Visco-hyperelastic Constitutive Model Research Articles

A TRANSVERSELY ISOTROPIC VISCO-HYPERELASTIC CONSTITUTIVE MODEL FOR SHORT FIBER REINFORCED EPDM

Short fiber reinforced EPDM inhibitor film is a new type composite material, which has been applied in solid rocket motor winding and coating. Based on viscoelastic theory and fiber reinforced continuum mechanics theory, a transversely isotropic visco-hyperelastic constitutive model is proposed to describe strain rate dependent mechanical behaviors under vibration, impact and other loading conditions. The strain energy function is decomposed into hyperelastic strain energy and viscous strain energy, in which hyperelastic strain energy includes two parts: representing the strain energy from isotropic rubber matrix and anisotropic fiber tensile deformation. A macro-phenomenological model is proposed to characterize the viscous response from rubber matrix and fibers. Then, select the function form of each strain energy. After a series of mathematical transformation, substitution and superposition, the final form of stress and strain is determined. Moreover, the specific steps to obtain model parameters are defined. Finally, the predicted and experimental results are compared and analyzed, which indicates high accuracy of the proposed model. Studies show that it can effectively predict their nonlinear and strain rate dependent mechanical behaviors in the fiber direction from 0° to 45° at low strain rate. It is concluded that the proposed model is easy to realize finite element development, which has reference value for the structural integrity analysis of solid rocket motor.

Numerical model for healthy and injured ankle ligaments.

The aim of this work is to provide a computational tool for the investigation of ankle mechanics under different loading conditions. The attention is focused on the biomechanical role of ankle ligaments that are fundamental for joints stability. A finite element model of the human foot is developed starting from Computed Tomography and Magnetic Resonance Imaging, using particular attention to the definition of ankle ligaments. A refined fiber-reinforced visco-hyperelastic constitutive model is assumed to characterize the mechanical response of ligaments. Numerical analyses that interpret anterior drawer and the talar tilt tests reported in literature are performed. The numerical results are in agreement with the range of values obtained by experimental tests confirming the accuracy of the procedure adopted. The increase of the ankle range of motion after some ligaments rupture is also evaluated, leading to the capability of the numerical models to interpret the damage conditions. The developed computational model provides a tool for the investigation of foot and ankle functionality in terms of stress-strain of the tissues and in terms of ankle motion, considering different types of damage to ankle ligaments.

A Visco-Hyperelastic Constitutive Model for Multilayer Polymer Membranes and its Application in Packaging Air Cushion

Air cushion is an important packaging material with admirable cushion property in protecting articles from damage. Polymer membrane in air cushion renders a highly nonlinear elastic and rate dependent mechanical behavior in experimental tensile test. A visco-hyperelastic constitutive model for a polymer membrane of an air cushion is developed by additively decomposing its mechanical response into a hyperelastic portion and a viscoelastic portion. Material parameters are consecutively obtained by matching experimental data of static and dynamic uni-axial tensile tests of the membrane, respectively. Compression test of a single air column of the air cushion is conducted as a means of validation on the proposed constitutive model. By comparing simulation results with experimental data, it is shown that the proposed visco-hyperelastic model can properly characterize the mechanical behavior of the air cushion packaging material. The model can be applied to evaluate cushion performance of air cushions and their optimum design.

Experimental investigation and modeling of mechanical behaviors of polyurea over wide ranges of strain rates and temperatures

Theoretical and experimental studies on the compressive mechanical behavior of two formulations of polyurea under uniaxial stress state and quasi-one dimensional strain state are conducted over the temperature range of −40°C–+20 °C and the strain rate range of 0.001/s–12000/s. The stress–strain behavior of polyurea samples is established at different strain rates and temperatures, and key mechanical properties of the materials are determined. The experimental results show the significant sensitivity of compressive stress–strain curves of polyurea to strain rate and temperature within and beyond linear viscoelastic regime. In addition, the mechanical properties of PU605 (Versalink P-650 reacted with 105% molar equivalent Isonate 143L) are compared to those of PU105 (Versalink P-1000 reacted with 105% molar equivalent Isonate 143L). Based on the experimental results with confined pressure, a calculation method is presented which is available to study the bulk modulus of polyurea. Finally, a visco-hyperelastic constitutive model is developed to describe the nonlinear mechanical behavior of polyurea over a wide range of strain rates and temperatures.

Biomechanical behavior of bovine periodontal ligament: Experimental tests and constitutive model

A viscohyperelastic constitutive model with the use of the internal variables approach was formulated to evaluate the nonlinear elastic and time dependent anisotropic mechanical behavior of the periodontal ligament (PDL). Since the relaxation response was found to depend on the applied stretch, the adoption of the nonlinear viscous behavior in the present model was necessary. In this paper, Helmholtz free energy function was assigned to the material as the sum of hyperelastic and viscous terms which is based on the physical concept of internal variables. The constitutive model parameters were evaluated from the comparison of the proposed model and experimental data. For this purpose, tensile response of the bovine PDL samples under different stretch rates was obtained. The good correspondence between the proposed model and the experimental results confirmed the capability of the model to interpret the stretch rate behavior of the PDL. Moreover, the validity of structural model parameters was checked according to the results of the stress relaxation tests.

Rate-dependent compressive behavior of EPDM insulation: Experimental and constitutive analysis

To fully characterize the compressive behavior of ethylene propylene diene monomer (EPDM), quasi-static and dynamic compression experiments were conducted for EPDM with a universal testing machine and split Hopkinson bar (SHPB), respectively. Dynamic experimental data employing the two-wave method were used to obtain the stress–strain curves, and the dynamic results were validated. The polymer was compressed under different strain rates varying from 10−4 to 103. The results indicate that the mechanical properties of EPDM insulation are obviously dependent on the strain rate. An improved Zhu–Wang–Tang (ZWT) nonlinear visco-hyperelastic constitutive model, in which the standard elastic component was replaced by the Mooney–Rivlin hyperelastic model, was developed to predict the mechanical behaviors of EPDM under quasi-static and dynamic impact loading. The model parameters were determined by fitting the model to the experimentally obtained curves by means of the least squares method. The stress–strain curves obtained from the improved ZWT model show good agreement with the experimental curves. This research will further improve the design of the internal insulation structure in solid rocket motors.

Tension testing of silicone rubber at high strain rates

The effect of strain rate on the tension behavior of filled silicone rubber was investigated over a wide range of strain rates. A non-contact optical measurement technique was used to accurately capture the deformation information of the tensile specimen under quasi-static loading conditions. Experimental methodology to investigate the tension response of rubber-like materials at high strain rates is presented. Dynamic tensile tests were performed using a split Hopkinson tension bar (SHTB) system. Specific specimen geometry and grip connection were designed to meet the requirements of one-dimensional experimental principle in the Hopkinson bar tests. The dynamic tensile stress-strain response of silicone rubber at high strain rates up to 1400 s−1was obtained. Experiments reveal that the adopted experimental technique is reasonable for testing the tension response of soft materials at high strain rates, and the tensile behavior of silicone rubber is greatly dependent on the strain rate. The values of stiffness and nominal stress at a given elongation all increase with increased strain rate. According to the incompressible assumption, a phenomenological-based visco-hyperelastic constitutive model is proposed to describe the tensile behavior of silicone rubber over a wide range of strain rates.

Bladder tissue biomechanical behavior: Experimental tests and constitutive formulation

A procedure for the constitutive analysis of bladder tissues mechanical behavior is provided, by using a coupled experimental and computational approach. The first step pertains to the design and development of mechanical tests on specimens from porcine bladders. The bladders have been harvested, and the specimens have been subjected to uniaxial cyclic tests at different strain rates along preferential directions, considering the distribution of tissue fibrous components. Experimental results showed the anisotropic, non-linear and time-dependent stress–strain behavior, due to tissue conformation with fibers distributed along preferential directions and their interaction phenomena with ground substance. In detail, experimental data showed a greater tissue stiffness along transversal direction. Viscous behavior was assessed by strain rate dependence of stress–strain curves and hysteretic phenomena. The second step pertains the development of a specific fiber-reinforced visco-hyperelastic constitutive model, in the light of bladder tissues structural conformation and experimental results. Constitutive parameters have been identified by minimizing the discrepancy between model and experimental data. The agreement between experimental and model results represent a term for evaluating the reliability of the constitutive models by means of the proposed operational procedure.

A constitutive model for ballistic gelatin at surgical strain rates

This paper describes a constitutive model for ballistic gelatin at the low strain rates experienced, for example, by soft tissues during surgery. While this material is most commonly associated with high speed projectile penetration and impact investigations, it has also been used extensively as a soft tissue simulant in validation studies for surgical technologies (e.g. surgical simulation and guidance systems), for which loading speeds and the corresponding mechanical response of the material are quite different. We conducted mechanical compression experiments on gelatin specimens at strain rates spanning two orders of magnitude (~0.001–0.1s−1) and observed a nonlinear load–displacement history and strong strain rate-dependence. A compact and efficient visco-hyperelastic constitutive model was then formulated and found to fit the experimental data well. An Ogden type strain energy density function was employed for the elastic component. A single Prony exponential term was found to be adequate to capture the observed rate-dependence of the response over multiple strain rates. The model lends itself to immediate use within many commercial finite element packages.

A 3-D Visco-Hyperelastic Constitutive Model for Rubberwith Damage for Finite Element Simulation

A 3-D Visco-Hyperelastic Constitutive Model for Rubberwith Damage for Finite Element Simulation

A visco-hyperelastic constitutive model for human spine ligaments.

Human spine ligaments show a highly non-linear, strain rate dependent biomechanical behavior under tensile tests. A visco-hyperelastic fiber-reinforced constitutive model was accordingly developed for human ligaments, in which the energy density function is decomposed into two parts. The first part represents the elastic strain energy stored in the soft tissue, and the second part denotes the energy dissipated due to its inherent viscous characteristics. The model is applied to various human spinal ligaments including the anterior and posterior longitudinal ligaments, ligamentum flavum, capsular ligament, and interspinous ligament. Material parameters for each type of ligament were obtained by curve-fitting with corresponding experimental data available in the literature. The results indicate that the model presented here can properly characterize the visco-hyperelastic biomechanical behavior of human spine ligaments.

A thermo-mechanical large deformation constitutive model for polymers based on material network description: Application to a semi-crystalline polyamide 66

A visco-hyperelastic constitutive model, based on an original approach initially developed by (Billon, 2012) and applied to amorphous rubbery polymers for a one-dimensional formalism, was extended in this study to three-dimensional constitutive equations based on a thermodynamic framework. The model was applied to a semi-crystalline polyamide polymer, PA66. The experiments included tension and shear testing coupled with synchronized digital image correlation and infrared measurements device for capturing the time, temperature, and stress state dependence, as well as the complex thermomechanical coupling exhibited by the material under large deformation. A notion of equivalent strain rate (based on the time–temperature principle superposition) was also introduced to show its capability to build master curves and therefore decrease the number of testing needed to build a material database. The model is based on the Edward Vilgis theory (1986) and accounts for chains network reorganization under external loading through the introduction of an evolution equation for the internal state variable, η¯, representing the degree of mobility of entanglement points. The model accounting for the equivalent strain rate notion was calibrated using master curves. The thermomechanical model agreed well with the experimental mechanical and temperature measurements under tension and shear conditions. The approach developed in this study may open a different way to model the polymer behavior.

Visco-hyperelastic constitutive model for modeling the quasi-static behavior of polyurethane foam in large deformation

Flexible polyurethane foam is widely used in numerous applications such as seats and mattresses, due to its low stiffness and its ability to absorb deformation energy. The main objective of this article is to model the quasi-static mechanical behavior of three types of polyurethane foam in large deformation and to compare these three foams with three proposed models. The uniaxial compression/decompression tests at three different strain rates were performed. The test results show that the three foams present different plateau stresses, maximum stresses, and abilities to absorb energy. Moreover, polyurethane foam also presents a nonlinear hyperelastic behavior and a viscoelastic behavior in large deformation. Three viscohyperelastic models which include a hyperelastic component and a memory component are proposed to model these behaviors. Model parameters were identified using the experimental data and a proper identification method. These models were validated on these three types of foam with the aim to present comparison results. The comparison results show that Ogden’s viscoelastic modelbest agrees with the experimental results.

Constitutive formulation and numerical analysis of the biomechanical behaviour of forefoot plantar soft tissue.

The aim of this work is to provide a numerical approach for the investigation of the mechanical behaviour of the forefoot soft tissues. The development of reliable numerical models of biological structures requires the definition of constitutive formulations that actually interpret the mechanical response of the constituent biological tissues and their structural arrangement. A specific visco-hyperelastic constitutive model is provided to account for the typical features of soft plantar tissue mechanics, as geometric and material non-linearity, almost-incompressible behaviour and time-dependent phenomena. Constitutive parameters are evaluated by the analysis of experimental data from compression and stress relaxation tests on tissue samples. A three-dimensional finite element model of the forefoot region is developed starting from the analysis of biomedical images, leading to the evaluation of overall structural response. The reliability of model and analyses is assessed by the comparison of experimental and numerical results pertaining to indentation tests. The numerical model developed allows to evaluate the mechanical response of plantar soft tissue in terms of stress and strain distribution.

A visco-hyperelastic approach to modelling rate-dependent large deformation of a dielectric acrylic elastomer

In this work, a new visco-hyperelastic constitutive model is proposed to describe the rate-dependent large deformation behaviour of an acrylic elastomer. The proposed model is based on the Zener model, which consists of a hyperelastic equilibrium spring and a Maxwell element to capture rate-dependent material response. The constitutive equation is based on the history integral of Gent strain energy function. The material constants of the developed model are determined with the aid of available different rate-dependent uniaxial tensile experimental results. The proposed model is validated with the earlier published experimental results of VHB 4910 acrylic elastomer which is considered now as one of the promising actuator materials. Fittings of the proposed model with the earlier published experimental results and present experimental stress-stretch results in different strain rates are found to be in good agreement.

A transversely isotropic visco-hyperelastic constitutive model for soft tissues

A transversely isotropic visco-hyperelastic constitutive model is provided for soft tissues, which accounts for large deformations, high strain rates, and short-term memory effects. In the first part, a constitutive model for quasi-static deformations of soft tissues is presented, in which a soft tissue is simulated as a transversely isotropic hyperelastic material composed of a matrix and reinforcing fibers. The strain energy density function for the soft tissue is additively decomposed into two terms: a neo-Hookean function for the base matrix, and a polyconvex polynomial function of four invariants for the fibers. A comparison with existing experimental data for porcine brain tissues and bovine pericardium shows that this new model can well represent the quasi-static mechanical behavior of soft tissues. In the second part, a viscous potential is proposed to describe the rate-dependent short-term memory effects, resulting in a visco-hyperelastic constitutive model. This model is tested for a range of strain rates from 0.1 /s to 90 /s and for multiple loading scenarios based on available experimental data for porcine and human brain tissues. The model can be applied to other soft tissues by using different values of material and fitting parameters.

A Thermovisco-Hyperelastic Constitutive Model of NEPE Propellant Over a Large Range of Strain Rates

The uniaxial compressive mechanical curves of nitrate ester plasticized polyether (NEPE) propellant under different temperatures and strain rates have been obtained with a universal testing machine and modified split Hopkinson pressure bar (SHPB). The experimental results show that the mechanical properties of NEPE propellant are both rate dependent and temperature dependent. With decreasing temperature or increasing strain rate, the modulus and rigidity obviously increase. Based on the previous models proposed by Yang and Pouriayevali, we propose a modified viscohyperelastic constitutive model which can describe the mechanical response over a large range of strain rates. Then we add a rate-dependent temperature item into the modified model to make a thermovisco-hyperelastic constitutive model. By comparing the experimental results with the model, we find that the thermovisco-hyperelastic constitutive model can correctly describe the uniaxial compressive mechanical properties of NEPE propellant at different temperatures and over a large range of strain rates from the static state to 4500 s−1.

A visco-hyperelastic constitutive model for rubber-like materials: A rate-dependent relaxation time scheme

A three-dimensional visco-hyperelastic constitutive model is developed to describe the rate-dependent behavior of rubber-like materials at large deformations. The model encompasses a hyperelastic part which uses the “Exp–Ln” strain energy function to characterize the equilibrium response and a viscous part capturing the rate sensitivity using a hereditary integral form which links the overstress to the history of stored strain energy. A physically consistent rate-dependent relaxation time scheme is introduced which reduces the number of required material parameters and also facilitates the calibration process. The proposed model is verified using various uniaxial experimental data in different rate ranges. Furthermore, the model is incorporated via VUMAT in ABAQUS/Explicit to examine its performance in three-dimensional deformations. To this end, finite element analysis of an elastomeric bushing is performed and the results are compared to those of experiment. It is then concluded that, the proposed constitutive relations are quite efficient in predicting the behavior of rubber-like materials in different states of deformation and also in wide ranges of strain rate.

Constitutive Modeling of Time-Dependent Response of Human Plantar Aponeurosis

The attention is focused on the viscoelastic behavior of human plantar aponeurosis tissue. At this purpose, stress relaxation tests were developed on samples taken from the plantar aponeurosis of frozen adult donors with age ranging from 67 to 78 years, imposing three levels of strain in the physiological range (4%, 6%, and 8%) and observing stress decay for 240 s. A viscohyperelastic fiber-reinforced constitutive model with transverse isotropy was assumed to describe the time-dependent behavior of the aponeurotic tissue. This model is consistent with the structural conformation of the tissue where collagen fibers are mainly aligned with the proximal-distal direction. Constitutive model fitting to experimental data was made by implementing a stochastic-deterministic procedure. The stress relaxation was found close to 40%, independently of the level of strain applied. The agreement between experimental data and numerical results confirms the suitability of the constitutive model to describe the viscoelastic behaviour of the plantar aponeurosis.

A subject-specific anisotropic visco-hyperelastic finite element model of female pelvic floor stress and strain during the second stage of labor

ObjectivesTo develop an improved model representation of the biomechanics of the levator muscles during the second stage of labor and to use a sensitivity analysis to explore the pathomechanics of levator muscle injury. MethodsA subject-specific finite element model of human pelvic floor and fetal head was developed based on in vivo MRI data of a fetal head and maternal pelvis. An anisotropic visco-hyperelastic constitutive model employed material parameters estimated from biaxial tests on pelvic floor tissues. Boundary conditions reflected both anatomic constraints and the curve of Carus. A short second stage of labor, scaled to 10min, was then simulated using a single expulsive push made in the absence of levator co-contraction. ResultsLarge levator stresses occurred near the levator hiatus reaching 9MPa at the pubovisceral muscle enthesis. The dominant principal stresses were located at, and aligned with, the edge of the hiatus. Muscle stretch bordering the levator hiatus was inhomogeneous: the average levator stretch was 3.55 with a high of 4.64 at the pubovisceral muscle enthesis. Decreasing perineal body stiffness by 40%, 50%, and 60% led to reductions in the maximum principal stretch ratio at the pubovisceral muscle enthesis of 8%, 13%, and 18%, respectively. ConclusionsThe pubovisceral muscle enthesis and the muscle near the perineal body are the regions of greatest strain thereby placing them at highest risk for stretch-related injury. Decreasing perineal body tissue stiffness significantly reduced tissue stress and strain, and therefore injury risk, in those regions.