AN APPLICATION OF HYPERPLASTICITY TO DETERMINE THE BEHAVIOR OF A PLANE STRESS CANTILEVER BEAM

2016 ◽  
Vol 3 (2) ◽  
Author(s):  
Hai Than Nguyen ◽  
Lam Nguyen Sy
Keyword(s):  
Cantilever Beam ◽  
Energy Function ◽  
Kinematic Hardening ◽  
Scalar Potential ◽  
Yield Function ◽  
Dissipation Function ◽  
Surface Model ◽  
Free Energy Function ◽  
Sophisticated Model ◽  
Von Mises

Hyperplasticity is an approach to plasticity theory based on thermodynamic principles. By using this concept, the entire constitutive model behavior can be determined from two scalar potential functions, one is the energy function and the other is the yield function or the dissipation function. In this paper, the hyperplasticity model for homogeneous and isotropic material is derive and implemented in finite element method (FEM) to solve a particular problem in structure analysis, the behavior of a cantilever beam. The Gibbs free energy function and the Von Mises yield function are chosen to derive the elasto-plastic response of structures. Besides, kinematic hardening with single yield surface model is employed to describe the behavior when yield occur. The result shows that the application of hyperplasticity to FEM can be another proper way for non-linear analysis. Moreover, it reveals the ability to develop more sophisticated model using multiple yield surfaces in cases of cyclic loading.

The Modified Cam-Clay Model and the Constitutive Relation Principle of Thermodynamics with Internal Variables

2013 ◽  
Vol 353-356 ◽  
pp. 837-841 ◽  
Author(s):  
Jing Yu Chen ◽  
Ying Hai
Keyword(s):  
Free Energy ◽  
Constitutive Relation ◽  
Energy Function ◽  
Yield Function ◽  
Dissipation Function ◽  
Saturated Soils ◽  
Internal Variables ◽  
Free Energy Function ◽  
Modified Cam Clay ◽  
Cam Clay

According the theory of thermodynamics with internal variables, the relation between yield function and dissipation function and the condition of associated flow rule in stress space are presented; the elastoplastic matrix of the incremental form of the material constitutive equation is given out, this matrix is determined by the free energy function and the yield function. The Gibbs free energy function of solid phase of saturated soils subjected triaxial compression stress state is presented, and using the constitutive theory of thermodynamics with internal variables, yield function and stress-strain relation of the modified Cam-Clay model is obtained by the free energy function and the dissipation function. These results prove the correctness and feasibility for this constitutive theory to construct elastoplastic constitutive relation of saturated soils.

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.

On the Determination of Entropy From a Scalar Potential for Special Inelastic Materials

1999 ◽  
Author(s):  
George C. Johnson ◽  
Ali Imam
Keyword(s):  
Energy Function ◽  
Helmholtz Free Energy ◽  
Scalar Potential ◽  
Deformation Gradient ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Free Energy Function ◽  
Response Functions ◽  
Constitutive Response

Abstract A known version of the second law of thermodynamics embodying the notion of dissipation is employed to obtain restrictions among constitutive response functions for two classes of inelastic bodies. It is shown that for such bodies the entropy function can be determined once the constitutive relation for the Helmholtz free energy function is specified. In addition the internal energy function is shown to depend exclusively on the temperature and the deformation gradient.

scholarly journals Nonlinear regularization operators as derived from the micromorphic approach to gradient elasticity, viscoplasticity and damage

2016 ◽  
Vol 472 (2188) ◽  
pp. 20150755 ◽  
Author(s):  
Samuel Forest
Keyword(s):  
Free Energy ◽  
Energy Function ◽  
Kinematic Hardening ◽  
Deformation Gradient ◽  
Gradient Elasticity ◽  
Gradient Term ◽  
Deformation Model ◽  
Finite Width ◽  
Free Energy Function ◽  
Constitutive Material Model

The construction of regularization operators presented in this work is based on the introduction of strain or damage micromorphic degrees of freedom in addition to the displacement vector and of their gradients into the Helmholtz free energy function of the constitutive material model. The combination of a new balance equation for generalized stresses and of the micromorphic constitutive equations generates the regularization operator. Within the small strain framework, the choice of a quadratic potential w.r.t. the gradient term provides the widely used Helmholtz operator whose regularization properties are well known: smoothing of discontinuities at interfaces and boundary layers in hardening materials, and finite width localization bands in softening materials. The objective is to review and propose nonlinear extensions of micromorphic and strain/damage gradient models along two lines: the first one introducing nonlinear relations between generalized stresses and strains; the second one envisaging several classes of finite deformation model formulations. The generic approach is applicable to a large class of elastoviscoplastic and damage models including anisothermal and multiphysics coupling. Two standard procedures of extension of classical constitutive laws to large strains are combined with the micromorphic approach: additive split of some Lagrangian strain measure or choice of a local objective rotating frame. Three distinct operators are finally derived using the multiplicative decomposition of the deformation gradient. A new feature is that a free energy function depending solely on variables defined in the intermediate isoclinic configuration leads to the existence of additional kinematic hardening induced by the gradient of a scalar micromorphic variable.

scholarly journals Configurational forces in cyclic metal plasticity

2019 ◽  
Vol 300 ◽  
pp. 08009
Author(s):  
Aris Tsakmakis ◽  
Michael Vormwald
Keyword(s):  
Driving Force ◽  
Plastic Material ◽  
Kinematic Hardening ◽  
Yield Function ◽  
Configurational Forces ◽  
Isotropic Hardening ◽  
Crack Driving Force ◽  
Metal Plasticity ◽  
Elastic Plastic ◽  
Von Mises

The configurational force concept is known to describe adequately the crack driving force in linear fracture mechanics. It seems to represent the crack driving force also for the case of elastic-plastic material properties. The latter has been recognized on the basis of thermodynamical considerations. In metal plasticity, real materials exhibit hardening effects when sufficiently large loads are applied. Von Mises yield function with isotropic and kinematic hardening is a common assumption in many models. Kinematic and isotropic hardening turn out to be very important whenever cyclic loading histories are applied. This holds equally regardless of whether the induced deformations are homogeneous or non-homogeneous. The aim of the present paper is to discuss the effect of nonlinear isotropic and kinematic hardening on the response of the configurational forces and related parameters in elastic-plastic fracture problems.

REGULARITY RESULTS FOR THREE-DIMENSIONAL ISOTROPIC AND KINEMATIC HARDENING INCLUDING BOUNDARY DIFFERENTIABILITY

2009 ◽  
Vol 19 (12) ◽  
pp. 2231-2262 ◽  
Author(s):  
JENS FREHSE ◽  
DOMINIQUE LÖBACH
Keyword(s):  
Elastic Strain ◽  
Dirichlet Boundary ◽  
Kinematic Hardening ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Yield Function ◽  
Isotropic Hardening ◽  
Von Mises ◽  
Regularity Results ◽  
Elastic Strain Tensor

For a flat Dirichlet boundary we prove that the first normal derivatives of the stresses and internal parameters are in L∞(0, T; L1+δ) and in L∞(0, T; H½-δ) up to the boundary. This deals with solutions of elastic–plastic flow problems with isotropic or kinematic hardening with von Mises yield function. We show that the elastic strain tensor ε(u) of three-dimensional plasticity with isotropic hardening is contained in the space [Formula: see text] and in L∞(0,T;H4-δ) up to the flat Dirichlet boundary. We obtain related results concerning traces of ε(u). In the case of kinematic hardening we present a simple proof of the [Formula: see text] inclusion of the elastic strain tensor.

A canonical ensemble derivation of the McMillan-Mayer solution theory

1983 ◽  
Vol 48 (10) ◽  
pp. 2888-2892 ◽  
Author(s):  
Vilém Kodýtek
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Energy Function ◽  
Special Function ◽  
Helmholtz Free Energy ◽  
Canonical Ensemble ◽  
Free Energy Function ◽  
Solution Theory ◽  
Pure Solvent ◽  
The Common

A special free energy function is defined for a solution in the osmotic equilibrium with pure solvent. The partition function of the solution is derived at the McMillan-Mayer level and it is related to this special function in the same manner as the common partition function of the system to its Helmholtz free energy.

scholarly journals Run-and-Tumble Motion: The Role of Reversibility

2021 ◽  
Vol 183 (3) ◽  
Author(s):  
Bart van Ginkel ◽  
Bart van Gisbergen ◽  
Frank Redig
Keyword(s):  
Free Energy ◽  
Diffusion Coefficient ◽  
Large Deviations ◽  
Energy Function ◽  
Internal State ◽  
Rate Function ◽  
Free Energy Function ◽  
Large Deviations Principle ◽  
Preferred Direction ◽  
State Process

AbstractWe study a model of active particles that perform a simple random walk and on top of that have a preferred direction determined by an internal state which is modelled by a stationary Markov process. First we calculate the limiting diffusion coefficient. Then we show that the ‘active part’ of the diffusion coefficient is in some sense maximal for reversible state processes. Further, we obtain a large deviations principle for the active particle in terms of the large deviations rate function of the empirical process corresponding to the state process. Again we show that the rate function and free energy function are (pointwise) optimal for reversible state processes. Finally, we show that in the case with two states, the Fourier–Laplace transform of the distribution, the moment generating function and the free energy function can be computed explicitly. Along the way we provide several examples.

Modeling and Simulation of Damage Processes based on a Gradient-Enhanced Free Energy Function

PAMM ◽  
2014 ◽  
Vol 14 (1) ◽  
pp. 151-152
Author(s):  
Stephan Schwarz ◽  
Philipp Junker ◽  
Klaus Hackl
Keyword(s):  
Free Energy ◽  
Modeling And Simulation ◽  
Energy Function ◽  
Free Energy Function ◽  
Damage Processes

Elasto-Plastic Analysis of Reissner-Mindlin Plates

1990 ◽  
Vol 43 (5S) ◽  
pp. S40-S50 ◽  
Author(s):  
Panayiotis Papadopoulos ◽  
Robert L. Taylor
Keyword(s):  
Yield Function ◽  
Rate Equations ◽  
Test Problems ◽  
Field Equations ◽  
Element Analysis ◽  
Linear Hardening ◽  
Nonlinear Version ◽  
Plastic Analysis ◽  
Von Mises ◽  
Predictor Corrector

A finite element analysis of elasto-plastic Reissner-Mindlin plates is presented. The discrete field equations are derived from a nonlinear version of the Hu-Washizu variational principle. Associative plasticity, including linear hardening, is employed by means of a generalized von Mises-type yield function. A predictor/corrector scheme is used to integrate the plastic constitutive rate equations. Numerical simulations are conducted for a series of test problems to illustrate performance of the formulation.

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