Time-dependent Constitutive Model Research Articles

Time-dependent constitutive modeling of drive belts—II. The effect of the shape of material retardation spectrum on the strain accumulation process

This is the second paper in the series addressing the constitutive modeling of dynamically loaded elastomeric products such as power transmission belts. During the normal operation of such belts certain segments of the belt structure are loaded via tooth-like cyclical loading. When the time-dependent properties of the elastomeric material “match” the time-scale of the dynamic loading a strain accumulation (incrementation) process occurs. It was shown that the location of a critical rotation speed strongly depends on the distribution (shape) of the retardation spectrum, whereas the magnitude of the accumulated strain is governed by the strength of the corresponding spectrum lines. These interrelations are extremely non-linear. The strain accumulation process is most intensive at the beginning of the drive belt operation, and is less intensive for longer belts. The strain accumulation process is governed by the spectrum lines that are positioned within a certain region, which we call the Strain Accumulation Window (SAW). An SAW is always located to the right of the spectrum line, L i , at log (ω λ i )=0, where ω is the operational angular velocity. The width of the SAW depends on the width of the material spectrum. Based on the following analysis a new designing criterion is proposed for use in engineering applications for selecting a proper material for general drive-belt operations.

Constitutive response and mechanical properties of PFSA membranes in liquid water

The mechanical properties and swelling behavior of perfluorosulfonic acid (PFSA) membranes in liquid water have been investigated using a custom-built, temperature-controlled water bath. Interestingly, the theoretical models of Mooney–Rivlin and Ogden for rubber elasticity are shown to reproduce the major features of the experimentally obtained stress–strain relationships. In addition, stress relaxation of the membrane subjected to a fixed strain at room temperature fits time-dependent constitutive models used to describe nonlinear rubber elasticity. Thus, the experimental results suggest that even though PFSA is not an elastomer, the constitutive models developed for rubber-like behavior can be used for describing the ex situ constitutive response of PFSA membranes with high water content. This response is in contrast to the constitutive behavior of PFSA membranes swollen in water vapor (e.g. humid air and consequently lower water absorption in the membrane) where studies have suggested constitutive behavior corresponding to that of semicrystalline polymers, including distinct features such as a linear regime followed by onset of nonlinearity.

Deformation in viscoelastic sandwich composites subject to moisture diffusion

This study analyzes the effect of moisture diffusion on the deformation of viscoelastic sandwich composites, which are composed of orthotropic fiber-reinforced laminated skins and viscoelastic polymeric foam core. It is assumed that the elastic and time-dependent (transient) moduli at any particular location in the foam core depend on the moisture concentration at that location. Sequentially coupled analyses of moisture diffusion and deformation are performed to predict overall performance of the studied viscoelastic sandwich systems. Time and moisture dependent constitutive model is used for the polymer foam core, while skins are assumed linear elastic. The overall time-dependent responses of the sandwich composites subject to moisture diffusion are analyzed using finite element (FE) method. Experimental data available in the literature and analytical solutions are used to support convergence studies in the FE analyses. Contributions of moisture dependent elastic and the time-dependent moduli to the overall stress, strain and displacement field are studied. FE analyses of the delamination between skins and core in sandwich composite under combined moisture diffusion and mechanical loading are also performed.

Mesoscopic Analysis of Mortar under High-Stress Creep and Low-Cycle Fatigue Loading

Mesoscopic analyses of mortar failure under high-stress creep and low-cycle fatigue loading are presented using a newly developed time-dependent constitutive model for Rigid Body Spring Model, which is a discrete analysis method. The failure process over time was successfully expressed by adopting a four-component combined mechanical model as the time-dependent model of connected springs, and by developing a new method for determining the failure state for load-controlled analysis. The numerical model provides reasonable results not only for the stress-strain characteristics under cyclic loading but also for the inapplicability of Miner's law under varying stress levels. The mechanism of the time-dependent failure of mortar was clarified by investigating the local stress-strain behaviors.

A time and hydration dependent viscoplastic model for polyelectrolyte membranes in fuel cells

Ionomers are co-polymers with ionic groups. One of the interesting applications of ionomer membranes is as electrolytes in proton exchange membrane (PEM) fuel cells. The most commonly used membranes in PEM fuel cells are perfluorosulfonic acid (PFSA) membranes, e.g., Nafion® from DuPontTM. Besides its dependency on temperature and hydration due to phase inversion and cluster formation, Nafion® as a polymer, exhibits strong time and rate effects. In this work, the stress–strain behavior of Nafion® at different strain rates has been obtained in an environmental chamber for various temperatures and hydrations. After a certain strain was reached in each test, stress relaxation was performed for an hour to observe the relaxation behavior of Nafion®. We attempted to use a nonlinear, time-dependent constitutive model to predict the hygro-thermomechanical behavior of Nafion®. Because a substantial component of the response is unrecoverable, a viscoplastic model was employed. The proposed two-layer viscoplasticity model consisted of an elastoplastic network that was in parallel with an elastic-viscous network (Maxwell model) which separates the rate-dependent and rate-independent behavior of the material. After obtaining the necessary parameters for different hydrations, this model showed reasonably accurate success in predicting the stress–strain behavior at different strain rates, and matched the relaxation test results. Finite element simulations based on the proposed two-layer viscoplasticity model were in good agreement with test results and can be used to study the stress–strain state of the ionomer membranes in fuel cell configurations.

Constitutive Modeling for Uniaxial Time-Dependent Ratcheting of SS304 Stainless Steel

Based on the experimental results of uniaxial time-dependent ratcheting behavior of SS304 stainless steel at room temperature and 973K, three kinds of time-dependent constitutive models were employed to describe such time-dependent ratcheting by using the Ohno-Abdel-Karim kinematic hardening rule, i.e., a unified viscoplastic model, a creep-plasticity superposition model and a creep-viscoplasticity superposition model. The capabilities of such models to describe the time-dependent ratcheting were discussed by comparing with the corresponding experimental results. It is shown that the unified viscoplastic model cannot provide reasonable simulation to the time-dependent ratcheting, especially to those with certain peak/valley stress hold and at 973K; the proposed creep-plasticity superposition model is reasonable when the creep is a dominant factor of the deformation, however, it cannot provide a reasonable description when the creep is weak; the creep-viscoplastic superposition model is reasonable not only at room temperature but also at high temperature.

Micromechanics of Ferroelectrics: From Domain Walls to Piezoceramic Devices

A micromechanical approach utilizing the features of thermally activated domain wall motion is applied to simulate the structural changes in ferroelectric ceramics for the basic processes employed in piezoelectric devices. The approach combines an Arrhenius equation (with the temperature insensitive pre-exponential factor) for the domain wall mobility and a time-dependent constitutive model, using the volume fractions of domains with representative polarization directions as structural (internal) variables. Computer simulation of the piezoceramic poling process in a sheet actuator with interdigitated electrodes shows the formation of the inhomogeneous poling state and peculiarities of the nonlinear longitudinal piezoelectric effect. **Permanent address: Institute of Crystallography RAS, Moscow, Russia.

In-Plane Mechanical Properties of a Carbon-Epoxy Composite Laminate at Elevated Temperatures

This paper deals with the experimental determination of the in-plane mechanical properties of a carbon-epoxy composite laminate in the temperature range of 100 °C to 150 °C. Focus has been on the in-plane shear modulus of the laminate. A time-dependent constitutive model for the in-plane shear modulus has been developed. Material constants for the model were derived from the creep compliance of the laminate, obtained experimentally at various temperatures. The results show that the in-plane shear property of the composite laminate is linear viscoelastic within the temperature range and loading level investigated. The constitutive model was validated experimentally.

Constitutive modeling for uniaxial time-dependent ratcheting of SS304 stainless steel

Based on the experimental results of uniaxial time-dependent ratcheting behavior of SS304 stainless steel at room temperature and 973 K [Kang, G.Z., Kan, Q.H., Zhang, J., 2006. Time-dependent ratcheting experiments of SS304 stainless steel. Int. J. Plast. 22, 858–894], three kinds of time-dependent constitutive models were employed to describe such time-dependent ratcheting by using the Ohno–Abdel-Karim kinematic hardening rule [Abdel-Karim, M., Ohno, N., 2000. Kinematic hardening model suitable for ratchetting with steady-state. Int. J. Plast. 16, 225–240], i.e., a unified visco-plastic model, a creep-plasticity superposition model and a creep-visco-plasticity superposition model. The capabilities of such models to describe the time-dependent ratcheting were discussed by comparing with the corresponding experimental results. It is shown that the unified visco-plastic model cannot provide reasonable simulation to the time-dependent ratcheting, especially to those with certain peak/valley stress hold and at 973 K; the proposed creep-plasticity superposition model is reasonable when the creep is a dominant factor of the deformation, however, it cannot provide a reasonable description when the creep is weak; the creep-visco-plastic superposition model is reasonable not only at room temperature but also at high temperature.

Time-dependent constitutive modeling of drive belts – I. The effect of geometry and number of loading cycles

This paper presents constitutive modeling of dynamically loaded elastomeric products such as power transmission belts. During the normal operation of the belts certain segments of the belt structure are loaded with a tooth-like periodic (cyclic) loading. When the time-dependent properties of the elastomeric material “match” the time-scale of the dynamic loading a strain accumulation process occurs. The critical angular velocity is proportional to the ratio of the belt length to the common diameters of the pulleys. The magnitude of the strain accumulated in each loading cycle decreases with an increase in belt length. For a given belt geometry the critical angular velocity increases with the number of loading cycles. At the same time the magnitude of the accumulated strain decreases non-linearly as the number of loading cycles increases. However if the belt operates at or in the close vicinity of its critical angular velocity it will almost certainly fail!

Time-Dependent Constitutive Model of Solidifying Concrete Based on Thermodynamic State of Moisture in Fine Pores

An enhanced multi-chemo-physical model for the time-dependent deformation of concrete is proposed based on thermodynamic state of moisture in micro-pores. The moisture migration mechanism is divided into 1) moisture transport through CSH gel grains and 2) water in motion within the inter-particle spaces of hydrate micro-products. The new kinematic model makes it possible to simulate both long- and short-term concrete creep. An enhanced mechanistic law of stress path dependency is introduced to cope with a wide variety of stress and ambient histories as well. Time-dependency at elevated temperature is also investigated with current high-accuracy thermo-hygro dynamics. The instantaneous plasticity in direct connection with evaporating moisture from CSH crystal inter-layers is incorporated into the predictive system. Although some mechanisms remain unverified, drying shrinkage and creep at high temperature are fairly simulated.

Numerical simulations of non-Newtonian flows between eccentric cylinders by domain decomposition and stream-tube method

In this paper, we study the influence of rheological properties of inelastic and viscoelastic fluids in flows occurring in the annulus of rotating eccentric cylinders. To compute this flow where vortex regions are encountered, the physical domain is split up into a finite number of sub-domains that are mapped into domains where open and closed streamlines are parallel and straight by means of local mapping functions to be determined numerically. Such simplicity for the mapped streamlines makes it easy to handle time-dependent constitutive models in viscoelasticity. The governing non-linear equations are solved by means of an optimization algorithm. The results point out the influence of non-Newtonian properties of the fluids in annular flows between eccentric cylinders as also in particular cases of journal bearings, notably the role of elasticity. Results with Newtonian inertial flows with large gaps underline the possibility of the approach to investigate flows with multiple vortices.

A constitutive model with damage for cohesive soils

A realistic and broadly applicable time-dependent constitutive model has been developed for cohesive soils, and a damage law has been incorporated into the time-dependent model to appropriately predict the undrained creep behavior. The physical and mathematical formulation of the model was performed from the point of view that fewer parameters better be employed. The creep behavior predicted using the developed constitutive model were favorably compared with the experimental results including the undrained creep rupture, which is an important observed phenomenon for cohesive soils. Despite the simplicity of the constitutive model, it performs well as long as the time to failure ratio of the creep rupture tests is within the same order of magnitude.

Non-linear finite element analysis of composite planar frames with an interlayer slip

A new finite element formulation is presented for the non-linear analysis of two-layer composite planar frames with an interlayer slip. For each layer the geometrically non-linear Reissner’s beam theory is assumed. A small slip between the layers is considered. Non-linear, time-dependent constitutive models for the layers, and a non-linear relationship between the slip and the shear stress at the interface are accounted for. As only a few finite elements are needed to describe a beam or column of a frame with great precision, the new finite element formulation is prefectly suited for practical calculations.

In Situ Tests on Creep Behavior of Rock Mass with Joint or Shearing Zone in Foundation of Large-Scale Hydroelectric Projects

The time-dependent behavior of rock mass, which is generally governed by joints and shearing zones, is of great significance for engineering design and prediction of long-term deformation and stability. In situ creep test is a more effective method than laboratory test in characterizing the creep behavior of rock mass with joint or shearing zone due to the complexity of field conditions. A series of in situ creep tests on granite with joint at the shiplock area of the Three-Gorges Project and basalt with shearing zone at the right abutment of the Xiluodu Project were performed in this study. Based on the test results, the stress-displacement-time responses of the joints and basalt are analyzed, and their time-dependent constitutive model and model coefficients are given, which is crucial for the design to prevent the creep deformations of rock masses from causing the failure of the operation of the shiplock gate at the Three-Gorges Project and long-term stability of the Xiluodu arc dam.

Time-Dependent Post-Peak Softening of RC Members in Flexure

To investigate the rate effects on post-peak structural behavior accompanying the compression softening of structural concrete, experimental studies were carried out on over-reinforced concrete beams with and without confinement under varied rates of flexural loading. The effects of loading rate on the capacity and ductility of RC beams were found more pronounced in confined cases than unconfined cases. The generic time-dependent constitutive model of compression-softened concrete was applied to nonlinear collapse analysis and its applicability was verified by experiments. The strain rate in the compressive localized zone in structures rapidly increased after the member reached its peak capacity even though the rate of displacement was kept unchanged especially in the case of unconfined beams. In the case of confined RC beams, localization of weak strain occurred but with comparatively greater time-dependent plasticity and fracturing within the structure. These deformation characteristics were adequately simulated by nonlinear analysis using a time-dependent constitutive model for softened concrete in compression.

非線形移動硬化を有する分離型構成式のSn-3.0Ag-0.5Cuへの適用(OS7 計算固体力学とシミュレーション)

非線形移動硬化を有する分離型構成式のSn-3.0Ag-0.5Cuへの適用(OS7 計算固体力学とシミュレーション)

Time-Dependent Nonlinearity of Compression Softening in Concrete

As nonlinear post-peak mechanics is time dependent in nature and the transient process of collapse is influenced by loading rates, post-peak analyses have to be conducted considering softened structural concrete under varying rates of straining. To meet this challenge, a new time-dependent constitutive model, which encompasses both near- and post-peak regions in concrete compression, is proposed. Towards better evaluation of structural collapse under extreme loads, a coupled plastic-damaging law is presented. For the purpose of identifying evolution laws of plasticity and continuum damage, experimental investigation into rate-dependent nonlinearity was performed under different levels of lateral confinement. The plastic and damage evolutions were formulated with respect to paths of intrinsic stress intensity of damage continua and time. The combined law of short-term elasto-plastic and fracture successfully convey nonlinear creep deformation and rate dependent strength, as well as delayed creep rupture of material instability.

Three-dimensional stress effects on time-dependent swelling behaviour of shaly rocks

This paper presents a time-dependent constitutive model that has been developed for the swelling of shaly rocks. Laboratory test results on many shales, including Queenston shale, show that the swelling of these rocks depends on the applied stresses. The applied stress in one principal stress direction reduces swelling strain not only in that direction but also in the perpendicular directions. It was found that swelling strain reductions are nonlinearly dependent on applied stress. The reduction in lateral swelling caused as a result of axial stress is modeled using the "pseudo-Poisson's effect". The proposed model is used to simulate the development of swelling strain with time under uniaxial and biaxial stress conditions. Comparison between the computed and experimental results shows that the pseudo-Poisson's effect is a key parameter for simulating the observed time-dependent swelling.Key words: swelling, Queenston shale, modeling, three-dimensional stress effect, nonlinearity.

A THREE-DIMENSIONAL FINITE ELEMENT MODEL FOR POWDER COMPACTION—TIME-DEPENDENT FORMULATION AND VALIDATION

ABSTRACT Many industrial powders have been documented to have time-dependent compression response. However, in the literature very few time-dependent formulations are reported for three-dimensional analysis of powder compaction. In the paper, a time-dependent constitutive model, based on the theory proposed by Adachi and Oka, was used in a three-dimensional finite element formulation suitable for PC or desktop environments. The finite element model (FEM) predicts both the stress and density distributions in the powder mass during compression, i.e., from no load to the maximum compression load. A user-friendly interactive GUI (graphical user interface) was developed for the 3-D FEM, making it easy to use. To validate the FEM, microcrystalline cellulose was compressed to form cylindrical pellets using a press. The pellet was used to obtain spatial density distribution using the sectioning method. Then, the measured density distribution was compared with the Adachi and Oka model-based FEM calculated values. The density distributions were predicted within the 95% confidence interval of measured values. In addition, the overall error between the measured and predicted density values throughout the pressed pellet was less than 10%