Visco-hyperelastic Material Model Research Articles

Visco-hyperelastic material model fitting to experimental stress–strain curves using a genetic algorithm and its application to soft tissue simulants

Ballistic impacts on human thorax without penetration can produce severe injuries or even death of the carrier. Soft tissue finite element models must capture the non-linear elasticity and strain-rate dependence to accurately estimate the dynamic human mechanical response. The objective of this work is the calibration of a visco-hyperelastic model for soft tissue simulants. Material model parameters have been calculated by fitting experimental stress–strain relations obtained from the literature using genetic algorithms. Several parametric analyses have been carried out during the definition of the optimization algorithm. In this way, we were able to study different optimization strategies to improve the convergence and accuracy of the final result. Finally, the genetic algorithm has been applied to calibrate two different soft tissue simulants: ballistic gelatin and styrene–ethylene–butylene–styrene. The algorithm is able to calculate the constants for visco-hyperelastic constitutive equations with high accuracy. Regarding synthetic stress–strain curves, a short computational time has been shown when using the semi-free strategy, leading to high precision results in stress–strain curves. The algorithm developed in this work, whose code is included as supplementary material for the reader use, can be applied to calibrate visco-hyperelastic parameters from stress–strain relations under different strain rates. The semi-free relaxation time strategy has shown to obtain more accurate results and shorter convergence times than the other strategies studied. It has been also shown that the understanding of the constitutive models and the complexity of the stress–strain objective curves is crucial for the accuracy of the method.

Development and Validation of a New Anisotropic Visco-Hyperelastic Human Head Finite Element Model Capable of Predicting Multiple Brain Injuries

This paper reports on the latest refinement of the Finite Element Global Human Body Models Consortium 50th percentile (GHBMC M50) adult male head model by the development and incorporation of a new material model into the white matter tissue of the brain. The white matter is represented by an anisotropic visco-hyperelastic material model capable of simulating direction-dependent response of the brain tissue to further improve the bio-fidelity and injury predictive capability of the model. The parameters representing the material were optimized by comparing model responses to seven experimentally reported strain responses of brains of postmortem human subjects (PMHS) subjected to head impact. The head model was subjected to rigorous validation against experimental data on force–deflection responses in the skull and face, intracranial pressure, and brain strain responses from over 34 PMHS head impact experiments. Crash-induced injury indices (CIIs) for facial bone fracture, skull fracture, cerebral contusion, acute subdural hematomas (ASDHs), and diffuse brain injury were developed by reconstructing 32 PMHS and real-world injury cases with the model. Model predicted maximum principal strain (MPS) and stress were determined as fracture CIIs for compact bone and spongy bones, respectively, in the skull and face. Brain responses in terms of MPS, MPS rates, and pressure distribution in injury producing experimental impacts were determined using the model and analyzed with logistic regression and survival analysis to develop CIIs for brain contusions, diffuse brain injuries, and ASDH. The statistical models using logistic regression and survival analysis showed high accuracy with area under the receiver operating curve greater than 0.8. Because of lack of sufficient moderate diffuse brain injury data, a statistical model was not created, but all indications are that the MPS rate is an essential brain response that discriminates between moderate and severe brain injuries. The authors stated that the current GHBMC M50 v.6.0 is an advanced tool for injury prediction and mitigation of injuries in automotive crashes, sports, recreational, and military environments.

Mechanical characterisation of hydrophobic and hydrophilic acrylates used in intraocular lenses through depth sensing indentation

In this work, the mechanical behaviour of hydrophilic and hydrophobic acrylates has been characterised by depth sensing indentation. Time-dependent behaviour has been studied using load-relaxation tests. Experiments have been simulated with a finite element software using a visco-hyperelastic material model. The parameters of this model have been determined using deep learning techniques. The developed material models have been used to mechanically simulate a standard compression test of a prototype intraocular lens.

Application of micro-computer tomography and inverse finite element analysis for characterizing the visco-hyperelastic response of bulk liver tissue using indentation

In-vitro mechanical indentation experimentation is performed on bulk liver tissue of lamb to characterize its nonlinear material behaviour. The material response is characterized by a visco-hyperelastic material model by the use of 2-dimensional inverse finite element (FE) analysis. The time-dependent behaviour is characterized by the viscoelastic model represented by a 4-parameter Prony series, whereas the large deformations are modelled using the hyperelastic Neo-Hookean model. The shear response described by the initial and final shear moduli and the corresponding Prony series parameters are optimized using ANSYS with the Root Mean Square (RMS) error being the objective function. Optimized material properties are validated using experimental results obtained under different loading histories. To study the efficacy of a 2D model, a three dimensional (3D) model of the specimen is developed using Micro-CT of the specimen. The initial elastic modulus of the lamb liver obtained was found to 13.5 kPa for 5% indentation depth at a loading rate of 1 mm/sec for 1-cycle. These properties are able to predict the response at 8.33% depth and a loading rate of 5 mm/sec at multiple cycles with reasonable accuracy.Article highlightsThe visco-hyperelastic model accurately models the large displacement as well as the time-dependent behaviour of the bulk liver tissue.Mapped meshing of the 3D FE model saves computational time and captures localized displacement in an accurate manner.The 2D axisymmetric model while predicting the force response of the bulk tissue, cannot predict the localized deformations.

Material characterisation of additively manufactured elastomers at different strain rates and build orientations

Material jetting, particularly PolyJet technology, is an additive manufacturing (AM) process which has introduced novel flexible elastomers used in bio-inspired soft robots, compliant structures and dampers. Finite Element Analysis (FEA) is a key tool for the development of such applications, which requires comprehensive material characterisation utilising advanced material models. However, in contrast to conventional rubbers, PolyJet elastomers have been less explored leading to a few material models with various limitations in fidelity. Therefore, one aim of this study was to characterise the mechanical response of the latest PolyJet elastomers, Agilus30 (A30) and Tango+ (T+), under large strain tension-compression and time-dependent high-frequency/relaxation loadings. Another aim was to calibrate a visco-hyperelastic material model to accurately predict these responses. Tensile, compressive, cyclic, dynamic mechanical analysis (DMA) and stress relaxation tests were carried out on pristine A30 and T+ samples. Quasi-static tension-compression tests were used to calibrate a 3-term Ogden hyperelastic model. Stress relaxation and DMA results were combined to determine the constants of a 5-term Prony series across a large window of relaxation time (10 μs–100 s). A numerical time-stepping scheme was employed to predict the visco-hyperelastic response of the 3D-printed elastomers at large strains and different strain rates. In addition, the anisotropy in the elastomers, which stemmed from build orientation, was explored. Highly nonlinear stress-strain relationships were observed in both elastomers, with a strong dependency on strain rate. Relaxation tests revealed that A30 and T+ elastomers relax to 50 % and 70 % of their peak stress values respectively in less than 20 s. The effect of orientation on the loading response was most pronounced with prints along the Z-direction, particularly at large strains and lower strain rates. Moreover, the visco-hyperelastic material model accurately predicted the large strain and time-dependent behaviour of both elastomers. Our findings will allow for the development of more accurate computational models of 3D-printed elastomers, which can be utilised for computer-aided design in novel applications requiring flexible or rate-sensitive AM materials.

VALIDATION OF THE KUMMER FRICTION MODEL FOR RUBBER COMPOUNDS ON SINUSOIDAL TRACKS BY FEA SIMULATIONS AND EXPERIMENTAL TECHNIQUES

ABSTRACT A refinement of the Kummer friction model is considered to determine the friction coefficient through analysis of the mechanical properties of rubber compound materials. An experimental sets of trials was carried out with a linear friction tester evaluating the friction coefficient for CB filled SBR on an ideal sinusoidal substrate under lubricated conditions. Lubricated conditions were chosen to obtain the pure hysteresis contribution of the friction coefficient, eliminating the effect of adhesion. For finite element analysis (FEA) simulations a visco-hyperelastic material model is considered to estimate the actual strain level close to the contact area. Based on the proper analysis of the temperature and frequency dependence behavior of experimental model rubber compounds, master curves for the viscoelastic moduli are constructed. Dynamic data were selected based on the strain level evaluated by first FEA simulations, actual temperature, and excitation frequency of each experiment. The proposed refined friction model and the simulated friction coefficient from FEA based on the precise evaluation of the material property show good prediction within the ideal experimental conditions.

Cracking in paintings due to relative humidity cycles

A numerical study is performed using the finite element method to consider the effects of low-cycle fatigue, specifically induced through relative humidity cycles on paintings. It has been identified that there are two major crack types in paintings, these being (i) an interfacial crack (delamination) between paint and support and (ii) a through-thickness (channel) crack in the paint layer itself, arresting on the interface. Therefore a 2D plane strain model for each type of crack has been created, which both consist of an alkyd paint modelled using a visco-hyperelastic material model and a primed canvas which is assumed to behave in a linear elastic manner. To account for fatigue damage in both models, cohesive elements located along the interface or through the film thickness respectively, are used and the traction-separation law has been modified to incorporate a fatigue damage parameter. It is possible to expose the models to the same relative humidity cycles, which would typically be seen in museums, enabling the prediction of time to first crack and which crack type is more readily grown in the painting.

Developing a visco-hyperelastic material model for 3D finite deformation of elastomers

In this research, using a phenomenological strain energy function, a 3D visco-hyperelastic constitutive equation for the finite deformation of elastomers is developed. For the quasi-static response, a strain energy function, composed of two exponential terms, is employed. The same energy function is considered as the kernel in the hereditary integral approach to derive the visco-hyperelastic model for the time-dependent response. To reduce the number of material parameters, an inverse power-law function between relaxation time and strain rate is proposed. Discretization of the analytical formulation of the visco-hyperelastic model in time is performed to be used in numerical simulations. This approach provides a recursive formulation to update the stress in each time step based on the deformation history. Then, the model is used to study the behavior of elastomeric bushing in radial, torsional and axial deformations. In all these cases, the material parameters are determined by applying a multi-objective optimization algorithm, in which the objective function is the difference between experimental and numerical results. The proposed visco-hyperelastic model shows accurate results for elastomers under 3D quasi-static and time-dependent loadings. Moreover, the accuracy of the results is not dependent on the amount of strain, the strain rate, and modes of deformation.

Computational simulation of static/cyclic cell stimulations to investigate mechanical modulation of an individual mesenchymal stem cell using confocal microscopy

It has been found that cells react to mechanical stimuli, while the type and magnitude of these cells are different in various physiological and pathological conditions. These stimuli may affect cell behaviors via mechanotransduction mechanisms. The aim of this study is to evaluate mechanical responses of a mesenchymal stem cell (MSC) to a pressure loading using finite elements method (FEM) to clarify procedures of MSC mechanotransduction. The model is constructed based on an experimental set up in which statics and cyclic compressive loads are implemented on a model constructed from a confocal microscopy 3D image of a stem cell. Both of the applied compressive loads are considered in the physiological loading regimes. Moreover, a viscohyperelastic material model was assumed for the cell through which the finite elements simulation anticipates cell behavior based on strain and stress distributions in its components. As a result, high strain and stress values were captured from the viscohyperelastic model because of fluidic behavior of cytosol when compared with the obtained results through the hyperelastic models. It can be concluded that the generated strain produced by cyclic pressure is almost 8% higher than that caused by the static load and the von Mises stress distribution is significantly increased to about 150kPa through the cyclic loading. In total, the results does not only trace the efficacy of an individual 3D model of MSC using biomechanical experiments of cell modulation, but these results provide knowledge in interpretations from cell geometry. The current study was performed to determine a realistic aspect of cell behavior.

Visco-hyperelastic Characterization of Polymeric Foam Materials

This article presents the visco-hyperelastic material modelling approach for open-cell polymer foams. The visco-hyperelastic material models combine the long-term hyperelastic and viscoelastic material models using finite-strain formulation. The long-term behavior is modelled using the Ogden-Hill's compressible hyperelastic model termed as “hyperfoam” in the commercial finite element software ABAQUS. The time-dependent material response is modelled by adopting the finite-strain viscoelastic formalism implemented in ABAQUS. From the visco-hyperelastic material model a closed-form stress solution for uniaxial extension is derived, which provides a more accurate parameter-fitting method to determine the visco-hyperelastic material parameters from the measurement data.

Anisotropic viscohyperelastic behavior of intervertebral discs: Modeling and experimental validation

AbstractBiomechanical investigations of human cartilage, especially intervertebral discs (IVDs), have greatly helped to improve people's health over the last several decades. The study of the underlying biomechanical characteristics of cartilage tissues is a key issue to understand its physiological function and degeneration or damage behavior. The aim of this investigation is to describe the biomechnical behavior of healthy sheep IVDs under various loading conditions. Experimental and cartilage histological data, including fiber orientation, are used to develop a viscohyperelastic material model, which allowed us to numerically study the mechanical behavior of IVDs, consisting of a cartilaginous, fiber‐reinforced ring surrounding a highly hydrated, gelatinous core. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A Stochastic Visco-hyperelastic Model of Human Placenta Tissue for Finite Element Crash Simulations

Placental abruption is the most common cause of fetal deaths in motor-vehicle crashes, but studies on the mechanical properties of human placenta are rare. This study presents a new method of developing a stochastic visco-hyperelastic material model of human placenta tissue using a combination of uniaxial tensile testing, specimen-specific finite element (FE) modeling, and stochastic optimization techniques. In our previous study, uniaxial tensile tests of 21 placenta specimens have been performed using a strain rate of 12/s. In this study, additional uniaxial tensile tests were performed using strain rates of 1/s and 0.1/s on 25 placenta specimens. Response corridors for the three loading rates were developed based on the normalized data achieved by test reconstructions of each specimen using specimen-specific FE models. Material parameters of a visco-hyperelastic model and their associated standard deviations were tuned to match both the means and standard deviations of all three response corridors using a stochastic optimization method. The results show a very good agreement between the tested and simulated response corridors, indicating that stochastic analysis can improve estimation of variability in material model parameters. The proposed method can be applied to develop stochastic material models of other biological soft tissues.

A visco-hyperelastic constitutive description of elastomeric foam

This study focuses on the constitutive modelling of finite deformation in elastomeric polyurethane foams—in particular, PORON-4701-59-25045-1648 (0.4g/cm3 density) and PORON-4701-59-20093-1648 (0.32g/cm3 density). Their mechanical properties under compression, for engineering strains up to about 80%, are characterized over a range of strain rates between 10−2 and 103/s. Dynamic compression is applied using a split Hopkinson pressure bar device. Experimental results show that the behaviour of elastomeric foam is sensitive to strain rate and can be described by a visco-hyperelastic material model. In this model, the quasi-static response is defined by compressible hyperelasticity, whereby the strain energy potential is assumed to be representable by a newly proposed polynomial series with three independent parameters. Strain rate sensitivity is characterized by incorporating a nonlinear Maxwell relaxation model with four parameters. The (seven) material parameters in the constitutive model are determined from high-speed mechanical testing methods tailored for high-compliance materials. A comparison of predictions based on the proposed frame-independent constitutive equation with experiments shows that the model is able to describe the rate dependent behaviour of the elastomeric foams examined.

A visco-hyperelastic constitutive description of elastomeric foam

This study focuses on the constitutive modelling of finite deformation in elastomeric polyurethane foams—in particular, PORON-4701-59-25045-1648 (0.4 g/cm3 density) and PORON-4701-59-20093-1648 (0.32 g/cm3 density). Their mechanical properties under compression, for engineering strains up to about 80%, are characterized over a range of strain rates between 10−2 and 103/s. Dynamic compression is applied using a split Hopkinson pressure bar device. Experimental results show that the behaviour of elastomeric foam is sensitive to strain rate and can be described by a visco-hyperelastic material model. In this model, the quasi-static response is defined by compressible hyperelasticity, whereby the strain energy potential is assumed to be representable by a newly proposed polynomial series with three independent parameters. Strain rate sensitivity is characterized by incorporating a nonlinear Maxwell relaxation model with four parameters. The (seven) material parameters in the constitutive model are determined from high-speed mechanical testing methods tailored for high-compliance materials. A comparison of predictions based on the proposed frame-independent constitutive equation with experiments shows that the model is able to describe the rate dependent behaviour of the elastomeric foams examined.