Nonlinear Viscoelastic Material Research Articles

Modeling of the Stress-Strain Quality of Hydroentangled Nonwoven Fabrics

Hydroentanglement is a mechanical bonding process designed to produce nonwoven fabrics with appearances and textures that resemble woven and knitted fabrics. Eleven samples of hydroentangled nonwoven fabrics with different compositions and weights were subjected to a series of uniaxial stress-strain tests. Models, ranging from the simple Kelvin to the more complicated Kelvin–Vangheluwe, were fitted to the experimental data to find a generalized and universal model. In this model, a nonwoven fabric was considered a nonlinear viscoelastic material. The combination of Kelvin and Vangheluwe models resulted in an excellent fit to the uniaxial stress-strain curves. The model-predicted results almost overlapped with the experimental data, an indication of its excellent accuracy in predicting the mechanical behavior of nonwoven fabrics.

Treatment of inelastic material models within a dynamic ALE formulation for structures subjected to moving loads

AbstractThis article showcases the development of a dynamic Arbitrary Lagrangian Eulerian (ALE) formulation to account for inelastic material models within a finite element framework. Such a formulation is commonly utilized in research domains like fluid mechanics, fluid‐structure interaction, quasi static remeshing techniques, and quasi static load movement. The work at hand describes the application of the ALE formulation to efficiently analyse structures subjected to moving loads in the field of transient inelastic solid mechanics. In particular, structures such as pavements, gantry crane girders etc., which are subjected to moving loads, can be numerically simulated, and their transient response in the relevant region around the load can be obtained without relying on moving loads. The focus of this article is to facilitate the treatment of history variables stemming from inelastic material models. Of particular interest is the advection procedure required to transport the history variables through the mesh, as the material appears to flow through it. The mathematical framework necessary to treat this advection process is described in detail, considering a nonlinear viscoelastic material model on a neo‐Hookean base at finite deformations. Then, four methods for numerically achieving the advection are implemented within a transient finite element ALE formulation. These methods are compared against each other, and additionally with the conventional Lagrangian method for validation. The results demonstrate satisfactory agreement with conventional simulation methods, while offering a significant improvement in terms of computation speed. With the work at hand, the dynamic response of inelastic materials subjected to moving loads can be numerically simulated in a computationally efficient manner.

Numerical approximation for algorithmic tangent moduli for nonlinear viscoelastic model with CSDA method

This work revisits the notion of complex step derivative approximation (CSDA) and presents its use in constitutive model of a class of nonlinear viscoelastic materials. The effectiveness of a CSDA is evaluated by putting it through a series of straightforward examples. After that, the idea of the CSDA is put to use in order to carry out a numerical evaluation of the algorithmic tangent moduli of a viscoelastic constitutive model. The performance of the constitutive models is evaluated through the use of three different numerical tests, and the results are compared to those that were achieved by the application of an analytical method. In comparison to other numerical differentiation techniques, It has been found that the CSDA scheme is the most computationally efficient and robust method of numerical differentiation, regardless of the size of the finite difference interval.

Stress and Strain Characteristics in Flexible Pavement Using Three-Dimensional Nonlinear Finite Element Analysis

AbstractA new numerical simulation was developed to obtain various structural parameters by employing a nonlinear finite element method using ABAQUS: stress, strain, and the displacement response of five layers on the flexible pavement. The primary purpose of this study was to develop a new simulation that can accurately and effectively characterize stress and strain problems in flexible pavement. New constitutive model equations were developed based on Hooke’s law the three-dimensional model for stress and strain. 40 kN wheel load was used to represent a set of dual tires, assuming a uniformly distributed contact area between the tire-pavement surfaced using linear viscoelastic and nonlinear viscoelastic materials. Four tire-inflation pressures were used 380, 490, 630, and 700 kPa. Results indicated that each flexible pavement layer created with a nonlinear viscoelastic material exhibited a 40% vertical plastic strain reduction compared to linear viscoelastic materials after 7000 s and repeated for 30,000 cyclic loadings. The implication of this newly developed constitutive model was verified against published experimental data. Analyses were completed to simplify the results model results considering the effects of stress and strain on flexible pavement layers. The newly developed constitutive model for solving stress and strain characterization problems can predict the effects on flexible pavement layers and various types of observed flexible pavement failure.

Sensitivity analysis of truck tire tread material properties for on-road applications

This research delves into the sensitivity analysis of a truck tire rubber compound concerning its impact on tire–road interaction characteristics. Initially, the study employs finite element analysis to model a 315/80R22.5 truck tire, which is subsequently validated through static and dynamic response assessments via various simulation tests. Following validation, the established tire model is utilized to conduct a sensitivity analysis of the tire rubber compound specifically applied on the tread. This analysis encompasses several material definitions, including Mooney–Rivlin, visco-Mooney–Rivlin, linear viscoelastic, and nonlinear viscoelastic materials. By exploring the effects of these material models, the research scrutinizes their influence on tire–road interaction characteristics across diverse operating conditions. The tire–road interaction characteristics include the rolling resistance coefficient, and the cornering force at operating conditions including the longitudinal speed, vertical load, and slip angle. This comprehensive investigation offers insights into the intricate relationship between tire composition and performance, thereby enhancing our understanding of tire behavior and informing potential advancements in tire technology.

A thermo-mechanically coupled constitutive model for semi-crystalline polymers at finite strains: Mechanical and thermal characterization of polyamide 6 blends

In the field of material modeling, thermoplastic polymers are often studied because of their complex material behavior and their prevalence in industry applications due to their low cost and wide range of applications. Nowadays, where reusability becomes more and more important, materials which can undergo reversible thermomechanical deformations are appealing for, e.g., the construction of car body components. To predict such complex forming processes with multiple influencing factors, such as temperature, strain rate or underlying material morphology, model formulations are needed that account for these influences simultaneously and are validated against experimental data. Unfortunately, up to now only a few contributions are available which consider all these phenomena. In addition, the range of process parameters considered is often narrow due to the experimental effort required for testing. This usually results in limited predictive capabilities of the model. To overcome these limitations, in this work, a thermo-mechanically coupled material model is developed that accounts for the underlying morphology in terms of the degree of crystallinity (DOC). The model formulation is derived in a thermodynamically consistent manner, incorporating coupled nonlinear visco-elastic and elasto-plastic material behavior at finite strains. To characterize and further validate the model, mechanical as well as thermal experiments are conducted for polyamide 6 (PA6). Here, a blending strategy of PA6 together with an amorphous co-polymer is introduced during specimen production to achieve a wider range of stable DOCs(approximately 15%). The model formulation is successfully applied to experimental results and its predictions are in good agreement with experimental observations.

Performance Evaluation of Nonlinear Viscoelastic Materials using Finite Element Method

This research paper applies the finite element method as a methodology to evaluate the structural performance of nonlinear viscoelastic solids. A finite element algorithm was built and developed to simulate the mathematical nonlinear viscoelastic material behavior based on incremental constitutive equations. The derived Equation of the incremental constitutive included the complete strain and stress histories. The Schapery’s nonlinear viscoelastic material model was integrated within the displacement-based finite element environment to perform the analysis. A modified Newton-Raphson technique was used to solve the nonlinear part in the resultant equations. In this work, the deviatoric and volumetric strain–stress relations were decoupled, and the hereditary strains were updated at the end of each time increment. It is worth mentioning that the developed algorithm can be effectively employed for all the permissible values of Poisson’s ratio by using a selective integration procedure. The algorithm was tested for a number of applications, and the results were compared with some previously published experimental results. A small percentage error of (1%) was observed comparing the published experimental results. The developed algorithm can be considered a promising numerical tool that overcomes convergence issues, enhancing equilibrium with high-accuracy results.

Viscoelasticity of hydrating shotcrete as key to realistic tunnel shell stress assessment with the New Austrian Tunneling Method

The New Austrian Tunneling Method (NATM) essentially rests on observational information concerning displacements measured in selected positions at the inner surface of shotcrete tunnel shells. The combination of these measurements with advanced material and structural mechanics, in the course of so-called hybrid methods, have successfully delivered, for more than 20 years, practically relevant estimations of internal and external forces and corresponding degrees of utilization. The reliability of the latter, however, may crucially depend on the used material model. Based on a recently proposed analytical structural mechanics model [Acta Mech 233, 2989–3019 (2022)], and focusing on the benchmark example of measurement cross section MC1452 of the Sieberg tunnel, driven in the 1990s in Miocene clay marl, the present paper compares the estimations of forces and degrees of utilization arising from differently refined constitutive concepts, namely (i) aging elasticity, (ii) aging linear viscoelasticity, and (iii) aging nonlinear viscoelasticity. It turns out that only the consideration of aging nonlinear viscoelastic material behavior provides access to realistic values for the degree of utilization, being lower than one. Simpler material models would indicate local material failure, which was not observed in situ.

Transient analysis of trusses considering nonlinear elastic and viscoelastic material models

Transient analysis of trusses considering nonlinear elastic and viscoelastic material models

A mechanics-informed deep learning framework for data-driven nonlinear viscoelasticity

A mechanics-informed, data-driven framework for learning the constitutive law of a nonlinear viscoelastic material from stress–strain data using deep artificial neural networks (ANNs) is proposed. In this framework, each ANN architecture is designed and its input and output are selected such that fundamental laws of mechanics and thermodynamics relevant to nonlinear viscoelasticity are strongly satisfied by the resulting data-driven constitutive model. The framework itself extends a previously developed mechanics-informed methodology for the data-driven constitutive modeling of nonlinear elasticity to account for the dependence of the stress on the entire strain history. It is grounded in an additive decomposition of the strain energy density and an internal variable approach to viscoelasticity. Collectively, these are characterized by three potentials whose ANN representations are taught the second law of thermodynamics, various stability conditions, consistency (preservation of rigid body modes), and the recovery of elastic limits. The proposed mechanics-informed deep learning framework for data-driven nonlinear viscoelasticity is illustrated and its performance is assessed for one academic problem where synthetic data is generated by a nonlinear convolution; a coupon-level application associated with a multi-scale homogenization of a viscoelastic woven fabric material; and two representative finite element analyses performed using the material law generated during the previous application, to highlight different features of the framework.

Rubber Comprehensive Constitutive Equation and the Prediction of Tire Temperature and Rolling Resistance

ABSTRACT Cooler running tires with a reduced rolling resistance is a consideration for both tire makers and automotive original equipment manufacturers. To investigate the mechanics of energy loss and temperature rise, a nonlinear viscoelastic model suitable for numerical analysis of rolling tires is developed and demonstrated. The rubber compounds are represented as nonlinear viscoelastic materials with temperature and frequency, strain, and strain history–dependent response. Several applications to different tire designs are provided to demonstrate the impact of this new material constitutive law in improving the quality of the numerical predictions over other methods. One application is a rolling tire model that was used to delineate the tire temperature distribution and the resultant rolling resistance for different three-dimensional tread patterns.

Modeling stress relaxation under conditions of cyclic deformation of nonlinear viscoelastic materials using the Heaviside function

The problem of calculating the stress relaxation of nonlinear viscoelastic materials under conditions of cyclic deformation is considered, which is given in the form of cyclic alternations of loading and unloading of equal amplitude in rectangular cycles, while the duration of half-cycles of loading and unloading coincide. The load program is implemented in the form of a sequence of elementary loads, which is specified using Heaviside's unit functions. A nonlinear creep model with time-independent nonlinearity of the Rabotnov model is used to describe the deformation process. The heredity kernels are given by Rabotnov's fractional-exponential function.

Existence and uniqueness for a viscoelastic Kelvin–Voigt model with nonconvex stored energy

We consider nonlinear viscoelastic materials of Kelvin–Voigt-type with stored energies satisfying an Andrews–Ball condition, allowing for nonconvexity in a compact set. Existence of weak solutions with deformation gradients in [Formula: see text] is established for energies of any superquadratic growth. In two space dimensions, weak solutions notably turn out to be unique in this class. Conservation of energy for weak solutions in two and three dimensions, as well as global regularity for smooth initial data in two dimensions are established under additional mild restrictions on the growth of the stored energy.

Experimental characterization and phenomenological modeling of nonlinear viscoelasticity, plasticity and damage of continuous carbon fiber-reinforced thermoplastics

The presented work addresses the experimental characterization and phenomenological modeling of the complex rate dependent mechanical response of continuous fiber-reinforced thermoplastics (cFRTP). The theoretical basis is given by the concept of an equilibrium curve of the material which provides a comprehensive framework for separating the mechanical response into a rate dependent overstress and a rate independent equilibrium stress. In long-term creep and relaxation tests, it is shown that relaxation tests provide several advantages over creep tests when determining the equilibrium response. A stepwise loading–unloading relaxation (SR) test is proposed which makes it possible to extract nonlinear viscoelasticity, damage and plasticity present in the material from a single test. The application to cFRTP is exemplified by using the proposed method for the experimental characterization of a continuous carbon fiber-reinforced polycarbonate (CF-PC). Based on the obtained experimental data, a phenomenological material model is developed which describes the mechanical response of a unidirectional ply. The model consists of an overstress branch addressing the nonlinear viscoelastic material response and an equilibrium branch that utilizes a coupled damage-plasticity approach. After calibrating the model using the experimental data, it is shown that the proposed model is able to accurately reproduce the mechanical response of cFRTP.

Thermomechanical response of nonlinear viscoelastic materials

In this article, the thermomechanical properties of the classical and nonclassical viscoelastic materials with particular emphasis on the entropy are studied in the framework of continuum thermodynamics. Specifically, considering the Clausius integral as “Part I” of the second law of thermodynamics in the classical formulation of continuum thermodynamics, the entropy function for various classes of nonclassical thermo-viscoelastic materials is shown to exist. This is achieved by employing the first law of thermodynamics and a scalar potential known as the Helmholtz free energy function. In addition, another function known as the internal rate of production of entropy defined for the classical and nonclassical thermo-viscoelastic materials is adopted to obtain a balance law for the entropy. Finally, upon linearizing the theory, a coupled system of differential equations is obtained for the nonclassical thermo-viscoelastic materials, which under some special circumstances, permits propagation of damped harmonic waves in the viscoelastic medium.

A non-linear viscoelastic material model with progressive damage based on microstructural evolution and phase transition in polycrystalline ice for design against ice impact

This study presents a nonlinear viscoelastic material model incorporating a progressive damage framework with an iterative algorithm for glacial/freshwater polycrystalline ice subject to compressive impact load induced by ice-structure interaction. The damage model accounts for microcracking, dynamic recrystallisation, pressure melting, and high-shear elastic failure with a pressure- and rate-dependent convex failure locus. The constitutive laws are written in Fortran and implemented as a vectorised user material (VUMAT) in Abaqus with three different numerical methods, Lagrangian FEM, coupled FEM-SPH, and ALE-FEM. The constitutive model together with the implemented numerical methods are validated against two different types of laboratory-scale physical tests, indentation of cone-shaped ice and triaxial creep. The proposed model implemented with the coupled FEM-SPH method enables simulation of the cyclic transition from solid-like intact ice to the fluid-like pulverised/granular substance, progressively extruded with viscous rheology.

Nonlinear viscoelastic analysis based on dual neural networks

Due to the complexity of materials, the mechanical analysis of viscoelastic problems becomes relatively difficult, so it has been widely concerned by scholars. Although the linear viscoelastic theory has been improved, there are still a lot of problems to be solved in the study of nonlinear theory and effective numerical methods. In this paper, the nonlinear viscoelastic problem is solved by the viscoelastic correspondence principle. In order to construct the nonlinear viscoelastic constitutive relation, the method of solving the elastic mechanics problem with dual neural network is presented, and the instantaneous stress and strain components in the nonlinear viscoelastic constitutive relation are calculated. Aiming at the problem that unknown parameters in the relaxation modulus fitting model are difficult to obtain, a custom neural network fitting method is introduced to fit the relaxation modulus. Dual neural network integral method is used to solve the integral problem in viscoelastic constitutive relation, the present stress and strain of a class of nonlinear viscoelastic materials are obtained, and the nonlinear viscoelastic problem is solved. Numerical examples show that the proposed method is an efficient and high-precision method for solving nonlinear viscoelastic problems.

Investigation of the relationship between tensile viscoelasticity and unloaded ultrasound shear wave measurements in ex vivo tendon

Mechanical properties of biological tissues are of key importance for proper function and in situ methods for mechanical characterization are sought after in the context of both medical diagnosis as well as understanding of pathophysiological processes. Shear wave elastography (SWE) and accompanying physical modelling methods provide valid estimates of stiffness in quasi-linear viscoelastic, isotropic tissue but suffer from limitations in assessing non-linear viscoelastic or anisotropic material, such as tendon. Indeed, mathematical modelling predicts the longitudinal shear wave velocity to be unaffected by the tensile but rather the shear viscoelasticity. Here, we employ a heuristic experimental testing approach to the problem to assess the most important potential confounders, namely tendon mass density and diameter, and to investigate associations between tendon tensile viscoelasticity with shear wave descriptors. Small oscillatory testing of animal flexor tendons at two baseline stress levels over a large frequency range comprehensively characterized tensile viscoelastic behavior. A broad set of shear wave descriptors was retrieved on the unloaded tendon based on high frame-rate plane wave ultrasound after applying an acoustic deformation impulse. Tensile modulus and strain energy dissipation increased logarithmically and linearly, respectively, with the frequency of the applied strain. Shear wave descriptors were mostly unaffected by tendon diameter but were highly sensitive to tendon mass density. Shear wave group and phase velocity showed no association with tensile elasticity or strain rate-stiffening but did show an association with tensile strain energy dissipation.The longitudinal shear wave velocity may not characterize tensile elasticity but rather tensile viscous properties of transversely isotropic collagenous tissues.

Multi-scale constitutive model of human trabecular bone

The present study aims to formulate a new multiscale constitutive model of human trabecular bone. The trabecular bone was modelled as a nonlinear viscoelastic material. The viscoelastic effects of single trabeculae were considered by means of a hereditary integral in which stress depends on time and strain, while the elastic response was described by the hyperelastic Mooney–Rivlin model. The cuboid bone sample was extracted from the femoral head during the hip replacement surgery. The material constants in the constitutive equation were identified based on the stress relaxation test performed on the cuboid sample and the microindentation tests performed on trabeculae using the curve-fitting procedure. The microindentation tests were performed using a spherical tip instead of Vickers or Berkovich tip to minimize plastic effects during trabecular deformation. In order to validate formulated constitutive model, results from a FE simulation of stress relaxation test and uniaxial compression test were compared to the results of the corresponding experiments conducted on a macroscopic bone sample. Good agreement was observed between numerical and experimental results. The viscoelastic behaviour predicted by the proposed constitutive equation corresponds well to the response of human trabecular bone under various types of load conditions. This demonstrates the high ability of our constitutive model to simulate the behaviour of trabecular bone on a micro- and macroscopic scale. Thus, we conclude that the model, which was formulated for a single trabecula, can be successfully applied to simulate mechanical behaviour of the tissue in a macroscale.

Mechanical Behavior of Human Cancellous Bone in Alveolar Bone under Uniaxial Compression and Creep Tests.

In the process of orthodontic treatment, the remodeling of cancellous bone in alveolar bone (in this paper, cancellous bone in alveolar bone is abbreviated as CBAB) is key to promoting tooth movement. Studying the mechanical behavior of CBAB is helpful to predict the displacement of teeth and achieve the best effect of orthodontic treatment. Three CBAB samples were cut from alveolar bone around the root apex of human teeth. A uniaxial compression test was used to study the transient elastic properties of CBAB. A creep test was used to study the time-dependent viscoelastic properties of CBAB. Both tests were carried out at the loading rates of 0.02 mm/min, 0.1 mm/min and 0.5 mm/min. The results revealed that CBAB is a nonlinear viscoelastic and hyperelastic material. The stress–strain curve obtained from the uniaxial compression test could be divided into three stages: the collapse stage of the front section, the exponential stage of the middle section and the almost linear stage of the rear end. According to the strain–time curve obtained from the compression creep test, a trend of increasing strain over time was relatively obvious within the first 30 s. After 200 s, the curve gradually tended to plateau. Four hyperelastic models and three viscoelastic models were used to fit the test data. Finally, the fifth-order polynomial hyperelastic model (coefficient of determination “R2 > 0.999”) was used to describe the hyperelastic properties of CBAB, and the seven-parameter model of the generalized Kelvin modified model (“R2 > 0.98”) was used to describe the viscoelastic properties of CBAB.