The Application of Standard Nonlinear Solid Material Models in Modelling the Tensile Behaviour of the Supraspinatus Tendon

Tendons transmit forces from muscles to bones through joints. Typically, tendons and muscles work together to innovate a particular type of motion. Therefore, in order for the tendons to find attachment to the bones, they are naturally adapted as much thinner strands than the muscles that they serve. Thus, they are often subjected to much higher stresses than the muscles that they actually serve in any given action. As a result, tendons are susceptible to injuries that may lead to a permanent dysfunction in joint mobility due to the fact that the scar tissue that forms after healing does not often have the same mechanical properties of the original tissue. It is, therefore, very important to understand the mechanical response of tendons. This paper examines the performances of two viscoelastic standard nonlinear models in modelling the elastic and plastic behaviour of the tendon in the light of a well-known hyperelastic Yeoh model. The use of the Yeoh model is more for validating the performances of the viscoelastic models within the elastic region rather than for comparison purposes. Yeoh model’s selection was based on its superior performance in modelling the elastic phase of soft tissue as reported in previous studies combined with its simplicity. The results show that the two standard nonlinear solid models perform extremely well both in fitting accuracies and in correlating stress results. The most promising result is the fact that the two standard nonlinear models can model tendon behaviour in the nonlinear plastic region. It is also noted that the two standard nonlinear models are physically insightful since their optimisation parameters can be easily interpreted in terms of tendon elasticity and viscoelastic parameters.

NUMERICAL-EXPERIMENTAL EVALUATION OF A HYPERELASTIC POLYURETHANE ADHESIVE

This article presents the results of the experimental tests carried out on a polyurethane hyperelastic adhesive. The Mooney-Rivlin, Ogden and Yeoh models were analyzed between others, with different order and parameters using the finite element method and the Ansys V17.1 package, with the aim of evaluating the convergence of a general hyperelastic model, to subsequently manufacture specimens and perform experimental uniaxial stress tests. The information obtained from the tests was supplied to a curve fitting model for several hyperelastic models, seeking to obtain a correlation between these tests. New analyzes were performed with the finite element method with the materials considered and the curves adjusted. The results were studied and the numerical hyperelastic model closest to reality was selected, observing that the 1st order Yeoh model presented significant deviations between -30% to 60% in the experimental stiffness, the 3rd order Yeoh model presented deviations of -5% to -30%, while Ogden models of 1st and 3rd order presented deviations of -3.5% to 25% and -3% to 20%, before approaching the critical load, where the model of Ogden of 1st order presented a deviation of 0.66% and that of 3rd order of -3.59%. The 2 parameter Mooney-Rivlin model presents a deviation of 3.9% when it approaches the critical load, but values from -2.04% to 15% during the development of the stress test, so that model proved to be the most appropriate to analyze the material investigated in this work. Key Words: Hyperelastic material, Experimental Methods, Numerical Methods, FEA

Design, Kinematics, and Application of Axially and Radially Expandable Modular Soft Pneumatic Actuators

Recently, soft pneumatic actuators (SPAs) have drawn increasing attention due to their ease of fabrication, high customizability and innately softness. Inspired by modular design, two kinds of SPAs including an axial elongation soft pneumatic actuator (aeSPA) and a radial expansion soft pneumatic actuator (reSPA) are proposed in this paper, followed by their modeling, fabrication, and application in locomotion robots. The relationships between pressure and displacement of these SPAs are deduced based on the Yeoh model and the principle of virtual work, which has a good agreement with experimental results. Five modular worm-like crawling robots are fabricated by assembling the aeSPAs and reSPAs in different morphology, and crawling tests are performed under different conditions to show the adaptivity of robots.

Ability of Constitutive Models to Characterize the Temperature Dependence of Rubber Hyperelasticity and to Predict the Stress-Strain Behavior of Filled Rubber under Different Defor Mation States

In this paper, some representative hyperelastic constitutive models of rubber materials were reviewed from the perspectives of molecular chain network statistical mechanics and continuum mechanics. Based on the advantages of existing models, an improved constitutive model was developed, and the stress–strain relationship was derived. Uniaxial tensile tests were performed on two types of filled tire compounds at different temperatures. The physical phenomena related to rubber deformation were analyzed, and the temperature dependence of the mechanical behavior of filled rubber in a larger deformation range (150% strain) was revealed from multiple angles. Based on the experimental data, the ability of several models to describe the stress–strain mechanical response of carbon black filled compound was studied, and the application limitations of some constitutive models were revealed. Combined with the experimental data, the ability of Yeoh model, Ogden model (n = 3), and improved eight-chain model to characterize the temperature dependence was studied, and the laws of temperature dependence of their parameters were revealed. By fitting the uniaxial tensile test data and comparing it with the Yeoh model, the improved eight-chain model was proved to have a better ability to predict the hyperelastic behavior of rubber materials under different deformation states. Finally, the improved eight-chain model was successfully applied to finite element analysis (FEA) and compared with the experimental data. It was found that the improved eight-chain model can accurately describe the stress–strain characteristics of filled rubber.

Large bending deformation of cantilevered soft beam under external load: the applicability of inextensibility assumption of the centerline

Background: Soft materials including elastomers and gels are pervasive in biological systems and technological applications. Whereas the deformation of soft structures may be extremely large, it is still challenging to theoretically model and predict the large-deformation behaviors of soft structures. Objective: The goal of this work is to give a general theoretical model to investigate the large deformation of a cantilevered soft beam under various loads. In particular, the applicability condition of the inextensibility assumption of the beam centerline is explored. Methods: The governing equations of the soft beam system are derived according to the principle of minimum potential energy. In order to investigate the large deformation of the soft beam, the curvature of the beam centerline is exactly considered and Yeoh model is utilized to account for the hyperelasticity of the soft beam. The derived ordinary differential equations are discretized by Galerkin method and then solved by iterative algorithm. Results: Based on the proposed theoretical model, large bending deformations of the cantilevered soft beam are analyzed for various types of external loads including uniformly distributed force, tip-end concentrated force and non-uniformly distributed force. Different values of the amplitude of the external loads are considered and fruitful deformed configurations are presented. Conclusion: The proposed model is able to study the large deformation of the soft beam effectively. The inextensibility assumption of the beam centerline is applicable when the amplitude of the external load is relatively small. When the amplitude of the external load is sufficiently large, the extension of the centerline needs to be considered.

A Study on the Mechanical Characteristics of String Planes of Badminton Racquets by Nonlinear Finite Element Analysis

In this study, the finite element analysis of the string planes of badminton racquets was investigated to evaluate the effect of the mechanical characteristics of polymer strings. The nonlinear mechanical characteristics of commercially available polymer strings were obtained by the uniaxial loading tests experimentally. The effects of the strain rate on the mechanical characteristics of the polymer strings were also investigated to consider the dynamic effect on the numerical simulation. The numerical simulation code used to analyze the string planes of the badminton racquets was developed originally. A nonlinear elastic model (Yeoh model) was applied to the mechanical characteristics of the polymer string. Simulated results were compared with the experimental results. The effect of the mechanical characteristics of the polymer strings and the geometrical shape of the badminton racquets on the out-of-plane stiffnesses were investigated.

Comparative behavior of local hyperelastic lowgrade rubbers for low-cost base isolation

As the second largest rubber producer in the world, Indonesia has a very potential opportunity to support the development of rubber base isolation. Various grades of rubber are produced by the local rubber manufacturers starting from the low to high grade rubbers. In the study, the local rubbers were also compared to the rubbers from another developing country, e.g. India. The laboratory test results used to develop the suitable constitutive model for hyperelastic material and then compared to the hyperelastic model of Shahzad et al. Several tests on the local low-grade rubbers have been conducted, namely the uniaxial tensile, planar shear, and equibiaxial tensile tests. From the tests, it can be concluded the behavior of the local low-grade rubber can be fitted with the Ogden model different from the characteristic of rubber tested by Shahzad et al. which was fitted with the Yeoh model.

Quantifying Tensile Properties of Bamboo Silicone Biocomposite using Yeoh Model

The utilisation of bamboo has the potential of improving the properties of silicone. However, a thorough investigation has yet to be reported on the mechanical properties of bamboo silicone biocomposite. This study was carried out with the aim to quantify the tensile properties and assess the tensile behaviour of bamboo silicone biocomposite using Yeoh hyperelastic constitutive function. The specimens were prepared from the mix of bamboo particulate and pure silicone at various fibre composition ratio (0wt%, 1wt%, 3wt% and 5wt%) cured overnight at room temperature. A uniaxial tensile test was carried out by adopting the ASTM D412 testing standard. The Coefficient of Variation, CV, and the Coefficient of Determination, r2, were determined to assess the reliability of the experimental data and fitting model. The results of the determined Yeoh material constants for 5wt% specimen is found to be C1 = 12.0603×10-3 MPa, C2 = 8.7353×10-5 MPa and C3 = -11.6165×10-8 MPa, compared to pure silicone (0wt%) C1 = 5.6087×10-3 MPa, C2 = 8.6639×10-5 MPa and C3 = -7.6510×10-8 MPa. The results indicate that the bamboo fibre improves the stiffness of the silicone rubber by 115 percent. A low variance was exhibited by the experimental data with a CV value of less than 8 percent. The Yeoh Model demonstrated an excellent prediction of the elastic behaviour of bamboo silicone biocomposite with a fitting accuracy of more than 99.93 percent.

Modelling, simulation and experiment of the spherical flexible joint stiffness

The spherical flexible joint is extensively used in engineering. It is designed to provide flexibility in rotation while bearing vertical compression load. The linear rotational stiffness of the flexible joint is formulated. The rotational stiffness of the bonded rubber layer is related to inner radius, thickness and two edge angles. FEM is used to verify the analytical solution and analyze the stiffness. The Mooney–Rivlin, Neo Hooke and Yeoh constitutive models are used in the simulation. The experiment is taken to obtain the material coefficient and validate the analytical and FEM results. The Yeoh model can reflect the deformation trend more accurately, but the error in the nearly linear district is bigger than the Mooney–Rivlin model. The Mooney–Rivlin model can fit the test result very well and the analytical solution can also be used when the rubber deformation in the flexible joint is small. The increase of Poisson's ratio of the rubber layers will enhance the vertical compression stiffness but barely have effect on the rotational stiffness.