• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.4
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• pp.619-628
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• 2001

A viscoelastic constitutive equation of rubber is proposed under small oscillatory load superimposed on large static deformation. The proposed model is derived through linearization of Simos nonlinear viscoelastic constitutive model and reference configuration transformation. Statically pre-deformed state is used as reference configuration. The model is extended to a generalized viscoelastic constitutive equation including widely-used Mormans model. Static deformation correction factor is introduced to consider the influence of pre-strain on the relaxation function. The model is tested for dynamic behavior of rubbers with different carbon black fractions. It is shown that the constitutive equation with static deformation correction factor agrees well with test results.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.7
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• pp.930-939
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• 2004

Constitutive models for final stage densification of metal powder compacts with power-law creep deformation were investigated. The constitutive models were implemented into a finite element program (ABAQUS) by using user subroutine CREEP and, from FEM results, useful densification curves were obtained when hydrostatic and uniaxial stress were applied to the powder compacts at various pressures and temperatures. Because the densification behavior varied as the constitutive models, the equivalent stress surface on each constitutive equation was investigated to analyze the difference of densification behavior.

• Structural Engineering and Mechanics
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• v.80 no.5
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• pp.539-551
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• 2021

With the continuous increase of computational capacity, more and more complex nonlinear elastoplastic constitutive models were developed to study the mechanical behavior of elastoplastic materials. These constitutive models generally contain a large amount of physical and phenomenological parameters, which often require a large amount of computational costs to determine. In this paper, an inverse parameter determination method is proposed to identify the constitutive parameters of elastoplastic materials, with the consideration of both strain rate effect and temperature effect. To carry out an efficient design, a hybrid optimization algorithm that combines the genetic algorithm and the Nelder-Mead simplex algorithm is proposed and developed. The proposed inverse method was employed to determine the parameters for an elasto-viscoplastic constitutive model and Johnson-cook model, which demonstrates the capability of this method in considering strain rate and temperature effect, simultaneously. This hybrid optimization algorithm shows a better accuracy and efficiency than using a single algorithm. Finally, the predictability analysis using partial experimental data is completed to further demonstrate the feasibility of the proposed method.

• Computers and Concrete
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• v.8 no.4
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• pp.371-388
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• 2011

In this paper, time-continuous constitutive equations for strain rate-dependent materials are presented first, among which those for the overstress and the consistency viscoplastic models are considered. By allowing the stress states to be outside the yield surface, the overstress viscoplastic model directly defines the flow rule for viscoplastic strain rate. In comparison, a rate-dependent yield surface is defined in the consistency viscoplastic model, so that the standard Kuhn-Tucker loading/unloading condition still remains true for rate-dependent plasticity. Based on the formulation of the consistency viscoplasticity, a computational elasto-viscoplastic constitutive model is proposed for the short fiber-reinforced fresh cementitious paste for extrusion purpose. The proposed constitutive model adopts the von-Mises yield criterion, the associated flow rule and nonlinear strain rate-hardening law. It is found that the predicted flow stresses of the extrudable fresh cementitious paste agree well with experimental results. The rate-form constitutive equations are then integrated into an incremental formulation, which is implemented into a numerical framework based on ANSYS/LS-DYNA finite element code. Then, a series of upsetting and ram extrusion processes are simulated. It is found that the predicted forming load-time data are in good agreement with experimental results, suggesting that the proposed constitutive model could describe the elasto-viscoplastic behavior of the short fiber-reinforced extrudable fresh cementitious paste.

• Earthquakes and Structures
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• v.4 no.6
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• pp.607-627
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• 2013

The application of shape memory alloys (SMAs) to the seismic response reduction of civil engineering structures has attracted growing interest due to their self-centering feature and excellent fatigue performance. The loading rate dependence of SMAs raises a concern in the seismic analysis of SMA-based devices. However, the implementation of micromechanics-based strain-rate-dependent constitutive models in structural analysis software is rather complicated and computationally demanding. This paper investigates the feasibility of replacing complex rate-dependent models with rate-independent constitutive models for superelastic SMA elements in seismic time-history analysis. Three uniaxial constitutive models for superelastic SMAs, including one rate-dependent thermomechanical model and two rate-independent phenomenological models, are considered in this comparative study. The pros and cons of the three nonlinear constitutive models are also discussed. A parametric study of single-degree-of-freedom systems with different initial periods and strength reduction factors is conducted to examine the effect of the three constitutive models on seismic simulations. Additionally, nonlinear time-history analyses of a three-story prototype steel frame building with special SMA-based damping braces are performed. Two suites of seismic records that correspond to frequent and design basis earthquakes are used as base excitations in the seismic analyses of steel-braced frames. The results of this study show that the rate-independent constitutive models, with their parameters properly tuned to dynamic test data, are able to predict the seismic responses of structures with SMA-based seismic response modification devices.

• Structural Engineering and Mechanics
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• v.20 no.5
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• pp.495-504
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• 2005

This article explores a constitutive equation that is able to correlate stress, strain and strain rate. In order to show the advantages of the constitutive equation here proposed and how its material parameters are obtained, data extracted from the literature, for materials as different as polymers and metallic alloys, are used. Finite element simulation of the impact behaviour of a beam is presented to highlight the care one needs to exercise when using the more traditional Cowper-Symonds equation. The present constitutive equation has shown to be accurate for a wide range of strains, stresses and strain rates.

• Korea-Australia Rheology Journal
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• v.14 no.1
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• pp.33-45
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• 2002

Recent results obtained for the port-pom model and the constitutive equations with time-strain separability are examined. The time-strain separability in viscoelastic systems Is not a rule derived from fundamental principles but merely a hypothesis based on experimental phenomena, stress relaxation at long times. The violation of separability in the short-time response just after a step strain is also well understood (Archer, 1999). In constitutive modeling, time-strain separability has been extensively employed because of its theoretical simplicity and practical convenience. Here we present a simple analysis that verifies this hypothesis inevitably incurs mathematical inconsistency in the viewpoint of stability. Employing an asymptotic analysis, we show that both differential and integral constitutive equations based on time-strain separability are either Hadamard-type unstable or dissipative unstable. The conclusion drawn in this study is shown to be applicable to the Doi-Edwards model (with independent alignment approximation). Hence, the Hadamardtype instability of the Doi-Edwards model results from the time-strain separability in its formulation, and its remedy may lie in the transition mechanism from Rouse to reptational relaxation supposed by Doi and Edwards. Recently in order to describe the complex rheological behavior of polymer melts with long side branches like low density polyethylene, new constitutive equations called the port-pom equations have been derived in the integral/differential form and also in the simplifled differential type by McLeish and carson on the basis of the reptation dynamics with simplifled branch structure taken into account. In this study mathematical stability analysis under short and high frequency wave disturbances has been performed for these constitutive equations. It is proved that the differential model is globally Hadamard stable, and the integral model seems stable, as long as the orientation tensor remains positive definite or the smooth strain history in the flow is previously given. However cautious attention has to be paid when one employs the simplified version of the constitutive equations without arm withdrawal, since neglecting the arm withdrawal immediately yields Hadamard instability. In the flow regime of creep shear flow where the applied constant shear stress exceeds the maximum achievable value in the steady flow curves, the constitutive equations exhibit severe instability that the solution possesses strong discontinuity at the moment of change of chain dynamics mechanisms.

• Computers and Concrete
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• v.22 no.2
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• pp.227-237
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• 2018

Today, the modeling of concrete as a material within finite element simulations is predominantly done through nonlinear material models of concrete. In current sophisticated computational systems, there are a number of complex concrete material models which are based on theory of plasticity, damage mechanics, linear or nonlinear fracture mechanics or combinations of those theories. These models often include very complex constitutive relations which are suitable for the modeling of practically any continuum mechanics tasks. However, the usability of these models is very often limited by their parameters, whose values must be defined for the proper realization of appropriate constitutive relations. Determination of the material parameter values is very complicated in most material models. This is mainly due to the non-physical nature of most parameters, and also the large number of them that are frequently involved. In such cases, the designer cannot make practical use of the models without having to employ the complex inverse parameter identification process. In continuum mechanics, however, there are also constitutive relations that require the definition of a relatively small number of parameters which are predominantly of a physical nature and which describe the behavior of concrete very well within a particular task. This paper presents an example of such constitutive relations which have the potential for implementation and application in finite element systems. Specifically, constitutive relations for modeling the plane stress state of concrete are presented and subsequently tested and evaluated in this paper. The relations are based on the incremental theory of elastic strain-hardening plasticity in which a non-associated flow rule is used. The calculation result for the case of concrete under uniaxial compression is compared with the experimental data for the purpose of the validation of the constitutive relations used.

• Transactions of Materials Processing
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• v.19 no.8
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• pp.468-473
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• 2010

Shape memory alloys (SMAs) have the ability to recover their original shape upon thermo-mechanical loading even after large inelastic deformation. The unique feature is known as pseudoelasticity and shape memory effect caused by the crystalline structural transformation between two solid-state phases called austenite and martensite. To support the engineering application, a number of constitutive models, which can be formally classified into either micromechanics-based or phenomenological model, have been developed. Most of the constitutive models include a kinetic law governing the crystallographic transformation. The present work presents a one-dimensional, phenomenological constitutive model for SMAs in the context of the unified viscoplasticity theory. The proposed model does not incorporate the complex mechanisms of phase transformation. Instead, the effects induced by the transformation are depicted through the growth law for the back stress that is an internal state variable of the model.

• Structural Engineering and Mechanics
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• v.59 no.4
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• pp.601-619
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• 2016

In this study, developments of an efficient visco-hyperelastic constitutive equation for describing the time dependent material behavior accurately in dynamic and impact loading and finding related materials constants are considered. Based on proposed constitutive model, behaviour of a hollow cylinder elastomer bushing under different dynamic and impact loading conditions is studied. By implementing the developed visco-hyperelastic constitutive equation to LS-DYNA explicit dynamic finite element software a three dimensional model of the bushing is developed and dynamic behaviour of that in axial and torsional dynamic deformation modes are studied. Dynamic response and induced stress under different impact loadings which is rarely studied in previous researches have been also investigated. Effects of hyperelastic and visco-hyperelastic parameters on deformation and induced stresses as well as strain rate are considered.