Hyperelastic constitutive relationship for the strain-rate dependent behavior of shoulder and other joint cartilages

Non-linear finite deformations of articular cartilages under physiological loading conditions can be attributed to hyperelastic behavior. This paper contains experimental results of indentation tests in finite deformation and proposes an empirical based new generalized hyperelastic constitutive model to account for strain-rate dependency for humeral head cartilage tissues. The generalized model is based on existing hyperelastic constitutive relationships that are extensively used to represent biological tissues in biomechanical literature. The experimental results were obtained for three loading velocities, corresponding to low (1x10-3 s-1), moderate and high strain-rates (1x10-1 s-1), which represent physiological loading rates that are experienced in daily activities such as lifting, holding objects and sporting activities. Hyperelastic material parameters were identified by non linear curve fitting procedure. Analysis demonstrated that the material behavior of cartilage can be effectively decoupled into strain-rate independent(elastic) and dependent parts. Further, experiments conducted using different indenters indicated that the parameters obtained are significantly affected by the indenter size, potentially due to structural inhomogeneity of the tissue. The hyperelastic constitutive model developed in this paper opens a new avenue for the exploration of material properties of cartilage tissues.

VAM applied to dimensional reduction of non-linear hyperelastic plates

This work aims at dimensional reduction of non-linear isotropic hyperelastic plates in an asymptotically accurate manner. The problem is both geometrically and materially non-linear. The geometric non-linearity is handled by allowing for finite deformations and generalized warping while the material non-linearity is incorporated through hyperelastic material model. The development, based on the Variational Asymptotic Method (VAM) with moderate strains and very small thickness to shortest wavelength of the deformation along the plate reference surface as small parameters, begins with three-dimensional (3-D) non-linear elasticity and mathematically splits the analysis into a one-dimensional (1-D) through-the-thickness analysis and a two-dimensional (2-D) plate analysis. Major contributions of this paper are derivation of closed-form analytical expressions for warping functions and stiffness coefficients and a set of recovery relations to express approximately the 3-D displacement, strain and stress fields. Consistent with the 2-D non-linear constitutive laws, 2-D plate theory and corresponding finite element program have been developed. Validation of present theory is carried out with a standard test case and the results match well. Distributions of 3-D results are provided for another test case. (c) 2012 Elsevier Ltd. All rights reserved.

A finite element framework for the interplay between delamination and buckling of rubber-like bi-material systems and stretchable electronics

In this study, a finite element (FE) framework for the analysis of the interplay between buckling and delamination of thin layers bonded to soft substrates is proposed. The current framework incorporates the following modeling features: (i) geometrically nonlinear solid shell elements, (ii) geometrically nonlinear cohesive interface elements, and (iii) hyperelastic material constitutive response for the bodies that compose the system. A fully implicit Newton–Raphson solution strategy is adopted to deal with the complex simultaneous presence of geometrical and material nonlinearities through the derivation of the consistent FE formulation. Applications to a rubber-like bi-material system under finite bending and to patterned stiff islands resting on soft substrate for stretchable solar cells subjected to tensile loading are proposed. The results obtained are in good agreement with benchmark results available in the literature, confirming the accuracy and the capabilities of the proposed numerical method for the analysis of complex three-dimensional fracture mechanics problems under finite deformations.

A finite element model of seat cushion indentation with a soft tissue human occupant model

Effective digital human model (DHM) simulation of automotive driver packaging ergonomics, safety and comfort depends on accurate modelling of occupant posture, which is strongly related to the mechanical interaction between human body soft tissue and flexible seat components. This paper presents a finite-element study simulating the deflection of seat cushion foam and supportive seat structures, as well as human buttock and thigh soft tissue when seated. The three-dimensional data used for modelling thigh and buttock geometry were taken on one 95th percentile male subject, representing the bivariate percentiles of the combined hip breadth (seated) and buttock-to-knee length distributions of a selected Australian and US population. A thigh-buttock surface shell based on this data was generated for the analytic model. A 6mm neoprene layer was offset from the shell to account for the compression of body tissue expected through sitting in a seat. The thigh-buttock model is therefore made of two layers, covering thin to moderate thigh and buttock proportions, but not more fleshy sizes. To replicate the effects of skin and fat, the neoprene rubber layer was modelled as a hyperelastic material with viscoelastic behaviour in a Neo-Hookean material model. Finite element (FE) analysis was performed in ANSYS V13 WB (Canonsburg, USA). It is hypothesized that the presented FE simulation delivers a valid result, compared to a standard SAE physical test and the real phenomenon of human-seat indentation. The analytical model is based on the CAD assembly of a Ford Territory seat. The optimized seat frame, suspension and foam pad CAD data were transformed and meshed into FE models and indented by the two layer, soft surface human FE model. Converging results with the least computational effort were achieved for a bonded connection between cushion and seat base as well as cushion and suspension, no separation between neoprene and indenter shell and a frictional connection between cushion pad and neoprene. The result is compared to a previous simulation of an indentation with a hard shell human finite-element model of equal geometry, and to the physical indentation result, which is approached with very high fidelity. We conclude that (a) SAE composite buttock form indentation of a suspended seat cushion can be validly simulated in a FE model of merely similar geometry, but using a two-layer hard/soft structure. (b) Human-seat indentation of a suspended seat cushion can be validly simulated with a simplified human buttock-thigh model for a selected anthropomorphism.

Porohyperelastic finite element model for the kangaroo humeral head cartilage based on experimental study and the consolidation theory

Solid-extracellular fluid interaction is believed to play an important role in the strain-rate dependent mechanical behaviors of shoulder articular cartilages. It is believed that the kangaroo shoulder joint is anatomically and biomechanically similar to human shoulder joint and it is easy to get in Australia. Therefore, the kangaroo humeral head cartilage was used as the suitable tissue for the study in this paper. Indentation tests from quasi-static (10-4/sec) to moderately high strain-rate (10-2/sec) on kangaroo humeral head cartilage tissues were conduced to investigate the strain-rate dependent behaviors. A finite element (FE) model was then developed, in which cartilage was conceptualized as a porous solid matrix filled with incompressible fluids. In this model, the solid matrix was modeled as an isotropic hyperelastic material and the percolating fluid follows Darcy’s law. Using inverse FE procedure, the constitutive parameters related to stiffness, compressibility of the solid matrix and permeability were obtained from the experimental results. The effect of solid-extracellular fluid interaction and drag force (the resistance to fluid movement) on strain-rate dependent behavior was investigated by comparing the influence of constant, strain dependent and strain-rate dependent permeability on FE model prediction. The newly developed porohyperelastic cartilage model with the inclusion of strain-rate dependent permeability was found to be able to predict the strain-rate dependent behaviors of cartilages.

Soft tissue human thigh and buttock finite element model to simulate vehicle seat cushion indentation

Accurate modelling of automotive occupant posture is strongly related to the mechanical interaction between human body soft tissue and flexible seat components. This paper presents a finite-element study simulating the deflection of seat cushion foam and supportive seat structures, as well as human buttock and thigh soft tissue when seated. The thigh-buttock surface shell model was based on 95th percentile male subject scan data and made of two layers, covering thin to moderate thigh and buttock proportions. To replicate the effects of skin and fat, the neoprene rubber layer was modelled as a hyperelastic material with viscoelastic behaviour. The analytical seat model is based on a Ford production seat. The result of the finite-element indentation simulation is compared to a previous simulation of an indentation with a hard shell human model of equal geometry, and to the physical indentation result. We conclude that SAE composite buttock form and human-seat indentation of a suspended seat cushion can be validly simulated.

Deep transverse metatarsal ligaments mechanical response during landing

The deep transverse metatarsal ligaments play an important role in stabilizing the metatarsal bones and manipulating foot transverse arch deformation. However, the biomechanical research about transverse metatarsal ligaments in the foot maneuver is quite few. Due to the difficulties and lack of better measurement technology for these ligaments experimental monitor, the load transfer mechanism and internal stress state also hadn't been well addressed. The purpose of this study was to develop a detailing foot finite element model including transverse metatarsal ligaments tissues, to investigate the mechanical response of transverse metatarsal ligaments during the landing condition. The transverse metatarsal ligaments were considered as hyperelastic material model was used to represent the nonlinear and nearly incompressible nature of the ligament tissue. From the simulation results, it is clearly to find that the peak maiximal principal stress of transverse metatarsal ligaments was between the third and fourth metatarsals. Meanwhile, it seems the transverse metatarsal ligaments in the middle position experienced higher tension than the sides transverse metatarsal ligaments.

Finite element analysis of deep transverse metatarsal ligaments mechanical response during landing

The deep transverse metatarsal ligaments (DTML) play an important role in stabilizing the metatarsal bones and manipulating foot transverse arch deformation. However, the biomechanical research about DTML in the foot maneuver is quite few. Due to the difficulties and lack of better measurement technology for these ligaments experimental monitor, the load transfer mechanism and internal stress state also hadn't been well addressed. The purpose of this study was to develop a detailing foot finite element model including DTML tissues, to investigate the mechanical response of DTML during the landing condition. The DTML was considered as hyperelastic material model was used to represent the nonlinear and nearly incompressible nature of the ligament tissue. From the simulation results, it is clearly to find that the peak maiximal principal stress of DTML was between the third and fourth metatarsals. Meanwhile, it seems the DTML in the middle position experienced higher tension than the sides DTML.

A study on the usefulness of Support Vector Machines for the realtime computational simulation of soft biological organs

Realistic and realtime computational simulation of soft biological organs (e.g., liver, kidney) is necessary when one tries to build a quality surgical simulator that can simulate surgical procedures involving these organs. Since the realistic simulation of these soft biological organs should account for both nonlinear material behavior and large deformation, achieving realistic simulations in realtime using continuum mechanics based numerical techniques necessitates the use of a supercomputer or a high end computer cluster which are costly. Hence there is a need to employ soft computing techniques like Support Vector Machines (SVMs) which can do function approximation, and hence could achieve physically realistic simulations in realtime by making use of just a desktop computer. Present work tries to simulate a pig liver in realtime. Liver is assumed to be homogeneous, isotropic, and hyperelastic. Hyperelastic material constants are taken from the literature. An SVM is employed to achieve realistic simulations in realtime, using just a desktop computer. The code for the SVM is obtained from [1]. The SVM is trained using the dataset generated by performing hyperelastic analyses on the liver geometry, using the commercial finite element software package ANSYS. The methodology followed in the present work closely follows the one followed in [2] except that [2] uses Artificial Neural Networks (ANNs) while the present work uses SVMs to achieve realistic simulations in realtime. Results indicate the speed and accuracy that is obtained by employing the SVM for the targeted realistic and realtime simulation of the liver.

Deformation Of Pdms Membrane And Microcantilever By A Water Droplet: Comparison Between Mooney-Rivlin And Linear Elastic Constitutive Models

In this paper, we studied the role of vertical component Of Surface tension of a water droplet on the deformation of membranes and microcantilevers (MCLs) widely used in lab-on-a-chip and micro-and nano-electromechanical system (MEMS/NEMS). Firstly, a membrane made of a rubber-like material, poly(dimethylsiloxane) (PDMS), was considered. The deformation was investigated using the Mooney-Rivlin (MR) model and the linear elastic constitutive relation, respectively. By comparison between the numerical solutions with two different models, we found that the simple linear elastic model is accurate enough to describe such kind of problem, which would be quite convenient for engineering applications. Furthermore, based on small-deflection beam theory, the effect of a liquid droplet on the deflection of a MCL was also studied. The free-end deflection of the MCL was investigated by considering different cases like a cylindrical droplet, a spherical droplet centered on the MCL and a spherical droplet arbitrarily positioned on the MCL. Numerical simulations demonstrated that the deflection might not be neglected, and showed good agreement with our theoretical analyses. (C) 2008 Elsevier Inc. All rights reserved.

Assessment of nose protector for sport activities: finite element analysis

There has been a significant increase in the number of facial fractures stemming from sport activities in recent years, with the nasal bone one of the most affected structures. Researchers recommend the use of a nose protector, but there is no standardization regarding the material employed. Clinical experience has demonstrated that a combination of a flexible and rigid layer of ethylene vinyl acetate (EVA) offers both comfort and safety to practitioners of sports. The aim of the present study was the investigation into the stresses generated by the impact of a rigid body on the nasal bone on models with and without an EVA protector. For such, finite element analysis was employed. A craniofacial model was constructed from images obtained through computed tomography. The nose protector was modeled with two layers of EVA (1 mm of rigid EVA over 2 mm of flexible EVA), following the geometry of the soft tissue. Finite element analysis was performed using the LS Dyna program. The bone and rigid EVA were represented as elastic linear material, whereas the soft tissues and flexible EVA were represented as hyperelastic material. The impact from a rigid sphere on the frontal region of the face was simulated with a constant velocity of 20 m s-1 for 9.1 mu s. The model without the protector served as the control. The distribution of maximal stress of the facial bones was recorded. The maximal stress on the nasal bone surpassed the breaking limit of 0.130.34 MPa on the model without a protector, while remaining below this limit on the model with the protector. Thus, the nose protector made from both flexible and rigid EVA proved effective at protecting the nasal bones under high-impact conditions.

Coupled Biomechanical Response of the Cornea Assessed by Non-Contact Tonometry. A Simulation Study

The mechanical response of the cornea subjected to a non-contact air-jet tonometry diagnostic test represents an interplay between its geometry, the corneal material behavior and the loading. The objective is to study this interplay to better understand and interpret the results obtained with a non-contact tonometry test. A patient-specific finite element model of a healthy eye, accounting for the load free configuration, was used. The corneal tissue was modeled as an anisotropic hyperelastic material with two preferential directions. Three different sets of parameters within the human experimental range obtained from inflation tests were considered. The influence of the IOP was studied by considering four pressure levels (10–28 mmHg) whereas the influence of corneal thickness was studied by inducing a uniform variation (300–600 microns). A Computer Fluid Dynamics (CFD) air-jet simulation determined pressure loading exerted on the anterior corneal surface. The maximum apex displacement showed a linear variation with IOP for all materials examined. On the contrary, the maximum apex displacement followed a cubic relation with corneal thickness. In addition, a significant sensitivity of the apical displacement to the corneal stiffness was also obtained. Explanation to this behavior was found in the fact that the cornea experiences bending when subjected to an air-puff loading, causing the anterior surface to work in compression whereas the posterior surface works in tension. Hence, collagen fibers located at the anterior surface do not contribute to load bearing. Non-contact tonometry devices give useful information that could be misleading since the corneal deformation is the result of the interaction between the mechanical properties, IOP, and geometry. Therefore, a non-contact tonometry test is not sufficient to evaluate their individual contribution and a complete in-vivo characterization would require more than one test to independently determine the membrane and bending corneal behavior.

Conditions for the onset of elastic and material instabilities in hyperelastic materials

Several constitutive inequalities have been proposed in the literature to quantify the notion that ‘stress increases with strain’ in an elastic material. Due to some inherent shortcomings in them, which we discuss, we propose a new tensorial criterion for isotropic materials. We also present necessary conditions in terms of elasticity tensors for the onset of elastic instabilities.