidating the load transfer mechanism in muscle tissue and aiding in the development of future modelling strategies. Further, a Bayesian hierarchical modelling approach was used to consider the experimental fluctuations in a parameter identification scheme, leading to more comprehensive parameter distributions that reflect the entire observed experimental uncertainty. STATEMENT OF SIGNIFICANCE: This article examines for the first time the mechanical properties of skeletal muscle fibres under axial tension, axial compression, and transversal compression, leading to a highly comprehensive data set. Moreover, a Bayesian hierarchical modelling concept is presented to identify model parameters in a broad way. The results of the deformation states allow a new and comprehensive understanding of muscle fibres' load transfer mechanisms; one example is the effect of tension-compression asymmetry. On the one hand, the results of this study contribute to the understanding of muscle mechanics and thus to the muscle's functional understanding during daily activity. On the other hand, they are relevant in the fields of skeletal muscle multiscale, constitutive modelling.

Hyperelastic modeling of the human brain tissue: Effects of no-slip boundary condition and compressibility on the uniaxial deformation.

Being extremely soft, brain tissue is among the most challenging materials to be mechanically quantified. Despite recent advances in mechanical testing of ultra-soft matters, there still exists a need for robust procedures to analyze their behavior at large deformation. In this paper, it is shown how failing to taking into account the precise boundary conditions can result in substantial variation from the "assumed" ideal behavior, even for the case of simple loading conditions such as the uniaxial mode. For an accurate analysis, the mathematical modeling is combined with the finite element simulation to interpret the mechanical behavior of the brain tissue based on the comprehensive experiments conducted by Budday et al. (2017). It is demonstrated herein that only an Ogden hyperelastic model with both negative and positive nonlinearity constants can predict the mechanical behavior of the brain tissue in tension and compression, and the tension-compression asymmetry might arise from the difference in compressibility behavior in tension and compression. This hypothesis is utilized for modeling the mechanical behavior of the brain tissue in uniaxial loading condition and exhibits excellent agreement with the experiments. This study also provides a comprehensive explanation for nonlinear analysis of soft matters, in general, and the brain tissue, in particular, with thoroughly describing the concept of hyperelasticity and modeling incompressible or compressible behaviors utilizing the Ogden strain energy function.

A continuum model for tension-compression asymmetry in skeletal muscle.

Experiments on passive skeletal muscle on different species show a strong asymmetry in the observed tension-compression mechanical behavior. This asymmetry shows that the tension modulus is two orders of magnitude higher than the compression modulus. Until now, traditional analytical constitutive models have been unable to capture that strong asymmetry in anisotropic solids using the same material parameters. In this work we present a model which is able to accurately capture five experimental tests in chicken pectoralis muscle, including the observed tension-compression asymmetry. However, aspects of the anisotropy of the tissue are not captured by the model.

Collagen fibril organization in chicken and porcine skeletal muscle perimysium under applied tension and compression.

The tension/compression asymmetry observed in the stress-stretch response of skeletal muscle is not well understood. The collagen network in the extracellular matrix (ECM) almost certainly plays a major role, but the details are unknown. This paper reports qualitatively and quantitatively on skeletal muscle ECM reorganization during applied deformation using confocal imaging of collagen through use of a fluorescently-tagged specific collagen binding protein (CNA35-EGFP) of porcine and chicken muscle samples under tensile and compressive deformation in both the fibre and cross-fibre directions. This reveals the overall three-dimensional structure of collagen in perimysium in planes perpendicular and parallel to the muscle fibres in both species. Furthermore, there is clear evidence of the reorganization of these structures under compression and tension applied in both the muscle fibre and cross-fibre directions. These observations improve our understanding of perimysium structure and response to three-dimensional deformations and are an important basis for constitutive models of passive skeletal muscle. Although overall behaviour was similar, some differences in perimysium structure were observed between chicken and porcine muscle tissue. Further work is required to better understand which structures are responsible for the tension and compression stress-strain asymmetry previously observed in the mechanical response of passive skeletal muscle.

The in vitro passive elastic response of chicken pectoralis muscle to applied tensile and compressive deformation.

The mechanics of passive skeletal muscle are important in impact biomechanics, surgical simulation, and rehabilitation engineering. Existing data from porcine tissue has shown a significant tension/compression asymmetry, which is not captured by current constitutive modelling approaches using a single set of material parameters, and an adequate explanation for this effect remains elusive. In this paper, the passive elastic deformation properties of chicken pectoralis muscle are assessed for the first time, to provide deformation data on a skeletal muscle which is very different to porcine tissue. Uniaxial, quasi-static compression and tensile tests were performed on fresh chicken pectoralis muscle in the fibre and cross-fibre directions, and at 45° to the fibre direction. Results show that chicken muscle elastic behaviour is nonlinear and anisotropic. The tensile stress-stretch response is two orders of magnitude larger than in compression for all directions tested, which reflects the tension/compression asymmetry previously observed in porcine tissue. In compression the tissue is stiffest in the cross-fibre direction. However, tensile deformation applied at 45° gives the stiffest response, and this is different to previous findings relating to porcine tissue. Chicken muscle tissue is most compliant in the fibre direction for both tensile and compressive applied deformation. Generally, a small percentage of fluid exudation was observed in the compressive samples. In the future these data will be combined with microstructural analysis to assess the architectural basis for the tension/compression asymmetry now observed in two different species of skeletal muscle.

Control of tension-compression asymmetry in Ogden hyperelasticity with application to soft tissue modelling.

This paper discusses tension-compression asymmetry properties of Ogden hyperelastic formulations. It is shown that if all negative or all positive Ogden coefficients are used, tension-compression asymmetry occurs the degree of which cannot be separately controlled from the degree of non-linearity. A simple hybrid form is therefore proposed providing separate control over the tension-compression asymmetry. It is demonstrated how this form relates to a newly introduced generalised strain tensor class which encompasses both the tension-compression asymmetric Seth-Hill strain class and the tension-compression symmetric Bazant strain class. If the control parameter is set to q=0.5 a tension-compression symmetric form involving Bazant strains is obtained with the property Ψ(λ1,λ2,λ3)=Ψ(1λ1,1λ2,1λ3). The symmetric form may be desirable for the definition of ground matrix contributions in soft tissue modelling allowing all deviation from the symmetry to stem solely from fibrous reinforcement. Such an application is also presented demonstrating the use of the proposed formulation in the modelling of the non-linear elastic and transversely isotropic behaviour of skeletal muscle tissue in compression (the model implementation and fitting procedure have been made freely available). The presented hyperelastic formulations may aid researchers in independently controlling the degree of tension-compression asymmetry from the degree of non-linearity, and in the case of anisotropic materials may assist in determining the role played by, either the ground matrix, or the fibrous reinforcing structures, in generating asymmetry.

Rate sensitivity and tension-compression asymmetry in AZ31B magnesium alloy sheet.

The constitutive response of a commercial magnesium alloy rolled sheet (AZ31B-O) is studied based on room temperature tensile and compressive tests at strain rates ranging from 10(-3) to 10(3) s(-1). Because of its strong basal texture, this alloy exhibits a significant tension-compression asymmetry (strength differential) that is manifest further in terms of rather different strain rate sensitivity under tensile versus compressive loading. Under tensile loading, this alloy exhibits conventional positive strain rate sensitivity. Under compressive loading, the flow stress is initially rate insensitive until twinning is exhausted after which slip processes are activated, and conventional rate sensitivity is recovered. The material exhibits rather mild in-plane anisotropy in terms of strength, but strong transverse anisotropy (r-value), and a high degree of variation in the measured r-values along the different sheet orientations which is indicative of a higher degree of anisotropy than that observed based solely upon the variation in stresses. This rather complex behaviour is attributed to the strong basal texture, and the different deformation mechanisms being activated as the orientation and sign of applied loading are varied. A new constitutive equation is proposed to model the measured compressive behaviour that captures the rate sensitivity of the sigmoidal stress-strain response. The measured tensile stress-strain response is fit to the Zerilli-Armstrong hcp material model.

Crystallographic Orientation Influence on the Serrated Yielding Behavior of a Single-Crystal Superalloy.

Since Ni-based single-crystal superalloys are anisotropic materials, their behavior in different crystal orientations is of great interest. In this study, the yielding behavior in both tension and compression for , and oriented materials at 500 °C has been investigated. The direction showed a serrated yielding behavior, a great tension/compression asymmetry in yield strength and visible deformation bands. However, the and directions showed a more homogeneous yielding, less tension/compression asymmetry in yield strength and no deformation bands. Microstructure investigations showed that the serrated yielding behavior of the direction can be attributed to the appearance of dynamic strain aging (DSA) and that only one slip system is active in this direction during plastic deformation.