Ogden Constitutive Model Research Articles

Study on the Performance of Polyurea Anti-Seepage Spray Coating for Hydraulic Structures

The surfaces of hydraulic structures are vulnerable to damage and cracking, which can result in high-pressure reservoir water entering cracks and endangering the safety of the structures. Therefore, it is necessary to strengthen the anti-seepage treatment and protection on the surfaces of the structures. In this paper, we explore the tensile and high-water-pressure breakdown resistance properties of polyurea coating material. To do so, we independently designed and manufactured a high-water-pressure breakdown test device for coating. Our experimental results indicated that the thickness of the polyurea coating decreased with an increase in elongation. Furthermore, we found that the breakdown resistance of the polyurea coating was related to the coating thickness and the bottom free section width. We then fitted the stress–strain curve obtained from the experimental test using the Ogden constitutive model. Based on this, we numerically simulated the high-water-pressure breakdown performance of the polyurea coating using the finite element software ABAQUS 2022. We obtained the relationships among maximum displacement, free section width, and coating thickness under high water pressure. Our numerical findings indicated that the vertical displacement of the midpoint increased linearly with width in the case of the same coating thickness under water pressure load. Conversely, for the same free section width, the vertical displacement decreased with increasing coating thickness.

Polynomial chaos expansion surrogate modeling of passive cardiac mechanics using the Holzapfel–Ogden constitutive model

Cardiovascular diseases, such as heart failure and hypertrophic cardiomyopathy, may cause changes in the heart, resulting in modifications of its biomechanical response. The medical exam information is very useful but insufficient for an early diagnosis. Then, computational models and patient-specific simulations can provide new information about heart function in normal or pathological conditions. Personalized simulations usually involve parameter estimation and geometry reconstruction from medical data, which are steps subjected to many sources of uncertainties. Therefore, it is important to know how these uncertainties influence clinical quantities computed from the simulations and which inputs are responsible for this output variability. Studies of uncertainty quantification, sensitivity analysis, and parameter estimation using evaluations of the cardiac model based on partial differential equations demand a substantial computational effort, being important to find cheap alternatives for conducting these analyses. The present work proposes using Polynomial Chaos Expansion surrogate modeling to accelerate uncertainty quantification, global sensitivity analysis, and parameter estimation for the Holzapfel–Ogden model of cardiac tissue during the passive filling phase. The results showed which outputs are most impacted by uncertainties in constitutive parameters, while the SA identified which ones are the most influential and which are negligible. Finally, using surrogate models, we showed how parameter estimation could be accelerated and improved using the sensitivity analysis results via the input fixing strategy.

Regional variation in the mechanical properties of the skeletal muscle

Regional mechanics of skeletal muscle were investigated from equibiaxial testing in vitro on tissue samples. Samples were collected in three excising zones in transversal direction to the myofibers. Thus, the transverse plane stiffness, likely to be dictated by extracellular matrix collagen (ECM), was studied. For that, distal, middle, and proximal samples of healthy brachial biceps of rats have been tested. Data was used to generate the material parameters of the first order Ogden constitutive model at these different zones of skeletal muscle. In addition to having a nonlinear mechanical behavior, the analysis of the material parameters of the model showed that the stiffness value of the skeletal muscle tissue may on average have doubled depending on the collected sample location (p < 0.001). Furthermore, it was also shown that during the tests, when the storage temperature of the samples increases from 22 °C to 37 °C, the stiffness of the muscle tissue becomes more important (p < 0.05), which may be due to the rigor mortis phenomenon. Thus, these results contribute to investigating the regional change of mechanical properties of skeletal muscle, particularly those of ECM that play a major role in stiffness tissue, which is essential for the development of accurate computational models.

Establishment of constitutive model based on Ogden strain energy storage function and its matching with the mechanical properties of polyurethane dielectrics

In order to find the constitutive relationship of mechanical properties suitable for polyurethane dielectric elastomer, the constitutive model of dielectric elastomer based on Ogden strain energy storage function was established. Then taking polyether MDI polyurethane as the research object, the first-order, second-order and third-order Ogden constitutive models were fitted by the preparation and mechanical properties test of polyurethane dielectric elastomer with different soft and hard segment contents. It is found that the second-order Ogden constitutive model fits the stress-strain curve of polyurethane dielectric elastomer well, and the highest modified fitting coefficient is as high as 0.9996. At the same time, we found that the fitting effect of the third-order Ogden constitutive model is greatly affected by the soft segment content, and the fitting effect is good when the soft segment content is high, while the fitting effect of the first-order Ogden model is bad. In addition, there is no effect when the drawing rate and shape change. This is because the first-order Ogden model can be simplified into Neo Hooken model and Mooney Rivlin model, which are suitable for the mechanical behavior of small deformation range and have poor fitting for the nonlinear large deformation process of the system.

Virgin Passive Colon Biomechanics and a Literature Review of Active Contraction Constitutive Models

The objective of this paper is to present our findings on the biomechanical aspects of the virgin passive anisotropic hyperelasticity of the porcine colon based on equibiaxial tensile experiments. Firstly, the characterization of the intestine tissues is discussed for a nearly incompressible hyperelastic fiber-reinforced Holzapfel–Gasser–Ogden constitutive model in virgin passive loading conditions. The stability of the evaluated material parameters is checked for the polyconvexity of the adopted strain energy function using positive eigenvalue constraints of the Hessian matrix with MATLAB. The constitutive material description of the intestine with two collagen fibers in the submucosal and muscular layer each has been implemented in the FORTRAN platform of the commercial finite element software LS-DYNA, and two equibiaxial tensile simulations are presented to validate the results with the optical strain images obtained from the experiments. Furthermore, this paper also reviews the existing models of the active smooth muscle cells, but these models have not been computationally studied here. The review part shows that the constitutive models originally developed for the active contraction of skeletal muscle based on Hill’s three-element model, Murphy’s four-state cross-bridge chemical kinetic model and Huxley’s sliding-filament hypothesis, which are mainly used for arteries, are appropriate for numerical contraction numerical analysis of the large intestine.

Finite element analysis of silicone rubber based on Yeoh constitutive model and Ogden constitutive model

Based on the two constitutive models of Yeoh constitutive model and Ogden constitutive model, a finite element model of uniaxial compression experiment of silicone rubber was established. The stress-strain curves and stress clouds of different models of silicone rubber were compared to further verify the two models. It is found that the Ogden model (N=3, N=5) has a good fit between the stress-strain curve simulation results and the nominal stress-strain curve when there is only uniaxial compression test, and the model constant Compare solutions.

Finite element analysis of rubber material cross specimen based on ANSYS Workbench

The finite element analysis software ANSYS Workbench was used to fit and analyze the Ogden constitutive model, and the effect of the arm seam and its parameters on the stress distribution uniformity in the central test area was simulated and analyzed. The results show that different chamfering radii and the number of arm seams have an effect on the stress distribution in the center test area of the sample. The chamfering radius of 1.5mm in the center test area has a high uniformity of uniform stress distribution and a small degree of stress concentration. As the number of arm seams increases, the uniform stress distribution in the central test area increases slightly. This study can provide a reference for the preparation of standard specimens for bidirectional tensile testing of rubber materials.

Compressive behaviour of soft contact lenses and its effect on refractive power on the eye and handling off the eye.

PurposeTo investigate the stress-strain behaviour of 9 soft contact lens materials, that are commonly used in the market, under uniaxial compression loading.MethodsSeven types of hydrogel and two types of silicone-hydrogel soft contact lens materials were hydrated in phosphate-buffered saline (PBS) solution then subjected to uniaxial compression loads. The load rate was set to 16.0 N/min starting with two consecutive initial 5.0 N loading cycles followed by three relaxation periods of 4.0 min within which there were two more 5.0 N loading cycles and eventually, a full loading cycle that stopped at a load of 49.0 N. The load and contraction data obtained experimentally were analysed to derive the stress-strain behaviour. Finite Element (FE) analysis was then utilised to evaluate the performance of soft contact lenses on the human eye and handling lenses off the eye.ResultsUnlike tensile tests, all tested materials showed nonlinear behaviour when tested under compression. When fitted to first-order Ogden hyperelastic model, parameter μ was found to be varying in the range 0.12 to 0.74 MPa and material parameter α was found to be varying in the range 8.2 to 20.326 among the nine tested materials. Compression modulus of elasticity was 2.2 times higher than the tensile modulus of elasticity on average. FE simulation with nonlinear Ogden constitutive model showed a limited change (8%~12%) in the optical performance when compared to other material models, however, it predicted higher stress when the lens was simulated under bending during off-eye handling.ConclusionsCompression tests revealed slightly nonlinear behaviour when materials were strained under compression stress down to 15% ~ 30% of their nominal heights. Considering the physiological compression loading range of 8 mmHg, secant moduli of elasticity were 1.5% to 6.9% higher than the tension moduli of elasticity depending on the material. Tensile-based moduli of elasticity could be used in FE analysis as a step towards simulating the optical performance of soft contact lenses on-eye. However, nonlinear compression-based material models are recommended for FE analysis of soft contact lenses when lens-handling is investigated off-eye.

Elasto-hydrodynamic analysis of reciprocating piston seals with micro-asperities on cylinder surface

ABSTRACT The reciprocating piston seals are crucial parts in the hydraulic system, which are widely used in aerospace and military industry. A direct fluid–structure coupling method with high efficiency is proposed for solving the transient elaso-hydrodynamic-lubrication problem in the hydropneumatic suspension reciprocating piston seal system. A detailed three-dimensional fluid–structure coupling model is built using finite element discretization. Material tests are carried out to obtain the parameters of the third-order Ogden constitutive model of the rubber O-ring. The sealing performance and friction force of the sealing system are analysed for different piston speed. The critical speed from mixed lubrication to full-film lubrication is obtained. Three different micro-asperity geometries on cylinder surface are researched for their influence on piston sealing and lubrication performance.

Three-dimensional numerical simulation of soft-tissue wound healing using constrained-mixture anisotropic hyperelasticity and gradient-enhanced damage mechanics.

Healing of soft biological tissues is the process of self-recovery or self-repair after injury or damage to the extracellular matrix (ECM). In this work, we assume that healing is a stress-driven process, which works at recovering a homeostatic stress metric in the tissue by replacing the damaged ECM with a new undamaged one. For that, a gradient-enhanced continuum healing model is developed for three-dimensional anisotropic tissues using the modified anisotropic Holzapfel-Gasser-Ogden constitutive model. An adaptive stress-driven approach is proposed for the deposition of new collagen fibres during healing with orientations assigned depending on the principal stress direction. The intrinsic length scales of soft tissues are considered through the gradient-enhanced term, and growth and remodelling are simulated by a constrained-mixture model with temporal homogenization. The proposed model is implemented in the finite-element package Abaqus by means of a user subroutine UEL. Three numerical examples have been achieved to illustrate the performance of the proposed model in simulating the healing process with various damage situations, converging towards stress homeostasis. The orientations of newly deposited collagen fibres and the sensitivity to intrinsic length scales are studied through these examples, showing that both have a significant impact on temporal evolutions of the stress distribution and on the size of the damage region. Applications of the approach to carry out in silico experiments of wound healing are promising and show good agreement with existing experiment results.

Direct fluid–structure coupling analysis of reciprocating series seals in hydropneumatic suspension

The reciprocating piston seals are crucial parts in hydraulic system, which are widely used in aerospace and military industry. A direct fluid–structure coupling method with high efficiency is proposed for solving the transient Elaso-Hydrodynamic-Lubrication problem in float piston series seal system of hydropneumatic suspension. The method is validated by theory solution of a simple pad-bearing film model. Detailed three-dimensional fluid–structure coupling model of the seal system is built using finite element discretization. Rubber material tests are carried out to obtain parameters of the third-order Ogden constitutive model for the O-ring seal. The sealing performance and friction force of the complicated series seal system are analyzed with direct fluid–structure dynamic coupling simulation in high pressure and high speeds conditions. The critical speed from mixed lubrication to full film lubrication is obtained. The fluid velocity and pressure distribution in the sealing gap along axial direction is compared. The outlet volume flux leakage in different piston speeds and inlet pressures is calculated to evaluate the sealing performance. The friction force experiment for the float piston system is carried out in various speeds. The friction force from direct fluid–structure interface simulation coincides well with the test result.

Fluid-Structure Coupling Analysis of Non-linear Reciprocating Piston Seals in Series

The reciprocating piston seals are crucial parts in hydraulic system which are widely used in aerospace and military industry. A direct fluid-structure coupling method with high efficiency is proposed for solving the transient Elaso-Hydrodynamic-Lubrication (EHL) problem in hydropneumatic suspension reciprocating piston seal system. Detailed 3D fluid-structure coupling model is built using finite element discretization. Material tests are carried out to obtain the parameters of the 3rd-oder Ogden constitutive model of the rubber O-ring. The sealing performance and friction force of the sealing system are analyzed in different piston speed. The critical speed from mixed lubrication to full film lubrication is obtained.

Pseudo-Elastic Analysis with Permanent Set in Carbon-Filled Rubber

Via cyclic loading and unloading tests of natural/styrene-butadiene rubber (NSBR) blends at room temperature, the effects of the stretching, rate, temperature, and volume fraction of carbon black in the filled rubber on a permanent set (residual strain) were studied. The results showed that increasing the stretching, rate, and volume fraction of carbon black and reducing the temperature yielded greater residual strain. The uniaxial tensile behaviors of composites with the Mullins effect and residual strain were simulated using the ABAQUS software according to the aforementioned data. An Ogden-type constitutive model was derived, and the theory of pseudo-elasticity proposed by Ogden and Roxburgh was used in the model. It was found that the theory of pseudo-elasticity and the Ogden constitutive model are applicable to this composite, and if combined with plastic deformation, the models are more accurate for calculating the residual strain after unloading.

Pseudo Elastic Analysis of Carbon Reinforced Natural/Styrene-Butadiene Blend Rubber (NSBR) with Ogden Constitutive Model

In this paper, experimental results that illustrate stress softening in carbon filled natural/styrene-butadiene blend rubber (NSBR) together with Mullins effect are introduced firstly. Then, based on these data, the Ogden constitutive model is derived. The theory of pseudo-elasticity is used in the model. It is found that theory of pseudo-elasticity and Ogden constitutive model is applicable in this composite.

Material Properties of Natural Rubber Solid Tires for Finite Element Analysis

The three natural rubber compounds of solid tires producing were performed the mechanical property test. The constitutive model of each material tire layer was determined by the curve fitting method of the true stress-strain characteristic results. The Ogden constitutive model was the most suitable material model for all layers of solid tires. It had the precise R2 result comprising of 0.990, 0.988 and 0.989 for the internal, middle and tread layer of solid tires, respectively. Subsequently, the material model was implemented for the finite element method (FEM) to test the rubber specimens. The FEM obtained an average error of 7.84%. Finally, the compression load test on solid tires was performed both FEM and physical experiment. The solid tire model with the Ogden constitutive model had a good agreement with the experimental data and obtained an average difference of 2.27 mm for the vertical deformation under compression test.

Material Characteristic for Capability Analysis of Solid Tire by Finite Element Method

The natural rubber compound of each layer of solid tire had determined the mechanical properties in tension. It was found that the stress-strain relation of each material tire layer was fitted very well with the Ogden constitutive model. The R2 which was 0.986, 0.996 and 0.985 represented the certain curve fitting on the internal, middle and tread layer of solid tire, respectively. Subsequently, the Ogden model was implemented in the finite element model of the rubber specimen and solid tire. The finite element analysis results obtained an average error of 18.00% and 14.63% for the specimen and solid tire model by comparing to the physical experiment, respectively. Particularly, the mechanical properties of the natural compounds could be used to predict the ultimate compression load for the solid tire failure.

Uncertainty quantification for constitutive model calibration of brain tissue.

The results of a study comparing model calibration techniques for Ogden's constitutive model that describes the hyperelastic behavior of brain tissue are presented. One and two-term Ogden models are fit to two different sets of stress-strain experimental data for brain tissue using both least squares optimization and Bayesian estimation. For the Bayesian estimation, the joint posterior distribution of the constitutive parameters is calculated by employing Hamiltonian Monte Carlo (HMC) sampling, a type of Markov Chain Monte Carlo method. The HMC method is enriched in this work to intrinsically enforce the Drucker stability criterion by formulating a nonlinear parameter constraint function, which ensures the constitutive model produces physically meaningful results. Through application of the nested sampling technique, 95% confidence bounds on the constitutive model parameters are identified, and these bounds are then propagated through the constitutive model to produce the resultant bounds on the stress-strain response. The behavior of the model calibration procedures and the effect of the characteristics of the experimental data are extensively evaluated. It is demonstrated that increasing model complexity (i.e., adding an additional term in the Ogden model) improves the accuracy of the best-fit set of parameters while also increasing the uncertainty via the widening of the confidence bounds of the calibrated parameters. Despite some similarity between the two data sets, the resulting distributions are noticeably different, highlighting the sensitivity of the calibration procedures to the characteristics of the data. For example, the amount of uncertainty reported on the experimental data plays an essential role in how data points are weighted during the calibration, and this significantly affects how the parameters are calibrated when combining experimental data sets from disparate sources.

Quantifying Variability in Lumbar L4-L5 Soft Tissue Properties for Use in Finite-Element Analysis

Soft tissue structures of the L4-L5 level of the human lumbar spine are represented in finite-element (FE) models, which are used to evaluate spine biomechanics and implant performance. These models typically use average properties; however, experimental testing reports variation up to 40% in ligament stiffness and even greater variability for annulus fibrosis (AF) properties. Probabilistic approaches enable consideration of the impact of intersubject variability on model outputs. However, there are challenges in directly applying the variability in measured load–displacement response of structures to a finite-element model. Accordingly, the objectives of this study were to perform a comprehensive review of the properties of the L4-L5 structures and to develop a probabilistic representation to characterize variability in the stiffness of spinal ligaments and parameters of a Holzapfel–Gasser–Ogden constitutive material model of the disk. The probabilistic representation was determined based on direct mechanical test data as found in the literature. Monte Carlo simulations were used to determine the uncertainty of the Holzapfel–Gasser–Ogden constitutive model. A single stiffness parameter was defined to characterize each ligament, with the anterior longitudinal ligament (ALL) being the stiffest, while the posterior longitudinal ligament and interspinous ligament (ISL) had the greatest variation. The posterior portion of the annulus fibrosis had the greatest stiffness and greatest variation up to 300% in circumferential loading. The resulting probabilistic representation can be utilized to include intersubject variability in biomechanics evaluations.

Determination of Mechanical Properties of Rat Aorta Using Ring-Shaped Specimen

Ring-shaped specimen is commonly used in tests for determination of mechanical properties for arteries in hoop direction, especially for small mammals such as rats or mice. Although ring test is a lot more convenient than the tests concerning strip specimens, interpretation of the experimental data might be inconclusive – it is difficult distinguish whether it's still straightening up or the actual tension begins. The basic problem is to properly define initial length of specimen, which is essential for strain calculation. The purpose of this study was to evaluate various methods for strain evaluation. Ten Wistar Albino Glaxo male rats (3 months old, body weight about 200g) were sacrificed by decapitation and arteries were immediately removed. Three specimens, each approximately 2–3mm long, from each rat were excised adjacent to the aortic arch. Couple different initial lengths, as well as Digital Image Correlation based extensometer results were used for strain-stress response calculations. In addition a 3D Finite Element model, with an Ogden constitutive model based material, was made for deeper investigation of specimen behavior. This study has shown that the testing procedure for determination of mechanical properties of arteries, based on ring-shaped specimen, is prone to errors. Stiffness calculations are very sensitive to the choice of initial length of the specimen. As the use of DIC proved to give very good correlation with experimental data this method will be used in further studies.

Uniaxial Stress-Strain Characteristics of Elastomeric Membranes: Theoretical Considerations, Computational Simulations, and Experimental Validation

This study presents an experimental methodology for the uniaxial stress-strain characterization of urethane and polyvinyl-alcohol (PVA) samples, and compares elicited results with an image-based methodology, simulations, and theory. Elicited results at 40% strain yield error differences between the experimentally measured and the simulated strain of −10 and −20% for the urethane and PVA samples, respectively. The corresponding stress differences were −22 and 11%. Experimental stress-strain responses were fitted using a piecewise linear model (urethane) and using a two-parameter Ogden constitutive model (PVA), based on the over-parameterization criterion. This work directly compares experimental and computational methodologies for the characterization of bio-materials and quantifies the elicited errors.