Visco-hyperelastic Constitutive Model Research Articles

Tuning the stiffness and stretchability of micro-scale-structured polymer membrane simultaneously by integrating mechanical modeling and spatiotemporal controllable photolithograph

Micro-scale structural polymer membranes with desired mechanical properties, such as modulus and stretchability, have extensive applications in repair scaffolds, stretchable electronic devices, etc., yet how to achieve the simultaneous tunability of high modulus (MPa-level) and excellent resilience in micron-scale polymer membrane remains challenge. In this work, based on the material-structure integrated design aided by mechanical modeling and photolithograph, a micro-scale-structured solid-state lithography polyurethane-urea (UVSLPU) membrane has been fabricated, achieving a wide range of controllability on elastic modulus of 25-55 MPa and stretchability of 2.7-7.6 by simultaneously controlling the exposure time and area. Based on the physical mechanism of solid-state lithography, a novel visco-hyperelastic constitutive model is developed to facilitate the quantitative tunning of the mechanical property of UVSLPU. According to the microstructure analysis, the model decomposes the free energy of UVSLPU into three components, including crosslinked network, free chains as well as dangling chains, and describes the influence of exposure time on their nonlinear evolutions through increasing chain density and reducing the number of Kuhn monomers per chain. The proposed model is validated through uniaxial tensile tests conducted at different strain rates and exposure conditions, and reveals the significant contribution of crosslinks and free chains in enhancing the modulus over exposure time. Then, by integrating constitutive modeling and spatiotemporal controllable photolithograph, the design and manufacture for the micro-scale-structured UVSLPU membrane achieving increasing stiffness without losing the stretchability is realized by precisely controlling the exposure area. This work offers a novel and efficient approach for the design and manufacture of micro-scale-structured membranes with desired mechanical properties.

Nonlinear mechanical behaviour and visco-hyperelastic constitutive description of isotropic-genesis, polydomain liquid crystal elastomers at high strain rates

The mechanical behaviour of isotropic-genesis, polydomain liquid crystal elastomers (I-PLCEs) at various strain rates is systematically investigated via experiments, theoretical analysis, and numerical modelling. Experiments encompassing SEM (scanning electron microscope), DSC (differential scanning calorimetry), TGA (thermogravimetric analyser), quasi-static and dynamic (SHPB – split Hopkinson pressure bar) mechanical tests, as well as drop-weight impact tests, are undertaken to identify the nonlinear, large-strain, rate-dependent relationship between compressive stress and deformation of the I-PLCEs studied. Subsequently, a three-dimensional compressible visco-hyperelastic constitutive model for the material is established based on the summation of Cauchy stress components. The as-used model yields good agreement with experimental data, particularly an excellent description of the mechanical responses at high strain rates of 103∼104 s−1. The fully-calibrated constitutive model is implemented in the commercial finite element code ABAQUS via a virtual user-defined material (VUMAT) subroutine. The inhomogeneous deformation processes of the I-PLCEs, corresponding to impact by a hemispherically-tipped drop weight, which induces complex stress states, are also well described. Finally, when evaluated by two dimensionless physical parameters, the I-PLCEs demonstrate a more pronounced strain rate sensitivity in terms of dynamic strength and impact toughness compared to other commonly used materials, highlighting their superior performance in dynamic loading scenarios. The present study is helpful for the design and development of impact-resistant LCE-based materials and structures.

Compressive behavior and visco-hyperelastic constitutive of polyurethane elastomer over a wide range of strain rates

Polyurethane elastomers (PUEs) will experience different strain rates in different application scenarios. Therefore, it is of great significance to study the mechanical properties of PUE under a wide range of strain rates and establish a constitutive model that considers strain rates with high accuracy and few parameters. In this study, the quasi-static and dynamic compression tests of two types of PUEs (PUE55 and PUE85) were carried out, and investigated the strain rate effect of the materials. Based on the Mooney-Rivlin hyperelastic model and the Prony series, a compressible visco-hyperelastic constitutive model for PUE was established. Different from the conventional constant relaxation time in Prony series, two relaxation times that vary exponentially with principal stretch were proposed based on the relaxation test to describe the strain rate effect of the material at low and high strain rate respectively. In addition, using the visco-hyperelastic constitutive model to obtain the model inputs of the Simplified rubber/foam model in LS-DYNA, the impact process of the Metal/PUE composite projectile was reproduced under different impact conditions through the finite element simulation. Simulation results verified the visco-hyperelastic model in generating numerical model material parameters and the rationality of the Simplified rubber/foam model in describing PUEs.

Mechanical behavior of PVA hydrogels over a wide strain rate range and a new two-phase visco-hyperelastic constitutive model

PVA hydrogels, as potential substitutes for soft biological tissues, are valuable in biomedical applications. However, studies on mechanical behavior at 100-500/s are scarce, where the inflection point of strain rate effect lies, prompting the utilization of bilinear models with inaccuracies. To improve accuracy, we developed a Hopkinson bar for ultra-soft materials and conducted experimental studies on PVA hydrogels at various strain rates. A new visco-hyperelastic model that incorporates the polymer network and water phases was developed and verified by experimental data. It captures both strain rate effects and water loss, providing insights for hydrogels and soft biomaterials.

Experimental and constitutive model investigation on the tensile mechanical properties of polyurea at wide strain-rate range

Polyurea is extensively utilized as a protective coating material for structures under impact and blast loadings, owing to its significant large tensile deformation capability and strain hardening effect. In this study, the tensile performance of polyurea was experimentally and theoretically investigated. Firstly, rational geometric shapes and dimensions were designed, and a series of quasi-static and dynamic uniaxial tensile tests were conducted to obtain the nonlinear stress-strain curves at different strain rates. The results indicated a notable strain-rate effect in polyurea, with an increase in elastic modulus and tensile stress as the strain rate increased. Moreover, as the strain rate escalates, the strain hardening effect becomes more pronounced, thereby enhancing the protective capabilities of polyurea. Subsequently, an existing hyperelastic model, namely the Mooney-Rivlin (MR) model, was modified to incorporate the strain rate effect, resulting in a non-linear visco-hyperelastic constitutive model. Furthermore, the proposed constitutive model and parameters were validated by simulating existing tensile and blast tests using the finite element (FE) program LS-DYNA. This work could provide a reference for the design of structural protection.

Compressive mechanical properties of styrene-butadiene rubber under medium-low strain rates: Experiments and modeling

Styrene-butadiene rubber (SBR) is widely employed as a cushioning material in engineering applications to resist impact loadings due to its excellent mechanical properties and energy absorption capacity. This paper aims to investigate the compressive mechanical properties and constitutive model of SBR under medium–low strain rates both experimentally and theoretically. Firstly, quasi-static and dynamic compression tests of SBR were carried out under the strain rate up to 220 s−1 using an electronic universal testing machine and a drop-weight machine, respectively. Subsequently, the effect of loading rate on mechanical properties, strain rate sensitivity and energy absorption capacity was examined. The results indicate that SBR exhibits visco-hyperelastic characteristics with reversible compression deformation and strain rate dependency, ie., the yield stress, flow stress and dynamic increase factor (DIF) increase approximately exponentially with increasing logarithmic strain rate. In addition, the SBR exhibits excellent energy absorption capacity during compression, especially under higher strain rates and larger strain levels. Finally, a visco-hyperelastic constitutive model was proposed by replacing the nonlinear spring with a hyperelastic element in Zhu-Wang-Tang (ZWT) viscoelastic constitutive model to describe the nonlinear mechanical behaviors in SBR, and an acceptable agreement between experimental results and model predictions were observed. The findings of this research can provide a valuable guide for designing and optimizing the impact resistance of SBR structures.

A visco-hyperelastic model for hydrogels with different water content and its finite element implementation

The visco-hyperelastic properties of hydrogels, which are greatly influenced by water content, play a crucial role in the potential applications in cutting-edge fields. Therefore, quantifying the effect of water content on the visco-hyperelastic behavior of hydrogels is necessary. In this work, we have proposed a visco-hyperelastic constitutive model which considers the water content for large deformation of hydrogels by introducing internal variables that can characterize the viscous dissipation. In the model, the evolution equation of the internal variable is established to achieve the coupling of viscoelastic and hyperelastic responses. To further understand the influence of water content on the visco-hyperelastic behavior of hydrogels, we modified the power-law relationship between water content and initial modulus through experiments. The accuracy of our visco-hyperelastic model is validated by uniaxial tension and relaxation experiments on hydrogels with varying water content. To facilitate the application of the constitutive model, we implement the constitutive model into ABAQUS user subroutine UMAT through constructing linear interpolation function. The results of the finite element analysis further confirm the capability of proposed model to describe the viscoelastic response of hydrogels under complex loading conditions.

Implicit multiscale finite element analysis of polymer physics-based multiscale constitutive model for elastomers

This paper proposes a multiscale visco-hyperelastic constitutive model that can predict the material behavior bridging molecular properties to response at the continuum level and its integration within implicit finite element analysis. The proposed model incorporates all parameters having actual physical meaning obtained from molecular simulations based on the tube theory. Despite the advantages that the constitutive equation was determined from molecular network characteristics, applications of the model have been restricted to the simple shape of Finite Element (FE) models with a few cases of specific deformations, owing to its complexity and absence of the implicit formulation. Therefore, the application of the model to the 3D implicit FE analysis with a tangent stiffness was proposed by applying numerical differentiation with the complex step derivative approximation (CSDA) method. Combined with the Neo-Hookean hyperelasticity model, the results from the example analysis applied to the tensile specimen model were examined to manifest the visco-hyperelastic characteristics of elastomers under cyclic loading, stability of the analysis, and further discussion on the visco-hyperelastic constitutive model were proposed.

Mechanical Behaviour of Plantar Adipose Tissue: From Experimental Tests to Constitutive Analysis.

Plantar adipose tissue is a connective tissue whose structural configuration changes according to the foot region (rare or forefoot) and is related to its mechanical role, providing a damping system able to adsorb foot impact and bear the body weight. Considering this, the present work aims at fully describing the plantar adipose tissue's behaviour and developing a proper constitutive formulation. Unconfined compression tests and indentation tests have been performed on samples harvested from human donors and cadavers. Experimental results provided the initial/final elastic modulus for each specimen and assessed the non-linear and time-dependent behaviour of the tissue. The different foot regions were investigated, and the main differences were observed when comparing the elastic moduli, especially the final elastic ones. It resulted in a higher level for the medial region (89 ± 77 MPa) compared to the others (from 51 ± 29 MPa for the heel pad to 11 ± 7 for the metatarsal). Finally, results have been used to define a visco-hyperelastic constitutive model, whose hyperelastic component, which describes tissue non-linear behaviour, was described using an Ogden formulation. The identified and validated tissue constitutive parameters could serve, in the early future, for the computational model of the healthy foot.

Effect of Resin Bleed Out on Compaction Behavior of the Fiber Tow Gap Region during Automated Fiber Placement Manufacturing.

Automated fiber placement is a state-of-the-art manufacturing method which allows for precise control over layup design. However, AFP results in irregular morphology due to fiber tow deposition induced features such as tow gaps and overlaps. Factors such as the squeeze flow and resin bleed out, combined with large non-linear deformation, lead to morphological variability. To understand these complex interacting phenomena, a coupled multiphysics finite element framework was developed to simulate the compaction behavior around fiber tow gap regions, which consists of coupled chemo-rheological and flow-compaction analysis. The compaction analysis incorporated a visco-hyperelastic constitutive model with anisotropic tensorial prepreg viscosity, which depends on the resin degree of cure and local fiber orientation and volume fraction. The proposed methodology was validated using the compaction of unidirectional tows and layup with a fiber tow gap. The proposed approach considered the effect of resin bleed out into the gap region, leading to the formation of a resin-rich pocket with a complex non-uniform morphology.

Finite Bending of Fiber-Reinforced Visco-Hyperelastic Material: Analytical Approach and FEM.

This paper presents a new anisotropic visco-hyperelastic constitutive model for finite bending of an incompressible rectangular elastomeric material. The proposed approach is based on the Mooney-Rivlin anisotropic strain energy function and non-linear visco-hyperelastic method. In this study, we aim to examine the mechanical response of a reinforced viscoelastic rectangular bar with a group of fibers under bending. Anisotropic materials are typically composed of one (or more) family of reinforcing fibers embedded within a soft matrix material. This operation may lead to an enhancement in the strength and stiffness of soft materials. In addition, a finite element simulation is carried out to validate the accuracy of the analytical solution. In this research, the well-known stress relaxation test, as well as the multi-step relaxation test, are examined both analytically and numerically. The results obtained from the analytical solution are found to be in good agreement with those from the finite element method. Therefore, it can be deduced that the proposed model is competent in describing the mechanical behavior of fiber-reinforced materials when subjected to finite bending deformations.

Modeling and experimental identification of thermo-kinetic and visco-hyperelastic coupling for semicrystalline thermoplastic continuous fiber composites subjected to processing temperatures

This paper presents a visco-hyperelastic constitutive model to characterize the temperature-dependent mechanical deformation of composite materials during thermoforming. The material of interest was a unidirectional or woven fibrous reinforcement filled with a semi-crystalline thermoplastic matrix. Based on the two laws of thermodynamics, the mechanical model was coupled with the heat equation and a crystallization kinetics model. As a result, the viscoelastic effects and exothermicity of the crystallization reaction, characteristic of the presence of the semicrystalline thermoplastic matrix, constituted internal heat sources taken into account by the heat equation. These were the first steps towards establishing a thermo-chemical–mechanical coupling. In order to validate and parameterize the present law, a thermomechanical characterization of in-plane shear was put forward.

A biomechanical perspective on perineal injuries during childbirth

Background and ObjectiveChildbirth trauma is a major health concern that affects millions of women worldwide. Severe degrees of perineal trauma, designated as obstetric anal sphincter injuries (OASIS), and levator ani muscle (LAM) injuries are associated with long-term morbidity. While significant research has been conducted on LAM avulsions, less attention has been given to perineal trauma and OASIS, which affect up to 90% and 11% of vaginal deliveries, respectively. Despite being widely discussed, childbirth trauma remains unpredictable. This work aims to enhance the modeling of the maternal musculature during childbirth, with a particular focus on understanding the mechanisms underlying the often overlooked perineal injuries. MethodsA geometrical model of the pelvic floor muscles (PFM) and perineum (including the perineal body, ischiocavernosus, bulbospongiosus, superficial and deep transverse perineal muscles) was created. The muscles were characterized by a transversely isotropic visco-hyperelastic constitutive model. Two simulations of vaginal delivery were conducted with the fetus in the vertex presentation and occipito-anterior position, with and without the perineum. ResultsThe simulation that considered the perineum exhibited higher stresses over an extended area of the PFM, which suggests that including additional structures can impact the obtained results. The maximum stretch of the urogenital hiatus was 2.94 and the maximum stress was 23.86 kPa. The perineal body reached a maximum stretch of 1.95, which was more pronounced near the urogenital hiatus, where perineal tears may occur. The external anal sphincter's transverse diameter decreased by 51% and the maximum principal stresses were observed in the area close to the perineal body, where OASIS can occur. ConclusionsThe present study emphasizes the importance of including most structures involved in vaginal delivery in its biomechanical analysis and represents another step further in the understanding of perineal injuries and OASIS. The superior region of the perineal body and its connection to the urogenital hiatus and anal sphincter have been identified as the most critical regions, highly susceptible to injury.

A Rate-Temperature-Dependent Visco-Hyperelastic Constitutive Model for UD CF/PEEK Prepregs During a One-Step Hot Stamping Forming Process

An anisotropic visco-hyperelastic constitutive model for rate-temperature-dependent deformation during one-step hot stamping forming simulation of unidirectional (UD) CF/PEEK prepregs is presented. This constitutive model is based on strain energy decomposition and a multiplicative decomposition of the deformation gradient. Two simple Maxwell models are used to characterize the viscoelastic behavior of the melted PEEK matrix and longitudinal shear deformation, respectively, and a shear invariant of [Formula: see text] is proposed to calculate the shear deformation. Moreover, the fiber stretching deformation is modeled by an anisotropic hyperelastic model. To obtain the model parameters, tensile tests at different strain rates and temperatures above the melt temperature of PEEK are performed on [Formula: see text], [Formula: see text], and [Formula: see text] CF/PEEK prepreg specimens, respectively. In parallel, the [0]8 and [45]8 curved beam specimens are experimentally fabricated to validate the constitutive model. The VUMAT subroutine is developed according to the proposed constitutive model and applied for a [Formula: see text] off-axis tensile simulation and hot-stamping forming simulation of CF/PEEK prepregs. The experimental and simulation results show that the materials flow, distribution of strain and stress, forming defects (wrinkles and overlap) of CF/PEEK curved beam can be captured by the proposed model.

An experimentally validated anisotropic visco-hyperelastic constitutive model for knitted fabric-reinforced elastomer composites

A new anisotropic visco-hyperelastic constitutive model has been developed to predict the time-dependent deformation response of flexible, knitted fabric-reinforced elastomer composites. These composites exhibit a time-dependent response due to the viscoelastic behavior of the elastomer, while the anisotropic reinforcement effect is attributed to the knitted fabrics. The proposed modeling approach features an invariant-based strain energy density function that incorporates the architecture of knitted fabrics and the hyper-viscoelastic behavior of elastomers. In this study, the elastomer is considered as a viscous neo-Hookean material, and the knitted fabrics are modeled as cords with negligible stiffness in bending. The proposed material model is implemented in commercial Finite Element Analysis (FEA) software, Abaqus (version 2017), through a user-defined material subroutine, UMAT. This approach enables the determination of the constitutive behavior of the composite based on the constituent elastomer, fiber properties, and fabric architectures. The proposed model is verified through a discrete 3D FEA model, in which the elastomer and fabric reinforcement are modeled explicitly. The approach is further validated through physical testing including uniaxial tension, torsion, and three-point bending. Since the proposed strain energy-based constitutive model can predict the deformation response of knitted fabric-reinforced elastomer composites based on the fabric architecture, it can be employed as an efficient modeling tool to aid the design of knitting pattern for target mechanical properties.

A Visco-Hyperelastic Constitutive Model to Characterize the Stress-Softening Behavior of Ethylene Propylene Diene Monomer Rubber.

Uniaxial and biaxial cyclic tensile tests and stress relaxation tests were performed on the ethylene propylene diene monomer (EPDM) material to investigate its stress-softening effect. The experimental results reveal that the EPDM material presents a significant Mullins effect during the cyclic stretching processes. Furthermore, it is found that the deformation of the EPDM material does not return to zero simultaneously with the stress, due to the viscoelasticity of the EPDM material. Therefore, this study combines pseudo-elasticity theory and viscoelastic theory to propose a visco-hyperelastic constitutive model. The proposed model is used to fit and analyze the uniaxial and biaxial cyclic test results of EPDM and a comparison is conducted with the corresponding hyper-elastic constitutive model. The results show that the proposed model is in good agreement with the experimental data and superior to the hyper-elastic constitutive model, especially when it comes to the stress-softening unloading process. This work is conducive to accurately characterizing the stress-softening behavior of rubber-like materials at large deformation and can provide some theoretical guidance for their widespread application in industry.

A visco-hyperelastic constitutive model and its application to the intestine

A visco-hyperelastic constitutive model and its application to the intestine

A Visco-hyperelastic Constitutive Model for Rubber Considering the Strain Level and One Case Study in the Sealing Packer

A Visco-hyperelastic Constitutive Model for Rubber Considering the Strain Level and One Case Study in the Sealing Packer

Research on NEPE Propellant at High Strain Rates

In order to study the mechanical properties of Nitrate Ester Plasticized Polyether (NEPE) propellant at high strain rates, the impact tests of NEPE propellant were carried out by the split Hopkinson bar, and the stress-strain curves of NEPE propellant under different strain rates ( 1500s−1-4500s−1 ) were obtained. The test results show that NEPE propellant has obvious nonlinear elasticity and strain rate sensitivity. The microstructure of NEPE propellant was observed by scanning electron microscope, and the fracture mechanism of NEPE propellant under high strain rate was obtained by analyzing the microstructure of propellant. In this paper, a nonlinear visco-hyperelastic constitutive model is adopted, in which Rivlin model and the viscoelastic model are used to describe the mechanical properties of materials. The constitutive parameters of the material were obtained by fitting the test data, and it was proved that the model could well describe the mechanical properties of NEPE propellant at high strain rates by comparing the test curve under different strain rates.

Parameter calibration and numerical algorithm realization of physically visco-hyperelastic constitutive model based on compression experiment of EPDM

Multi-constitutive models integrated with microstructure parameters are suitable to capture different rubberlike material mechanical characteristics such as large deformation, hysteresis. However, the typical models are less often adopted to analyze realistic engineering problems due to difficult derivation of numerical algorithm which can be embedded into FEM models. Therefore, we take numerical algorithm derivation of physically visco -hyperelastic constitutive model proposed by Yuhai Xiang as an application example to analyze mechanic performance of EPDM (Ethylene Propylene Diene Monomer), which is widely utilized as cushion members of rail structure. After numerical algorithm is derived, static and dynamic compression tests are designed to calibrate mechanical parameters of EPDM. Finally, FEM models integrated with above numerical algorithm and calibration parameters are established to simulate mechanical response under different boundary conditions. In comparison of results between experiments and FEM simulations, accuracy and precision of numerical iteration formula and practicality can meet demands of engineering design and application when deformation and distortion of the FEM model mesh are not severe. We hope our work can supply some inspiration and be expanded to characterize, analyze, simulate and even predict performance of other similar rubberlike materials by applying suitable constitutive models in future.