An Anisotropic Hardening Rule for Elastoplastic Solids Based on Experimental Observations

1989 ◽  
Vol 56 (3) ◽  
pp. 499-507 ◽  
Author(s):  
Fernand Ellyin
Keyword(s):  
Yield Surface ◽  
Maximum Load ◽  
Nonproportional Loading ◽  
Hardening Rule ◽  
Loading Paths ◽  
Hardening Law ◽  
Hardening Modulus ◽  
Modulus Curve ◽  
Nonlinear Hardening ◽  
Good Agreement

A hardening rule is described based on yield and memory surfaces. A memory surface indicates the extent of loading, and a yield surface is the locus of the elastic region. We define a hardening modulus curve which relates the change in size of the yield and memory surfaces to the tangent modulus of the material at the maximum load. The evolution of the yield surface is described for both the proportional and nonproportional loading paths. Both quasi-static and stable cyclic loading is considered. An attractive feature of this nonlinear hardening law is that the material constants associated with it are limited—three in all—and they can be easily determined from a simple test. The predictions of the proposed hardening law are compared with the experimental data for proportional and nonproportional loading paths, and are found to be in good agreement.

scholarly journals Plasticity based interface model for failure modelling of unreinforced masonry under cyclic loading

2020 ◽  
Vol 42 (3) ◽  
pp. 321-338
Author(s):  
P. V. S. K. Kumar ◽  
Amirtham Rajagopal ◽  
Manoj Pandey
Keyword(s):  
Cyclic Loading ◽  
Yield Surface ◽  
Failure Modes ◽  
Back Stress ◽  
Unreinforced Masonry ◽  
Interface Model ◽  
Linear Set ◽  
Mixed Hardening ◽  
Hardening Law ◽  
Backward Integration

In this work our objective is to understand the failure behaviour of unreinforced masonry under in-plane cyclic loading. For this purpose we proposed a plasticity based interface model consists of a single yield surface criteria which is a direct extension of Mohr-Coulomb criteria with a tension cut and compression cap and a back stress vector is introduced as a mixed hardening law variable  in the adopted yield surface to capture the unloading/reloading behaviour of masonry under cyclic loading. A simplified micromechanical interface modelling approach is adopted to capture all the failure modes of masonry. The integration of the differential constitutive equation is  done by using implicit Euler backward integration approach and the obtained non-linear set of equations are solved by a combined local/global Newton solver. The proposed constitutive model  is implemented in ABAQUS by writing  UMAT (user-defined subroutine) and the obtained numerical results are compared with  experimental results available in the literature.

Thermodynamic-Based Modified Cam-Clay Constitutive Model Considering the Effect of Fabric

2011 ◽  
Vol 71-78 ◽  
pp. 1073-1078
Author(s):  
Xiao Xia Guo ◽  
Bo Ya Zhao
Keyword(s):  
Constitutive Model ◽  
Granular Materials ◽  
Yield Surface ◽  
True Stress ◽  
Stress Space ◽  
Volume Strain ◽  
Hardening Rule ◽  
Modified Cam Clay ◽  
Fabric Tensors ◽  
Cam Clay

In order to construct a constitutive model taking into the effect of both the fabric tensors and their evolution modes, this paper links modern ideas of thermomechanics opinion to the theory of fabric tensors. The anisotropic dissipation incremental function of modified Cam-clay constitutive model considering the effect of fabric characteristic can be obtained by establishing the relation between microstructure and plastic volume strain. After discussing the yield surfaces in the dissipative and the true stress space from the viewpoint of the evolution mode of the fabric tensors, the results indicate that the slope of the normal consolidation line and the critical state line will be governed by changes of void fabric. The model successfully captures most salient behaviors of granular materials related to fabric issues. In the dissipative stress space, the void of granular materials can rearrange and show more anisotropic. In the true stress space, fabric not only affects the deflection of the yield surface, but also affects the hardening rule.

Cyclic Plasticity for Nonproportional Paths: Part 2—Comparison With Predictions of Three Incremental Plasticity Models

1978 ◽  
Vol 100 (1) ◽  
pp. 104-111 ◽  
Author(s):  
H. S. Lamba ◽  
O. M. Sidebottom
Keyword(s):  
Cyclic Loading ◽  
Material Property ◽  
Yield Surface ◽  
Strain Path ◽  
Kinematic Hardening ◽  
Cyclic Plasticity ◽  
Limit Surface ◽  
Hardening Rule ◽  
Hardening Models ◽  
Hardening Rules

Experiments that demonstrate the basic quantitative and qualitative aspects of the cyclic plasticity of metals are presented in Part 1. Three incremental plasticity kinematic hardening models of prominence are based on the Prager, Ziegler, and Mroz hardening rules, of which the former two have been more frequently used than the latter. For a specimen previously fully stabilized by out of phase cyclic loading the results of a subsequent cyclic nonproportional strain path experiment are compared to the predictions of the above models. A formulation employing a Tresca yield surface translating inside a Tresca limit surface according to the Mroz hardening rule gives excellent predictions and also demonstrates the erasure of memory material property.

Mean Strain Effect on Crack Initiation Lives for Notched Specimens Under Biaxial Nonproportional Loading Paths

1997 ◽  
Vol 119 (1) ◽  
pp. 104-112 ◽  
Author(s):  
Ming-Chuen Yip ◽  
Yi-Ming Jen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Crack Initiation ◽  
Strain Effect ◽  
Nonproportional Loading ◽  
Notched Specimens ◽  
Loading Paths ◽  
The Mean ◽  
Mean Strain ◽  
Element Method

This paper discusses the mean strain effect on the crack initiation lives for notched specimens under biaxial nonproportional loading paths. Elastic-plastic finite element method was used to evaluate the local stresses and strains. Several prediction models related to the mean stress/strain effect were employed to correlate the experimental results with reference fatigue data for smooth specimens. It is found that Fatemi-Socie model gives good prediction for the present research with the assistance of finite element method. The stress behavior in this deflection-controlled tests is discussed in this study, and the failure surfaces are also examined after tests.

A Stochastic Nonlinear Constitutive Law for Concrete

1989 ◽  
Vol 111 (4) ◽  
pp. 443-449 ◽  
Author(s):  
A. Fafitis ◽  
Y. H. Won
Keyword(s):  
Stochastic Model ◽  
Elastic Moduli ◽  
Three Dimensional ◽  
Path Dependency ◽  
Experimental Results ◽  
Constitutive Law ◽  
Induced Anisotropy ◽  
Nonproportional Loading ◽  
Strain Relationship ◽  
Good Agreement

An incremental three-dimensional stress-strain relationship for concrete with induced anisotropy has been developed. The nonlinearity and path-dependency are modeled by expressing the elastic moduli at each increment as function of the octahedral and deviatoric strains, based on a uniaxial stochastic model developed earlier. Predictions of multiaxial response under proportional and nonproportional loading are in good agreement with experimental results.

Experimental and Theoretical Studies of Nonlinear Resonances in a Si Microcantilever Constrained by a Polymer Attachment

2016 ◽  
Author(s):  
Keivan Asadi ◽  
Snehan Peshin ◽  
Junghoon Yeom ◽  
Hanna Cho
Keyword(s):  
Multiple Scales ◽  
Geometrically Nonlinear ◽  
Flexural Mode ◽  
Nonlinear Characteristics ◽  
Nonlinear Responses ◽  
Intentional Nonlinearity ◽  
Stiffness And Damping ◽  
Experimental And Theoretical Studies ◽  
Nonlinear Hardening ◽  
Good Agreement

In micro/nanometer scale mechanical resonators, constructive utilization of intentional nonlinearity has suggested ways to leverage beneficial nonlinear characteristics in their design for various applications. Previous studies have also shown that the geometric nonlinearity is effectively implemented and tailored through integration of nonlinear couplings to an otherwise linear microcantilever. Here, we demonstrate experimentally a nonlinear micromechanical resonator consisting of a silicon microcantilever axially constrained by a polymer attachment exhibiting a strong nonlinear hardening behavior not only in its first flexural mode but also in higher modes. A theoretical model representing the system with geometrically nonlinear stiffness and damping is analyzed by the method of multiple scales, which is favorably validated by good agreement with experimentally obtained nonlinear responses.

On the Foundations of Thermoplasticity—An Experimental Investigation

1973 ◽  
Vol 40 (4) ◽  
pp. 891-896 ◽  
Author(s):  
A. Phillips ◽  
R. Kasper
Keyword(s):  
Experimental Investigation ◽  
Yield Surface ◽  
Elevated Temperatures ◽  
Hardening Law

This paper studies the motion of the yield surface at elevated temperatures under prestressing. A new hardening law is proposed and experimentally verified.

A Generalized Anisotropic Hardening Rule Based on the Mroz Multi-Yield-Surface Model

2008 ◽  
Author(s):  
K. S. Choi ◽  
J. Pan
Keyword(s):  
Cyclic Loading ◽  
Yield Surface ◽  
Kinematic Hardening ◽  
Constitutive Relations ◽  
Yield Function ◽  
Surface Model ◽  
Loading Conditions ◽  
Anisotropic Hardening ◽  
Hardening Rule ◽  
Strain Data

In this paper, a generalized anisotropic hardening rule based on the Mroz multi-yield-surface model is derived. The evolution equation for the active yield surface is obtained by considering the continuous expansion of the active yield surface during the unloading/reloading process. The incremental constitutive relation based on the associated flow rule is then derived for a general yield function. As a special case, detailed incremental constitutive relations are derived for the Mises yield function. The closed-form solutions for one-dimensional stress-plastic strain curves are also derived and plotted for the Mises materials under cyclic loading conditions. The stress-plastic strain curves show closed hysteresis loops under uniaxial cyclic loading conditions and the Masing hypothesis is applicable. A user material subroutine based on the Mises yield function, the anisotropic hardening rule and the constitutive relations was then written and implemented into ABAQUS. Computations were conducted for a simple plane strain finite element model under uniaxial monotonic and cyclic loading conditions based on the anisotropic hardening rule and the isotropic and nonlinear kinematic hardening rules of ABAQUS. The results indicate that the plastic response of the material follows the intended input stress-strain data for the anisotropic hardening rule whereas the plastic response depends upon the input strain ranges of the stress-strain data for the nonlinear kinematic hardening rule.

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