Implementing Stretch-Based Strain Energy Functions in Large Coupled Axial and Torsional Deformations of Functionally Graded Cylinder

In this paper, coupled axial and torsional large deformation of an incompressible isotropic functionally graded nonlinearly elastic solid cylinder is investigated. Utilizing stretch-based constitutive models, where the deformation tensor is non-diagonal is complex. Hence, an analytical approach is presented for combined extension and torsion of functionally graded hyperelastic cylinder. Also, finite element analysis is carried out to verify the proposed analytical solutions. The Ogden model is employed to predict the mechanical behavior of hyperelastic materials whose material parameters are function of radius in an exponential fashion. Both finite element and analytical results are in good agreement and reveal that for positive values of exponential power in material variation function, stress decreases and the rate of stress variation intensifies near the outer surface. A transition point for the hoop stress is identified, where the distribution plots regardless of the value of stretch or twist, intersect and the hoop stress alters from compressive to tensile. For the Ogden model, the torsion induced force is always compressive which means the total axial force starts from being tensile and then eventually becomes compressive i.e., the cylinder always tends to elongate on twisting.

Characterisation of Skin Biomechanical Properties via Experiment-Numerical Integration

By having specific mechanical properties of skin, computational program and analysis become more reliable by showing the real skin behaviour. Up to date, mechanical properties of biological soft tissues (skin) haven’t been accepted solely for official usage. Therefore, characterisation of the skin biomechanical properties might contribute a new knowledge to the engineering and medical sciences societies. This paper highlights the success in characterising the hyperelastic parameters of leporine (rabbit) skin via experimental-numerical integration. A set of five sample of leporine skin were stretched using the conventional tensile test machine to generate the load-displacement graphs. Based on the Ogden’s constitutive equation and Mooney-Rivlin hyperelastic model, a stress-stretch equation was developed and a programme was written using Matlab. By varying the Ogden’s and Mooney-Rivlin’s parameters, the programme was capable of plotting stress-stretch and load-displacement graphs. The graphs that best match the experimental results will constitut to the corresponding coefficient, µ, and α for Ogden Model and C1 and C2 material parameter for Mooney-Rivlin Model that will best describe the behaviour of the leporine skin. The current results show that the Ogden’s coefficient and exponent for the subject was estimated to be (μ = 0.048MPa, α = 7.073) & (μ = 0.020MPa, α = 9.249) for Anterior-Posterior (AP) and Dorsal-Ventral (DV) respectively for Ogden Model. Meanwhile the value for Mooney-Rivlin Model were estimated to be (C1 = 1.271, C2 = 1.868) & (C1 = 1.128, C2 = 1.537) for AP and DV respectively, which is in close agreement to results found by other researchers. Further analyses for comparison could be carried out by developing mathematical model based on other constitutive equation such as Arruda-Boyce and Neo-Hookean. Nevertheless, this study has contributed to the knowledge about skin behaviour and the results are useful for references.

On Spherical Inhomogeneity With Steigmann–Ogden Interface

The problem of an infinite isotropic elastic space subjected to uniform far-field load and containing an isotropic elastic spherical inhomogeneity with Steigmann–Ogden interface is considered. The interface is treated as a shell of vanishing thickness possessing surface tension as well as membrane and bending stiffnesses. The constitutive and equilibrium equations of the Steigmann–Ogden theory for a spherical surface are written in explicit forms. Closed-form analytical solutions are derived for two cases of loading conditions—the hydrostatic loading and deviatoric loading with vanishing surface tension. The single inhomogeneity-based estimates of the effective properties of macroscopically isotropic materials containing spherical inhomogeneities with Steigmann–Ogden interfaces are presented. It is demonstrated that, in the case of vanishing surface tension, the Steigmann–Ogden model describes a special case of thin and stiff uniform interphase layer.

FE Model of Low Grade Rubber for Modeling Housing’s Low-Cost Rubber Base Isolators

An accurate selection of strain energy function (SEF) plays a very important role for predicting the actual behavior of rubber material in the finite element analysis (FEA). The common method for selecting the SEF is by using the curve fitting procedure. However, the behavior of some typical rubbers, such as low grade rubbers (average hardness value of 47.2), cannot be predicted well by only using the curve fitting procedure. To accurately predict the actual behavior of such specifically nearly incompressible material, a series of FEA were carried out to simulate the actual behavior of four physical testing materials, namely the uniaxial, the planar shear, the equibiaxial, and the volumetric tests. This FEA is intended to examine the most suitable constitutive model in representing the rubber characteristics and behavior. From the comparisons, it can be concluded that the Ogden model provides a reasonably accurate prediction compared to the remaining investigated constitutive material models. Finally, the appropriate SEF, i.e. the Ogden model, was adopted for modeling a low-cost rubber base isolator (LCRBI) in the finite element analysis (FEA). The simple uniaxial compression test of the LCRBI is required for validating that the selected SEF works for predicting the actual behavior of LCRBI.

THE SIMULATION STUDY ON THE DEFORMATION OF RABBIT CORNEA AFTER REFRACTIVE SURGERY WITH DIFFERENT CUTTING THICKNESS

Based on the inflation tests data of rabbit cornea, finite element analysis has been applied to determine the material parameters, simulate corneal refractive surgery and study postoperative corneal deformations. The corneal profile and apical displacement data were recorded during the inflation experiment of five rabbit corneas. Inverse finite element method was applied to determine the material parameters from the corneal apical displacements. Based on the determined material parameters and the corneal profile information, we established five corneal geometry models that simulate refractive surgery with different cutting amounts. We analyzed displacements at corneal apex and cutting edge, corneal surface curvatures under different pressures. Both Ogden model ([Formula: see text]) and Yeoh model ([Formula: see text]) gave good fits to the experiment data. The maximum of error square sum between the calculated value and the experimental value of the displacements per point at the corneal profile was less than 0.06[Formula: see text]mm. For each model with the increase of pressure, the displacement at cutting edge was larger than that at corneal apex, both of them increased, and curvature radius of anterior and posterior corneal surface increased slowly, but the refractive power decreased slowly and tended to be a stable value. Under the same pressure, the larger the cutting amount, the larger the displacements at corneal apex and cutting edge with a cutting edge displacement of about 1.10 (less ablation model) and 1.02 (larger ablation model) times the corneal vertex displacement. Both Ogden model and Yeoh model can be used to describe corneal mechanical responses of inflation experiment. After refractive surgery, the displacement at cutting edge is larger than that at corneal apex, the curvature radius of anterior (posterior) corneal surface increases (decreases), and the refractive power decreases.

RESEARCH OF MAXILLARY IMPACTED CANINE IN ORTHODONTIC TREATMENT BASED ON NANOINDENTATION EXPERIMENTS

This study selected the maxillary labial impacted canine as the research object to build the model of periodontal ligament (PDL) and simulate the process of orthodontic treatment. This paper obtained stress–strain curve by calculating and analyzing the data of nanoindentation experiments. The parameters were identified through curve fittings by ABAQUS. The fitting results show that the third-order Ogden model is in good agreement with the experimental data which demonstrate that the third-order Ogden model is able to reflect the material properties of the PDL. In this paper, orthodontic process of the maxillary labial impacted canine was simulated. The results show that inside and outside surfaces of PDL all have stress variation, the stress on the root apex and dental cervix of PDL is relatively large, the maximum appears at dental cervix and the minimum appears close to tooth impedance center.