Strain-Rate Effect in the Endochronic Theory of Viscoplasticity

1976 ◽  
Vol 43 (1) ◽  
pp. 92-96 ◽  
Author(s):  
H.-C. Lin ◽  
H.-C. Wu
Keyword(s):  
Strain Rate ◽  
Quantitative Agreement ◽  
Strain Rate Effect ◽  
Rate Effect ◽  
Strain Rate Effects ◽  
Endochronic Theory ◽  
One Dimensional ◽  
Time Profiles ◽  
Rate Effects ◽  
Theoretical Stress

An explicit function of material parameter β1 is proposed to accommodate the strain-rate effect in the endochronic theory of viscoplasticity developed by Valanis. The strain-rate effects are treated in a manner that includes strain-rate history dependence. The theoretical stress-strain curves at constant strain rates are presented and compared with the existing experimental data. Based on this constitutive equation, the solution of one-dimensional plastic wave propagation in thin rods is obtained for annealed aluminum and copper. The theoretical strain-time profiles are in qualitative and quantitative agreement with the experimental results. It has been shown theoretically that the consideration of the strain-rate effect in the endochronic theory lowers the final constant strain states in the strain-time profiles.

scholarly journals Strain-rate effects associated with the HJC concrete model

2018 ◽  
Vol 183 ◽  
pp. 01008 ◽  
Author(s):  
Gordon Johnson ◽  
Timothy Holmquist ◽  
Charles Gerlach
Keyword(s):  
Strain Rate ◽  
High Strain ◽  
Confining Pressure ◽  
Strain Rate Effect ◽  
Rate Effect ◽  
Published Data ◽  
Strain Rate Effects ◽  
Third Invariant ◽  
Rate Effects ◽  
Additive Term

The Holmquist-Johnson-Cook (HJC) model for concrete was presented in 1993 and has been used extensively since that time. Since then a third invariant effect has been added and the shear modulus has been revised to vary such that Poisson's ratio is held constant. It has always been diffcult, however, to determine the appropriate constant for the strain-rate effect as most of the published data are for the net stress as a function of the strain rate. Because concrete is both pressure dependent and strain-rate dependent, it is necessary to separate the individual effects. Recently strain-rate data for three concrete materials were presented by Piotrowska and others [1, 2], where the data are presented as equivalent stress versus confining pressure for a high strain rate and a quasi-static strain rate. This is the form necessary to determine the appropriate strain-rate effect, and the data show that the strain-rate effect is larger than used in the initial publication of the HJC model, and also that the strain-rate effect is a function of the confining pressure. For lower pressures the strain-rate effect is a factor to be applied to the quasi-static data (which is the effect represented in the original HJC model), but for higher pressures the strain rate effect is better represented by an additive term. With the addition of an another HJC constant (the pressure at which the strain rate effect transitions from a multiplied factor to an additive term) it is possible to more accurately represent the response of concrete under high pressures and high strain rates, and it is possible to compute more accurate results for projectile penetration into concrete targets. The paper presents the modified form of the HJC model, an analysis of the strain-rate effects, and results of penetration computations that are compared to experimental data in the literature.

Nonlinear Behavior of Metallic Material Under Constant Acceleration Loading

2010 ◽  
Author(s):  
Monir Takla ◽  
Reza N. Jazar
Keyword(s):  
Strain Rate ◽  
Strain Rate Effect ◽  
Rate Effect ◽  
Material Behavior ◽  
Constant Acceleration ◽  
Strain Rate Effects ◽  
Inertia Effects ◽  
Simple Tension ◽  
Rate Effects ◽  
Static Conditions

There is frequent confusion in literature and in published data of material properties between the strain rate effect and the inertia effect on the behavior of metallic materials. While the measured changes of material behavior due to dynamic loading are frequently referred to as strain rate effects, little emphasis has been given to separating the effects of material inertia. In this work, inertia effects have been investigated during elastic deformations using transient dynamic finite element simulations. The work presents a case study in which a metallic bar is dynamically loaded by constant acceleration in simple tension. The material is assumed to be simple linear elastic. The material behavior is assumed to be time independent, strain rate effect was not considered in the simulations. Controlled axial displacement loading is applied at constant acceleration. When loading the material in the elastic range at high accelerations, the deformation becomes more concentrated towards the point of load application and a larger load is required to achieve a pre-defined displacement at this point, thus resulting in an apparent elasticity modulus higher than that measured at quasi-static conditions. Moreover, the material apparent response becomes non-linear. Keeping in mind that time independent properties have been adopted in the simulation and no strain rate effects have been considered, the resulting changes can be referred to pure inertia effects. In experimental testing, these changes would have been referred to strain-rate effects.

Research Progress of Strain-Rate Effect on Mechanical Properties of Concrete

2014 ◽  
Vol 638-640 ◽  
pp. 1391-1396
Author(s):  
Hong Yu Zhou ◽  
Yi Bo Chen ◽  
Ya Ran Zhang ◽  
Hai Qian Wang
Keyword(s):  
Mechanical Properties ◽  
Strain Rate ◽  
Concrete Strength ◽  
Strain Rate Effect ◽  
Rate Effect ◽  
Research Progress ◽  
Uniaxial Tensile ◽  
Compression Tests ◽  
Strain Rate Effects ◽  
Deformation Properties

Introducing research progress of rate-dependent tests by domestic and foreign scholars, strain-rate effect on dynamic mechanical properties of concrete are reviewed. Classified descriptions of research results on dynamic load tests of concrete at home and abroad are provided, including uniaxial compression tests, uniaxial tensile tests, and multi-axis tests; strain-rate effects on concrete strength and deformation properties in each test are respectively discussed; and strain-rate effect on concrete energy absorption capability are described.

Constitutive Model of Shape Memory Alloys: One-Dimensional Phase Transformation Model

2008 ◽  
Vol 56 ◽  
pp. 84-91
Author(s):  
Tadashige Ikeda
Keyword(s):  
Phase Transformation ◽  
Constitutive Model ◽  
Shape Memory Alloys ◽  
Strain Rate ◽  
Shape Memory ◽  
Strain Rate Effect ◽  
Rate Effect ◽  
Reverse Transformation ◽  
Stress Strain ◽  
One Dimensional

A simple yet accurate macroscopic constitutive model of shape memory alloys has been developed. The features of this model are (1) energy-based phase transformation criterion, (2) one-dimensional phase transformation rule based on a micromechanical viewpoint, (3) dissipated energy with a form of a sum of two exponential functions, (4) duplication of the strain rate effect, and (5) adaptability to multi-phase transformation. This model is further improved to be able to express stress-strain relationships such that the reverse transformation starts at a higher stress than the martensitic transformation starts. Here, the ideal reversible transformation temperature is empirically described by a function of the martensite volume fraction. In this paper, an outline of our model is given, where the improvement is introduced. Then, it is shown that the model can quantitatively duplicate the major and minor hysteresis loops, strain rate effect, and asymmetry in tension and compression on the stress-strain relationship. And that it can also duplicate the stress-strain relationships having the reverse transformation start stress higher than the forward one.

scholarly journals Strain Rate Effect on the Progressive Collapse Analysis of RC Frame Structure under Earthquake

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Wenming Wang
Keyword(s):  
Strain Rate ◽  
Progressive Collapse ◽  
Strain Rate Effect ◽  
Frame Structure ◽  
Rc Frame ◽  
Strain Rate Effects ◽  
Rc Frame Structure ◽  
Rate Effects ◽  
Collapse Analysis ◽  
Progressive Collapse Analysis

The strain rate effect can influence the seismic responses of reinforced concrete (RC) structures because the constitutive relationship of concrete and rebar is rate-dependent. This paper carries out progressive collapse analysis to research the influence of strain rate effects on collapse-resistant capacity, collapse mode, and collapse path of the RC frame structure. A progressive collapse simulation program for the reinforced concrete (RC) structure with a static and dynamic constitutive relationship is coded individually using the user subroutine VUMAT and then implemented in the advanced finite element program ABAQUS. The good agreement between experimental and simulation results proves that the coded subroutine is reliable. With the coded subroutine, by conducting progressive collapse analyses of a four-story RC frame structure under earthquake, the effect of strain rate on the response is investigated. The numerical results demonstrate that the collapse-resistant capacity of the structure is underestimated when the strain rate effect is neglected. It is shown that strain rate effects influence the collapse mode and collapse path of the structure. Therefore, strain rate effects should be considered in the progressive collapse analysis of the RC frame structure.

Viscous–elastic–plastic modelling of one-dimensional time-dependent behaviour of clays

1989 ◽  
Vol 26 (2) ◽  
pp. 199-209 ◽  
Author(s):  
J.-H. Yin ◽  
J. Graham
Keyword(s):  
Strain Rate ◽  
Constitutive Models ◽  
Constitutive Modelling ◽  
Time Dependent ◽  
Creep Tests ◽  
Strain Rate Effects ◽  
One Dimensional ◽  
Elastic Plastic ◽  
Constant Rate ◽  
Rate Effects

Increased attention has recently been directed towards the influence of time and strain-rate effects on the behaviour of clays in one-dimensional (1-D) laboratory consolidation. The improved understanding coming from these studies must now be incorporated into improved constitutive models that can be used for analysis of foundation settlements. This paper presents a 1-D model for stepped loading using a new concept for establishing "equivalent times" during time-dependent straining. This model is then developed into a general constitutive equation for continuous loading. The model uses three parameters, λ, κ, and ψ, that can be easily found using conventional oedometer tests.The general model has been used to develop analytical solutions for creep tests, relaxation tests, constant rate of strain (CRSN) tests, and tests with constant rate of stress (CRSS). Results from three different clays have been used to examine the validity of the model. Key words: consolidation, constitutive modelling, elastic-plastic, viscous, time, creep, strain rate, relaxation.

Integration of Viscoplastic Effects in a One-Dimensional Constitutive Model for Ground Response Analysis

2020 ◽  
Author(s):  
Samuel Yniesta ◽  
Mallak Janati-Idrissi
Keyword(s):  
Strain Rate ◽  
Stress Component ◽  
Response Analysis ◽  
Shear Strain Rate ◽  
Ground Response ◽  
Ground Response Analysis ◽  
Strain Rate Effects ◽  
One Dimensional ◽  
Rate Effects ◽  
Modulus Reduction

During an earthquake, strain-rate effects affect both the stiffness and damping behaviour of soils, yet existing constitutive models for ground response analysis are typically formulated within a rate-independent framework. In this paper, a one-dimensional viscoplastic stress-strain model is presented to introduce strain rate effects in ground response analysis. Its constitutive equations are based on a model that uses a cubic spline fit of the modulus reduction curve and a coordinate transformation technique to match any input modulus reduction and damping curve. A viscous stress component is added to model the effect of strain rate on the mechanical behaviour of soils using a single input parameter. The model is able to reproduce the linear increase in shear strength with the logarithm of shear strain rate, and allows to introduce viscous effects in 1D ground response analysis with control over damping and modulus reduction behaviour. The model is implemented in a software for ground response analysis and used to predict the results of a centrifuge test modeling one-dimensional wave propagation. The results show that the model predicts accurately the amplification and attenuation of shear waves, in a context where strain rates impact significantly the response of the model.

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