A Unified Constitutive Model with Dislocation Densities as Internal Variables

1991 ◽  
pp. 385-388 ◽  
Author(s):  
Y. Estrin ◽  
H. Mecking
Keyword(s):  
Constitutive Model ◽  
Internal Variables ◽  
Dislocation Densities

A Dislocation Density Based Constitutive Model for Cyclic Deformation

1996 ◽  
Vol 118 (4) ◽  
pp. 441-447 ◽  
Author(s):  
Y. Estrin ◽  
H. Braasch ◽  
Y. Brechet
Keyword(s):  
Cyclic Loading ◽  
Dislocation Density ◽  
Constitutive Model ◽  
Constitutive Equations ◽  
Cyclic Deformation ◽  
Internal Variables ◽  
Density Evolution ◽  
Alloy 800H ◽  
Material Response ◽  
Dislocation Densities

A new constitutive model describing material response to cyclic loading is presented. The model includes dislocation densities as internal variables characterizing the microstructural state of the material. In the formulation of the constitutive equations, the dislocation density evolution resulting from interactions between dislocations in channel-like dislocation patterns is considered. The capabilities of the model are demonstrated for INCONEL 738 LC and Alloy 800H.

A constitutive model for Fe-based shape memory alloy considering martensitic transformation and plastic sliding coupling: Application to a finite element structural analysis

2012 ◽  
Vol 23 (10) ◽  
pp. 1143-1160 ◽  
Author(s):  
Walid Khalil ◽  
Alain Mikolajczak ◽  
Céline Bouby ◽  
Tarak Ben Zineb
Keyword(s):  
Finite Element ◽  
Phase Transformation ◽  
Structural Analysis ◽  
Shape Memory Alloy ◽  
Constitutive Model ◽  
Shape Memory ◽  
Internal Variables ◽  
Thermomechanical Loading ◽  
Proposed Model ◽  
Numerical Tool

In this article, we propose a finite element numerical tool adapted to a Fe-based shape memory alloy structural analysis, based on a developed constitutive model that describes the effect of phase transformation, plastic sliding, and their interactions on the thermomechanical behavior. This model was derived from an assumed expression of the Gibbs free energy taking into account nonlinear interaction quantities related to inter- and intragranular incompatibilities as well as mechanical and chemical quantities. Two scalar internal variables were considered to describe the phase transformation and plastic sliding effects. The hysteretic and specific behavior patterns of Fe-based shape memory alloy during reverse transformation were studied by assuming a dissipation expression. The proposed model effectively describes the complex thermomechanical loading paths. The numerical tool derived from the implicit resolution of the nonlinear partial derivative constitutive equations was implemented into the Abaqus® finite element code via the User MATerial (UMAT) subroutine. After tests to verify the model for homogeneous and heterogeneous thermomechanical loadings, an example of Fe-based shape memory alloy application was studied, which corresponds to a tightening system made up of fishplates for crane rails. The results we obtained were compared to experimental ones.

A finite-deformation constitutive model of particle-binder composites incorporating yield-surface-free plasticity

2021 ◽  
pp. 1-32
Author(s):  
Ankit Agarwal ◽  
Marcial Gonzalez
Keyword(s):  
Constitutive Model ◽  
Yield Surface ◽  
Finite Deformation ◽  
Large Strain ◽  
Elastic Response ◽  
Rate Equations ◽  
Internal Variables ◽  
Model Parameters ◽  
Stress Strain ◽  
Stress Softening

Abstract We present a constitutive model for particle-binder composites that accounts for finite-deformation kinematics, nonlinear elasto-plasticity without apparent yield, cyclic hysteresis, and progressive stress-softening before the attainment of stable cyclic response. The model is based on deformation mechanisms experimentally observed during quasi-static monotonic and cyclic compression of mock Plastic-Bonded Explosives (PBX) at large strain. An additive decomposition of strain energy into elastic and inelastic parts is assumed, where the elastic response is modeled using Ogden hyperelasticity while the inelastic response is described using yield-surface-free endochronic plasticity based on the concepts of internal variables and of evolution or rate equations. Stress-softening is modeled using two approaches; a discontinuous isotropic damage model to appropriately describe the softening in the overall loading-unloading response, and a material scale function to describe the progressive cyclic softening until cyclic stabilization. A nonlinear multivariate optimization procedure is developed to estimate the elasto-plastic model parameters from nominal stress-strain experimental compression data. Finally, a correlation between model parameters and the unique stress-strain response of mock PBX specimens with differing concentrations of aluminum is identified, thus establishing a relationship between model parameters and material composition.

A large deformation framework for shape memory polymers: Constitutive modeling and finite element implementation

2012 ◽  
Vol 24 (1) ◽  
pp. 21-32 ◽  
Author(s):  
Mostafa Baghani ◽  
Reza Naghdabadi ◽  
Jamal Arghavani
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Shape Memory ◽  
Finite Deformation ◽  
Deformation Gradient ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Shape Memory Polymers ◽  
Small Strain ◽  
Internal Variables

Shape memory polymers commonly experience both finite deformations and arbitrary thermomechanical loading conditions in engineering applications. This motivates the development of three-dimensional constitutive models within the finite deformation regime. In the present study, based on the principles of continuum thermodynamics with internal variables, a three-dimensional finite deformation phenomenological constitutive model is proposed taking its basis from the recent model in the small strain regime proposed by Baghani et al. (2012). In the constitutive model derivation, a multiplicative decomposition of the deformation gradient into elastic and inelastic stored parts (in each phase) is adopted. Moreover, employing the mixture rule, the Green–Lagrange strain tensor is related to the rubbery and glassy parts. In the constitutive model, the evolution laws for internal variables are derived during both cooling and heating thermomechanical loadings. Furthermore, we present the time-discrete form of the proposed constitutive model in the implicit form. Using the finite element method, we solve several boundary value problems, that is, tension and compression of bars and a three-dimensional beam made of shape memory polymers, and investigate the model capabilities as well as its numerical counterpart. The model is validated by comparing the predicted results with experimental data reported in the literature that shows a good agreement.

Application of Strain Gradient Plasticity Modelling to High Pressure Torsion

2008 ◽  
Vol 584-586 ◽  
pp. 1051-1056 ◽  
Author(s):  
Andrey Molotnikov
Keyword(s):  
High Pressure ◽  
Strain Gradient ◽  
High Pressure Torsion ◽  
Deformation Behaviour ◽  
Strain Gradient Theory ◽  
Ultrafine Grain ◽  
Internal Variables ◽  
Gradient Theory ◽  
Gradient Plasticity ◽  
Dislocation Densities

An analytical model describing the deformation behaviour of copper during the high-pressure torsion (HPT) processing is presented. The model was developed on the microstructural basis where the material is partitioned in two ‘phases’, the dislocation densities in cell walls and the dislocation densities cell interior, entering the model as scalar internal variables. The resulting ’phase mixture’ model is combined with strain gradient theory to account for strain non-uniformity inherent in SPD. It was demonstrated that gradient plasticity model is capable of describing the experimentally observed trends and accounting for a homogenisation of the accumulated shear strain across the HPT sample. The predictions of the model with respect to the ultrafine grain size produced by HPT and evolution of dislocation densities are in good agreement with experimental results reported by other research groups.

A constitutive model for shape memory polymers with application to torsion of prismatic bars

2012 ◽  
Vol 23 (2) ◽  
pp. 107-116 ◽  
Author(s):  
Mostafa Baghani ◽  
Reza Naghdabadi ◽  
Jamal Arghavani ◽  
Saeed Sohrabpour
Keyword(s):  
Heat Transfer ◽  
Constitutive Model ◽  
Shape Memory ◽  
Shape Memory Polymer ◽  
Shape Memory Polymers ◽  
Second Law Of Thermodynamics ◽  
Considerable Effect ◽  
Heat Transfer Analysis ◽  
Internal Variables ◽  
Rate Dependent

In this article, satisfying the second law of thermodynamics, we present a 3D constitutive model for shape memory polymers. The model is based on an additive decomposition of the strain into four parts. Also, evolution laws for internal variables during both cooling and heating processes are proposed. Since temperature has considerable effect on the shape memory polymer behavior, for simulation of a shape memory polymer–based structure, it is required to perform a heat-transfer analysis. Commonly, an experimentally observed temperature rate–dependent behavior of shape memory polymers is justified by a rate-dependent glassy temperature, but using the heat-transfer analysis, it is shown that the glassy temperature could be considered as a constant material parameter. To this end, implementing the constitutive model within a nonlinear finite element code, we simulate torsion of a shape memory polymer rectangular bar and a circular tube. Moreover, we compare the predicted results with experimental data recently reported in the literature, which shows a good agreement.

scholarly journals Macroscopic constitutive model for ergodic and non-ergodic lead-free relaxors

2021 ◽  
pp. 1045389X2110386
Author(s):  
Friedemann A Streich ◽  
Alexander Martin ◽  
Kyle G Webber ◽  
Marc Kamlah
Keyword(s):  
Constitutive Model ◽  
Time Integration ◽  
Three Dimensional ◽  
Solution Procedure ◽  
Ferroelectric Materials ◽  
Lead Free ◽  
Macroscopic Model ◽  
Internal Variables ◽  
Integration Scheme ◽  
Predictor Corrector

A fully electromechanically coupled, three dimensional phenomenological constitutive model for relaxor ferroelectric materials was developed for the use in a finite-element-method (FEM) solution procedure. This macroscopic model was used to simulate the macroscopic electromechanical response of lead-free ergodic [Formula: see text] and non-ergodic [Formula: see text] relaxor materials. The presented constitutive model is capable of accounting for the observed pinched hysteretic response as well as non-deviatoric polarization induced strain and internal order transitions. Time integration of the history dependent internal variables is done with a predictor-corrector integration scheme. The adaptability of the constitutive model regarding the pinching of the hystereses is shown. Simulations are compared to experimental observations.

An Extended 3D Finite Strain Constitutive Model for Shape Memory Alloys

2021 ◽  
pp. 1-37
Author(s):  
Mengqian Zhang ◽  
Theocharis Baxevanis
Keyword(s):  
Phase Transformation ◽  
Constitutive Model ◽  
Shape Memory Alloys ◽  
Shape Memory ◽  
Finite Strain ◽  
Volume Fraction ◽  
Internal Variables ◽  
Numerical Implementation ◽  
Deformation Response ◽  
Heat Effects

Abstract A 3D finite-strain constitutive model for shape memory alloys (SMAs) is proposed. The model can efficiently describe reversible phase transformation from austenite to self-accommodated and/or oriented martensite, (re)orientation of martensite variants, minor loops, latent heat effects, and tension–compression asymmetry based on the Eulerian logarithmic strain and the corotational logarithmic objective rate. It further accounts for transformation volume contraction, smooth thermomechanical response, temperature dependence of the critical force required for (re)orientation, temperature and load dependence of the hysteresis width, asymmetry between forward and reverse phase transformation, and is flexible enough to address the deformation response in the concurrent presence of several phases, i.e., when austenite, self-accommodated and oriented martensite co-exist in the microstructure. The ability of the proposed model to describe the aforementioned deformation response characteristics of SMAs under multiaxial, thermomechanical, nonproportional loading relies on the set of three independent internal variables, i.e., the average volume fraction of martensite variants, their preferred direction, and the magnitude of the induced inelastic strain, that further allow for an implicit description of a fourth internal variable, the volume fraction of oriented as opposed to self-accommodated martensite. The calibration of the model and its numerical implementation in an efficient scheme are presented. The model is validated against experimental results associated with complex thermomechanical paths, including tension/compression/torsion experiments and the efficiency of its numerical implementation is verified with simulations of the response of a biomedical superelastic SMA stent and an SMA spring actuator.

Parameter Evaluation for a Unified Constitutive Model

1993 ◽  
Vol 115 (2) ◽  
pp. 157-162 ◽  
Author(s):  
P. E. Senseny ◽  
N. S. Brodsky ◽  
K. L. DeVries
Keyword(s):  
Constitutive Model ◽  
Strain Rate ◽  
Least Squares ◽  
Constitutive Equations ◽  
Laboratory Data ◽  
Constant Strain Rate ◽  
Nonlinear Least Squares ◽  
Evolutionary Equation ◽  
Internal Variables ◽  
Isotropic Hardening

Parameters for the unified constitutive model MATMOD [1] were evaluated for rock salt (NaCl) by using nonlinear least squares to fit the model to isothermal laboratory data. MATMOD incorporates two internal variables that represent the effects of both kinematic and isotropic hardening. The constitutive equations contain nine parameters that must be evaluated to model isothermal deformation. Laboratory data from stress relaxation, constant strain rate, and long-term creep tests were used. The latter two test types included staged tests in which the strain rate or stress was changed step-wise during the test. The test conditions were precisely controlled by a computer and the constitutive equations were integrated to simulate the laboratory conditions closely. The MATMOD parameters were then evaluated by fitting the integrated equations to the laboratory data using nonlinear least squares. The model fits the data well, but the fit may be improved by changing the evolutionary equation for the internal variable that accounts for isotropic hardening.

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