A New Constitutive Model in the Theory of Plasticity—Part I: Theory

1995 ◽  
Vol 117 (4) ◽  
pp. 365-370 ◽  
Author(s):  
W. Jiang
Keyword(s):  
General Solution ◽  
Constitutive Model ◽  
Closed Form ◽  
Yield Surface ◽  
Kinematic Hardening ◽  
Material Response ◽  
Hardening Model ◽  
Theory Of Plasticity

By proposing two rules to regulate the movement of the yield surface, this paper develops a new kinematic hardening model in the theory of plasticity. A closed-form general solution is obtained in the case of linear stress paths, material response under cyclic loadings is discussed, and various tube problems are solved to demonstrate the model.

A New Constitutive Model in the Theory of Plasticity—Part II: Examples

1995 ◽  
Vol 117 (4) ◽  
pp. 371-377 ◽  
Author(s):  
W. Jiang
Keyword(s):  
Plastic Strain ◽  
Constitutive Model ◽  
Closed Form ◽  
Hardening Model ◽  
Closed Form Solutions ◽  
Loading Paths ◽  
Theory Of Plasticity ◽  
Thin Walled Tube ◽  
Thin Walled

This part of the paper presents several examples to further demonstrate the hardening model proposed in the first part of the paper. Closed-form solutions are achieved for a thin-walled tube subjected to linear, rectangular, and circular loading paths, and the corresponding yield center loci and plastic strain trajectories are illustrated. The features of this model are further discussed.

Effect of Yield Surface Curvature on Local Necking in Biaxially Stretched Sheets in Porous Materials

1992 ◽  
Vol 114 (2) ◽  
pp. 196-200 ◽  
Author(s):  
Xiangqiao Yan
Keyword(s):  
Porous Materials ◽  
Yield Surface ◽  
Kinematic Hardening ◽  
Material Model ◽  
Isotropic Hardening ◽  
Material Models ◽  
Hardening Model ◽  
Local Necking ◽  
Highly Sensitive ◽  
Isotropic Expansion

In this paper, a recently proposed material model (Sun model) that is based on the lower bound approach of plasticity is extended by introducing a family of dilatant plasticity theories. The yield surfaces change by a combination of isotropic expansion and kinematic translation. The sensitivity of the local necking predictions in biaxially stretched sheets to the curvature of the yield surface in porous materials is addressed. The results of the present analysis obtained by using four material models, the isotropic hardening version of Sun, the kinematic hardening version suggested in this paper, the Gurson model, and the Mear and Hutchinson model, indicate that the local necking predictions are highly sensitive to the curvature of the yield surface, and the predictions given by the kinematic hardening model are more reasonable for local necking analysis than those by the isotropic hardening model.

Hardening and Degradation Rules for Metals Under Monotonic and Cyclic Loading

1983 ◽  
Vol 105 (2) ◽  
pp. 113-118 ◽  
Author(s):  
Z. Mro´z
Keyword(s):  
Elevated Temperature ◽  
Cyclic Loading ◽  
Creep Deformation ◽  
Elevated Temperatures ◽  
Kinematic Hardening ◽  
Complex Loading ◽  
Material Response ◽  
Inelastic Response ◽  
Hardening Model ◽  
Temperature Creep

In order to describe inelastic response of metals at room or elevated temperatures for complex loading histories, the combined isotropic-kinematic hardening model is discussed. The monotonic and cyclic loading histories are associated with variation of two different hardening parameters and the maximal prestress is assumed to affect essentially the material response. First, the hardening model is applied within time-independent plasticity and next the elevated temperature creep deformation is studied for both monotonic and cyclic loading. The degradation rules are briefly discussed in the last part of the paper.

Uniaxial Ratchetting of 316FR Steel at Room Temperature— Part II: Constitutive Modeling and Simulation

1998 ◽  
Vol 122 (1) ◽  
pp. 35-41 ◽  
Author(s):  
N. Ohno ◽  
M. Abdel-Karim
Keyword(s):  
Constitutive Model ◽  
Constitutive Modeling ◽  
Critical State ◽  
Room Temperature ◽  
Stress Ratio ◽  
Dynamic Recovery ◽  
Kinematic Hardening ◽  
Hysteresis Loops ◽  
Hardening Model ◽  
Stress Cycling

Uniaxial ratchetting experiments of 316FR steel at room temperature reported in Part I are simulated using a new kinematic hardening model which has two kinds of dynamic recovery terms. The model, which features the capability of simulating slight opening of stress-strain hysteresis loops robustly, is formulated by furnishing the Armstrong and Frederick model with the critical state of dynamic recovery introduced by Ohno and Wang (1993). The model is then combined with a viscoplastic equation, and the resulting constitutive model is applied successfully to simulating the experiments. It is shown that for ratchetting under stress cycling with negative stress ratio, viscoplasticity and slight opening of hysteresis loops are effective mainly in early and subsequent cycles, respectively, whereas for ratchetting under zero-to-tension only viscoplasticity is effective. [S0094-4289(00)00501-6]

Analytical Solutions for Circular Bars Subjected to Large Strain Plastic Torsion

1990 ◽  
Vol 57 (2) ◽  
pp. 298-306 ◽  
Author(s):  
K. W. Neale ◽  
S. C. Shrivastava
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Large Strain ◽  
Kinematic Hardening ◽  
Flow Theory ◽  
Constitutive Laws ◽  
Isotropic Hardening ◽  
Large Strains ◽  
Inelastic Behavior ◽  
Rate Dependent

The inelastic behavior of solid circular bars twisted to arbitrarily large strains is considered. Various phenomenological constitutive laws currently employed to model finite strain inelastic behavior are shown to lead to closed-form analytical solutions for torsion. These include rate-independent elastic-plastic isotropic hardening J2 flow theory of plasticity, various kinematic hardening models of flow theory, and both hypoelastic and hyperelastic formulations of J2 deformation theory. Certain rate-dependent inelastic laws, including creep and strain-rate sensitivity models, also permit the development of closed-form solutions. The derivation of these solutions is presented as well as numerous applications to a wide variety of time-independent and rate-dependent plastic constitutive laws.

scholarly journals Thermodynamic compatibility conditions of a new class of hysteretic materials

2021 ◽  
Author(s):  
Salvatore Sessa
Keyword(s):  
Constitutive Model ◽  
Dynamic Analysis ◽  
Closed Form ◽  
Iterative Procedure ◽  
Displacement Amplitude ◽  
Compatibility Conditions ◽  
Algebraic Functions ◽  
New Class ◽  
Thermodynamic Compatibility ◽  
Constitutive Parameters

AbstractThe thermodynamic compatibility defined by the Drucker postulate applied to a phenomenological hysteretic material, belonging to a recently formulated class, is hereby investigated. Such a constitutive model is defined by means of a set of algebraic functions so that it does not require any iterative procedure to compute the response and its tangent operator. In this sense, the model is particularly feasible for dynamic analysis of structures. Moreover, its peculiar formulation permits the computation of thermodynamic compatibility conditions in closed form. It will be shown that, in general, the fulfillment of the Drucker postulate for arbitrary displacement ranges requires strong limitations of the constitutive parameters. Nevertheless, it is possible to determine a displacement compatibility range for arbitrary sets of parameters so that the Drucker postulate is fulfilled as long as the displacement amplitude does not exceed the computed threshold. Numerical applications are provided to test the computed compatibility conditions.

On a system of three difference equations of higher order solved in terms of Lucas and Fibonacci numbers

2020 ◽  
Vol 70 (3) ◽  
pp. 641-656
Author(s):  
Amira Khelifa ◽  
Yacine Halim ◽  
Abderrahmane Bouchair ◽  
Massaoud Berkal
Keyword(s):  
General Solution ◽  
Closed Form ◽  
Difference Equations ◽  
Fibonacci Numbers ◽  
Higher Order ◽  
Real Numbers ◽  
Lucas Numbers ◽  
Rational Difference Equations ◽  
Initial Values ◽  
Fibonacci And Lucas Numbers

AbstractIn this paper we give some theoretical explanations related to the representation for the general solution of the system of the higher-order rational difference equations$$\begin{array}{} \displaystyle x_{n+1} = \dfrac{1+2y_{n-k}}{3+y_{n-k}},\qquad y_{n+1} = \dfrac{1+2z_{n-k}}{3+z_{n-k}},\qquad z_{n+1} = \dfrac{1+2x_{n-k}}{3+x_{n-k}}, \end{array}$$where n, k∈ ℕ0, the initial values x−k, x−k+1, …, x0, y−k, y−k+1, …, y0, z−k, z−k+1, …, z1 and z0 are arbitrary real numbers do not equal −3. This system can be solved in a closed-form and we will see that the solutions are expressed using the famous Fibonacci and Lucas numbers.

scholarly journals Note on constructing a family of solvable sine-type difference equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ahmed El-Sayed Ahmed ◽  
Bratislav Iričanin ◽  
Witold Kosmala ◽  
Stevo Stević ◽  
Zdeněk Šmarda
Keyword(s):  
General Solution ◽  
Closed Form ◽  
Difference Equations ◽  
First Order ◽  
Solvable In Closed Form

AbstractWe obtain a family of first order sine-type difference equations solvable in closed form in a constructive way, and we present a general solution to each of the equations.

Calibration and Validation of an Elasto-Viscoplastic Material Model for a Hot Work Tool Steel Used in Pressure Casting Dies

2007 ◽  
Vol 345-346 ◽  
pp. 685-688 ◽  
Author(s):  
Werner Ecker ◽  
Thomas Antretter ◽  
R. Ebner
Keyword(s):  
Constitutive Model ◽  
Tool Steel ◽  
Mechanical Response ◽  
Mechanical Load ◽  
Kinematic Hardening ◽  
Ex Situ ◽  
Pressure Casting ◽  
Viscoplastic Material ◽  
Crack Network ◽  
Hot Work Tool Steel

Pressure casting dies are subjected to a large number of thermal as well as mechanical load cycles, which are leading to a characteristic thermally induced crack network on the die surface. As a typical representative for a die material the cyclic thermo-mechanical behavior of the hot work tool steel grade 1.2343 (X38CrMoV5-1) is investigated both experimentally as well as numerically. On the one hand the information from isothermal compression-tension tests is used in a subsequent analysis to calibrate a constitutive model that takes into account the characteristic combined isotropic-kinematic hardening/softening of the material. On the other hand the non-isothermal mechanical response of the material to thermal cycles is characterized by means of a periodic laser pulse applied to a small plate-like specimen which is cooled on the back. The residual stresses developing at the surface of the irradiated region of the specimen are determined ex-situ by means of X-ray diffraction. The obtained values agree well with the results of an accompanying finite-element study. This information is used to verify the calibrated constitutive model. The material law is finally used for the prediction of stresses and strains in a die.

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