A viscoelastic constitutive model with nonlinear evolutionary internal variables

Summary Based on the internal variable theory, a viscoelastic constitutive model of a highly deformable continuous medium is proposed. A set of second rank tensorial internal state variables corresponding to Biot's strain is introduced, and a nonlinear evolution law for these internal variables is suggested. The proposed model may be considered as an extension of the network theory of rubber elasticity to take the viscous effects into account. In order to verify the validity of the present model, uniaxial tension tests for HDPE are carried out at different strain rates. The prediction of the present model shows a good agreement with the experimental data. Finally, a discussion of the present constitutive model is given. It is found that the present constitutive model is more flexible to describe the strain rate sensitivity of polymeric materials in a wide range of strain rates.     

复合固体推进剂黏弹性微裂纹损伤本构模型

为建立复合固体推进剂的损伤本构模型,在介观尺度上视其为微裂纹损伤,选取微裂纹密度为损伤内变量。在Abdel-Tawab本构方程的基础上,基于微裂纹均匀化理论,推导了损伤映射张量的一般形式。该张量通常具有非完全对称性,其物理意义是将真实应力空间中各向异性材料的多轴加载映射为等效应力空间中各向同性材料的更为复杂的多轴加载。其次,基于黏弹性动态裂纹扩展模型和裂纹扩展阻力曲线的概念,建立了损伤内变量的演化方程。该演化方程仅含4个物理意义明确的细观参数,并且参数的取值规律与宏观应力曲线的变化规律相一致。数值结果表明,建立的模型能够有效反映材料损伤的应变率、温度依赖性及各向异性特征,并且具有一定的蠕变损伤预测能力。     

A thermovisco-hyperelastic constitutive model of HTPB propellant with damage at intermediate strain rates

The uniaxial compressive tests at different temperatures (223–298 K) and strain rates (\(0.40\mbox{--}63~\mbox{s}^{-1}\)) are reported to study the properties of hydroxyl-terminated polybutadiene (HTPB) propellant at intermediate strain rates, using a new INSTRON testing machine. The experimental results indicate that the compressive properties (mechanical properties and damage) of HTPB propellant are remarkably affected by temperature and strain rate and display significant nonlinear material behaviors at large strains under all the test conditions. Continuously decreasing temperature and increasing strain rate, the characteristics of stress-strain curves and damage for HTPB propellant are more complex and are significantly different from that at room temperature or at lower strain rates. A new constitutive model was developed to describe the compressive behaviors of HTPB propellant at room temperature and intermediate strain rates by simply coupling the effect of strain rate into the conventional hyperelastic model. Based on the compressive behaviors of HTPB propellant and the nonlinear viscoelastic constitutive theories, a new thermovisco-hyperelastic constitutive model with damage was proposed to predict the stress responses of the propellant at low temperatures and intermediate strain rates. In this new model, the damage is related to the viscoelastic properties of the propellant. Meanwhile, the effect of temperature on the hyperelastic properties, viscoelastic properties and damage are all considered by the macroscopical method. The constitutive parameters in the proposed constitutive models were identified by the genetic algorithm (GA)-based optimization method. By comparing the predicted and experimental results, it can be found that the developed constitutive models can correctly describe the uniaxial compressive behaviors of HTPB propellant at intermediate strain rates and different temperatures.     

A phenomenological constitutive model for the nonlinear viscoelastic responses of biodegradable polymers

We formulate a constitutive framework for biodegradable polymers that accounts for nonlinear viscous behavior under regimes with large deformation. The generalized Maxwell model is used to represent the degraded viscoelastic response of a polymer. The large-deformation, time-dependent behavior of viscoelastic solids is described using an Ogden-type hyperviscoelastic model. A deformation-induced degradation mechanism is assumed in which a scalar field depicts the local state of the degradation, which is responsible for the changes in the material’s properties. The degradation process introduces another timescale (the intrinsic material clock) and an entropy production mechanism. Examples of the degradation of a polymer under various loading conditions, including creep, relaxation and cyclic loading, are presented. Results from parametric studies to determine the effects of various parameters on the process of degradation are reported. Finally, degradation of an annular cylinder subjected to pressure is also presented to mimic the effects of viscoelastic arterial walls (the outer cylinder) on the degradation response of a biodegradable stent (the inner cylinder). A general contact analysis is performed. As the stiffness of the biodegradable stent decreases, stress reduction in the stented viscoelastic arterial wall is observed. The integration of the proposed constitutive model with finite element software could help a designer to predict the time-dependent response of a biodegradable stent exhibiting finite deformation and under complex mechanical loading conditions.     

A nonlinear viscoelastic constitutive model taking into account of physical aging

Mechanics of Time-Dependent Materials - Polymers exhibit viscoelastic behavior: their mechanical response depends on the loading time, or on the loading frequency. In addition, if a polymer...     

A viscoelastic continuum damage model and its application to uniaxial behavior of asphalt concrete

An existing viscoelastic constitutive model which accounts for the effects of rate-dependent damage growth is described and applied successfully to characterize the uniaxial stress, constant strain rate behavior of asphalt concrete. The special case of an elastic continuum damage model with multiaxial loading, which is based upon thermodynamics of irreversible processes with internal state variables, is first reviewed and then it is shown how this model has been extended to a corresponding viscoelastic damage model through the use of an elastic-viscoelastic correspondence principle. The general mathematical model is next specialized to uniaxial loading. A rate-type evolution law, similar in form to a crack growth law for a viscoelastic medium, is adopted for describing the damage growth within the body. Results from laboratory tests of uniaxial specimens under axial tension at different strain rates are then shown to be consistent with the theory. The discussion of data analysis describes the specific procedure used here to obtain the material parameters in the constitutive model for uniaxial loading and how the method may be generalized for multiaxial loading.     

Nonlinear viscoelastic and viscoplastic constitutive equations with growing damage

Nonequilibrium thermodynamics, rate-process theory, viscoelastic fracture mechanics and various experimentally-motivated simplifications are used to develop constitutive equations that account for effects of viscoelasticity, viscoplasticity, growing damage and aging. Their form is more general than previously developed by the author, and allows for relatively general tensorial effects of damage. Some important special cases are then covered, with emphasis on viscoelasticity. Evolution equations for the damage expressed in terms of internal state variables (ISVs) are discussed, comparing formulations using scalar ISVs and tensor ISVs. Finally, some experimental support for the theory is described. An Appendix illustrates the theory for an aging, linear viscoelastic material with growing cracks. This revised version was published online in July 2006 with corrections to the Cover Date.     

A nonlinear fractional viscoelastic material model for polymers

In this contribution a test scheme based on tensile tests at different velocities, relaxation experiments and deformation controlled loading and unloading processes with intermediate relaxations has been used to experimentally characterize the nonlinear, inelastic material behavior. Based on the experimental observations a small strain nonlinear fractional viscoelastic material model is derived. In order to use the model within a finite element analysis, the constitutive equations have been generalized for the multiaxial case. The experimental test scheme and the fractional viscoelastic material model are subsequently applied to characterize and compute the mechanical behavior of the thermoplastic Polypropylene. After the identification of the material parameters several uniaxial and multiaxial simulations have been carried out and compared with experimental results.     

A nonlinear elastic constitutive model for coated fabrics

A nonlinear elastic constitutive model for coated fabrics is developed. The model which accounts for the basic mechanisms of yarn rotation, yarn extension and coating extension is obtained by expressing the equations of equilibrium for a unit cell of the material in terms of effective continuum stresses and strains. A systematic method of determining the model parameters is proposed. Based on the parameters obtained from a single biaxial test, theoretical curves are plotted for various biaxial loading states and compared with experimental results for several commercially available structural fabrics.     

A model for anisotropic viscoelastic damage in composites

A model for continuous damage combined with viscoelasticity is proposed. The starting point is the formulation connecting the elastic properties to the tensor of damage variables. A hardening law associated with the damage process is identified from available experimental information and the rate-type constitutive equations are derived. This elastic damage formulation is used to formulate an internal variable approximation to viscoelastic damage in the form of a non-linear Kelvin chain. Elastic and viscoelastic equations are implemented into a finite element procedure. The code is verified by comparison with closed-form solutions in simplified configurations, and validated by fitting results of experimental creep tests.     

A variational constitutive framework for the nonlinear viscoelastic response of a dielectric elastomer

We formulate a variational constitutive framework that accounts for nonlinear viscous behavior of electrically sensitive polymers, specifically Dielectric Elastomers (DEs), under large deformation. DEs are highly viscoelastic and their actuation response is greatly affected in dynamic applications. We used the generalized Maxwell model to represent the viscoelastic response of DE allowing the material to relax with multiple mechanisms. The constitutive updates at each load increment are obtained by minimizing an objective function formulated using the free energy and electrostatic energy of the elastomer, in addition to the viscous dissipation potential of the dashpots in each Maxwell branch. The model is then used to predict the electromechanical instability (EMI) of DE. The electro-elastic response of the DE is verified with available analytical solutions in the literature and then the material parameters are calibrated using experimental data. The model is integrated with finite element software to perform a variety of simulations on different types of electrically driven actuators under various electromechanical loadings. The electromechanical response of the DE and the critical conditions at which EMI occurs were found to be greatly affected by the viscoelasticity. Our model predicts that under a dead load EMI can be avoided if the DE operates at a high voltage rate. Subjected to constant, ramp and cyclic voltage, our model qualitatively predicts responses similar to the ones obtained from the analytical solutions and experimental data available in the literature.     

A generalized model for the uniaxial isothermal deformation of a viscoelastic body

Summary Using the notion of a fractional derivative we formulate a new model for a uniaxial deformation of a visco-elastic body. The basic assumption is that all derivatives ₍₎ with respect to time of the stress depend (with specified weighting factor) on all derivatives ₍₎ with respect to time of the strain (multiplied with another weighting factor), for 01. In this respect our model is a generalization of the Zener model, i.e., it is a Zener fractional model with infinitely many terms. The relation between stress and strain is given in explicit form. For two specific choices of parameters the behavior of the model under suddenly applied stress (creep) and suddenly applied strain (stress relaxation) are examined.     

Process development of a nitramine propellant for the GAU-8 30 mm gun system

The Air Force is actively pursuing an alternative to the double-base propellant used in the 30 mm GAU-8 system on the A-10 aircraft. To suppress the seThe Naval Ordnance Station has just completed the manufacture of a 2268-kg (5000-lb) sample lot for the Air Force to be used for actual flight test and     

A viscoelastic constitutive model for constant rate loading at different relative humidities

A nonlinear viscoelastic strain model is developed for time-dependent ramp loading at different constant relative humidities. The model is applied to edgewise compression data on kraft paper linerboard at various constant relative humidities and constant load rates. The history-dependent term involves a reduced time in which the shift factor is taken to be the durability, written as a function of three material constants. The model generalizes nonlinear-viscoelastic, moisture-dependent creep models.     

The constitutive equation of a complete nonlinear viscoelastic material

Summary The present paper is concerned with a more general form of the constitutive equation for viscoelastic materials as given by the authors in [1] and [2]. The generalization consists in assuming the instantaneous part of deformation to be a nonlinear function of the time-dependent stress state. The constitutive equation is obtained on the basis of the generalized superposition principle formulated in [1] the sense of which is presently completed and analyzed from the mathematical point of view. It is shown that the present theory includes as a particular case the theory of creep for metals given byOdqvist [3].

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Zusammenfassung Die vorliegende Arbeit beschäftigt sich mit einer allgemeineren Form der Materialgleichung für viskoelastische Stoffe, als sie von den Autoren in [1] und [2] angegeben wurde. Die Verallgemeinerung besteht darin, daß der augenblickliche Anteil der Deformationen als nichtlineare Funktion des zeitabhängigen Spannungszustandes angenommen wird. Die Materialgleichung wird aufgrund des verallgemeinerten Superpositionsprinzips, wie es in [1] formuliert wurde, erhalten; dieses wird nun vervollständigt und einer mathematischen Analyse unterzogen. Es wird gezeigt, daß die vorliegende Theorie die Kriechtheorie der Metalle, wie sie vonOdqvist [3] angegeben wurde, als Spezialfall enthält.

     

Computational model for predicting nonlinear viscoelastic damage evolution in materials subjected to dynamic loading

Many inelastic solids accumulate numerous cracks before failure due to impact loading, thus rendering any exact solution of the IBVP untenable. It is therefore useful to construct computational models that can accurately predict the evolution of damage during actual impact/dynamic events in order to develop design tools for assessing performance characteristics. This paper presents a computational model for predicting the evolution of cracking in structures subjected to dynamic loading. Fracture is modeled via a nonlinear viscoelastic cohesive zone model. Two example problems are shown: one for model validation through comparison with a one-dimensional analytical solution for dynamic viscoelastic debonding, and the other demonstrates the applicability of the approach to model dynamic fracture propagation in the double cantilever beam test with a viscoelastic cohesive zone.     

混凝土正交各向异性动态损伤本构模型研究

为建立混凝土的正交各向异性动态损伤本构,首先采用动力放大系数的形式考虑材料的应变率效应,然后基于Sidoroff能量等价原理,建立动态条件下单元体的损伤刚度矩阵。同时在损伤演化模型中,采用Mazars损伤模型描述主轴方向的损伤变量。另外采用适用于正交各向异性的Hoffman屈服破坏准则,并考虑损伤及动力放大系数对强度的修正。以建筑结构受爆破震动荷载作用的实验资料,对本模型进行了验证     

A micromechanical model for non-linear viscoelastic behavior of particle-reinforced rubber with distributed damage

A model based on micromechanics for predicting effective viscoelastic stress-strain equations and microcrack growth in particle-reinforced rubber (or other relatively soft viscoelastic matrix) is described. Geometric idealization of the microstructure follows that of the composite spheres assemblage and generalized self-consistent scheme originally used for linear elastic composites without damage. The approach combines a perturbation analysis of the matrix, which becomes more accurate as the particle volume fraction is increased, with the Rayleigh-Ritz energy method for predicting mechanical response of the composite. Results for linear elastic behavior with crack growth are first obtained, and then extensions to linear and non-linear viscoelastic behavior are discussed. It is shown that the elasticity theory may be easily extended to predict mechanical response of a viscoelastic composite, and that an approximate equation governing microcrack growth is analogous to one for an aging elastic material. Finally, a limited assessment of the theory is made through comparison with some existing theoretical effective modulus results and experimental data on a particle-filled rubber.     

A model for nonlinear viscoelastic torsional response of an elastomeric bushing

Summary An elastomeric bushing is a device used in automotive suspension systems to cushion the loads transmitted from the wheel to the frame of the vehicle. A bushing is essentially an elastomeric hollow cylinder which is bonded to a solid metal shaft at its inner surface and a metal sleeve at its outer surface. The shaft is connected to the suspension and the sleeve is connected to the frame. The elastomeric cylinder provides the cushion when it deforms due to relative motion between the shaft and the sleeve. The relation between the force or moment applied to the shaft or sleeve and the relative displacements or rotations is nonlinear and exhibits features of viscoelasticity.A force(moment)-displacement(rotation) relation for elastomeric bushings is important for multibody dynamics numerical simulations. A boundary value problem for the bushing response leads to a relation which requires extensive computation time to implement and is hence unsuitable. In a separate study, a force(moment)-displacement(rotation) relation for single mode response has been proposed which can be used in multi-body dynamics simulations. The relation is expressed in terms of a force (moment) relaxation function for the bushing, and a method for its determination by experiments on bushings has been presented. The applicability of this relation for torsional mode bushing response is evaluated in the present work.A boundary value problem is formulated for torsional mode bushing response. Numerical solutions of the boundary value problem represent the exact bushing response and act as numerically generated experimental data. The proposed moment-rotation relation is constructed using this data. Numerical solutions of the boundary value problem also allow for comparison between the exact moment-rotation behavior and that predicted by the proposed model. It is shown that the method for determining the bushing relaxation function and the predictions of the proposed moment-rotation relation are in very good agreement with the exact results.