On Constitutive Relations in Non-Smooth Elasto/Viscoplasticity

2012 ◽  
Vol 566 ◽  
pp. 691-698 ◽  
Author(s):  
Fabio de Angelis
Keyword(s):  
Convex Analysis ◽  
Model Problem ◽  
Constitutive Relations ◽  
General Treatment ◽  
Elastoplastic Model ◽  
Smooth Functions ◽  
Subdifferential Calculus ◽  
Viscoplastic Model ◽  
Structural Problems ◽  
Variational Formulations

A general treatment of constitutive relations in elastoplasticity and elasto/viscoplasticity is presented. The treatment holds for general non-smooth problems and it applies to non-smooth yield criteria and to functions characterized by non-differentiability. The formulation is developed by resorting to the tools provided by convex analysis and subdifferential calculus which are the appropriate instruments for dealing with convex criteria and non-smooth functions. General formulations of constitutive relations and evolutive laws are presented for elastoplasticity and elasto/viscoplasticity and connections are illustrated between the general elastoplastic model problem and the general elasto/viscoplastic model problem. The presented generalized treatment proves to be well-suited for the development of variational formulations for structural problems in elastoplasticity and elasto/viscoplasticity.

A General Form of Constitutive Relations in Non-Smooth Elastoplasticity

2012 ◽  
Vol 256-259 ◽  
pp. 979-985 ◽  
Author(s):  
Fabio de Angelis
Keyword(s):  
Convex Analysis ◽  
Constitutive Relations ◽  
Theoretical Framework ◽  
Mathematical Treatment ◽  
Subdifferential Calculus ◽  
Yield Criteria ◽  
Structural Problems ◽  
Differentiable Functions ◽  
Variational Formulations

A general formulation of constitutive relations in non-smooth elastoplasticity is presented. The treatment applies to general non-smooth plasticity problems and to problems characterized by non-smooth yield criteria or dealing with non-differentiable functions. The mathematical tools and instruments of convex analysis and subdifferential calculus are suitably applied since they provide the proper mathematical instruments for dealing with non-smooth problems and non-differentiable functions. General formulations of constitutive relations and evolutive laws in non-smooth elastoplasticity are illustrated within the presented theoretical framework. Connections between the proposed mathematical treatment and the classical relations in elastoplasticity are illustrated and discussed in detail. The presented generalized treatment is equipped with considerable advantages since it shows to be ideally suited for the development of variational formulations of structural problems in non-smooth elastoplasticity.

Evolutive Laws and Constitutive Relations in Nonlocal Viscoplasticity

2012 ◽  
Vol 152-154 ◽  
pp. 990-996 ◽  
Author(s):  
Fabio de Angelis
Keyword(s):  
Constitutive Relations ◽  
Material Model ◽  
Standard Material ◽  
Viscoplastic Model ◽  
Proposed Model

In the present work the evolutive laws and the constitutive relations for a model of nonlocal viscoplasticity are analyzed. Nonlocal dissipative variables and suitable regularization operators are adopted. The proposed model is developed within the framework of the generalized standard material model. Suitable forms of the elastic and dissipative viscoplastic potentials are defined and the associated constitutive relations are specialized. The evolutive laws for the proposed nonlocal viscoplastic model are presented in a general form which can be suitably specialized in order to include different models of nonlocal viscoplasticity.

An anisotropic elastoplastic model for soft clays

2003 ◽  
Vol 40 (2) ◽  
pp. 403-418 ◽  
Author(s):  
Simon J Wheeler ◽  
Anu Näätänen ◽  
Minna Karstunen ◽  
Matti Lojander
Keyword(s):  
Experimental Data ◽  
Yield Curve ◽  
Constitutive Relations ◽  
Stress Path ◽  
Elastoplastic Model ◽  
Soft Clays ◽  
Rotational Hardening ◽  
Modified Cam Clay ◽  
Cam Clay

An anisotropic elastoplastic model for soft clays is presented. Experimental data from multistage drained triaxial stress path tests on Otaniemi clay from Finland provide support for the proposed shape of the yield curve and for the proposed relationship describing the change of yield curve inclination with plastic straining. Procedures are proposed for determining the initial inclination of the yield curve and the values of the two additional soil constants within the model. Comparisons of model simulations with experimental data demonstrate significant improvements in the performance of the new model over the Modified Cam Clay model. The remaining discrepancies are mainly attributable to the important role of destructuration in the sensitive Otaniemi clay.Key words: anisotropy, constitutive relations, elastoplasticity, laboratory tests, rotational hardening, soft clays.

On the Relation between Two Constitutive Models Frequently Adopted in Viscoplasticity

2012 ◽  
Vol 256-259 ◽  
pp. 995-1003 ◽  
Author(s):  
Fabio de Angelis
Keyword(s):  
Constitutive Model ◽  
Convex Analysis ◽  
Constitutive Models ◽  
Unified Framework ◽  
Subdifferential Calculus

The constitutive models of plasticity and viscoplasticity are formulated in a unified framework by taking advantage of the appropriate mathematical tools of convex analysis and subdifferential calculus. Two viscoplastic constitutive models frequently adopted in viscoplasticity are analyzed, the Duvaut and Lions viscoplastic constitutive model and the Perzyna viscoplastic constitutive model. In literature these two models are frequently adopted as alternatives. In the present paper it is discussed on the relation between the two models and it is shown that, under certain conditions and assumptions, the Duvaut-Lions model may be considered as derived from the Perzyna model.

Approximation De Fonctions Convexes Sur Un Espace De Mesures Et Applications

1982 ◽  
Vol 25 (4) ◽  
pp. 392-413 ◽  
Author(s):  
R. Temam
Keyword(s):  
Calculus Of Variations ◽  
Convex Analysis ◽  
Variational Problems ◽  
Existence Theory ◽  
Smooth Functions ◽  
Perfect Plasticity ◽  
Basic Properties ◽  
Convex Functionals

AbstractIn the first part of this article we recall the definition and a few basic properties of convex functionals defined on a space of bounded measures. In the second part we show several results of approximation of the following type: Although a measure μ cannot be approximated in the sense of the norm by smooth functions, we can find an appropriate sequence of smooth functions which converge weakly to the measure μ, the corresponding value of the functional converging to the value of the functional at μ.This article is part of a series on the existence theory of solution of variational problems of mechanics (perfect plasticity), which is based on a systematic utilization of the methods of convex analysis and the calculus of variations.

scholarly journals Foundations and Their Practical Implications for the Constitutive Coefficients of Poromechanical Dual-Continuum Models

2019 ◽  
Vol 130 (3) ◽  
pp. 699-730 ◽  
Author(s):  
Mark Ashworth ◽  
Florian Doster
Keyword(s):  
Model Problem ◽  
Constitutive Relations ◽  
Continuum Models ◽  
Mechanical Interaction ◽  
Effective Parameters ◽  
Governing Equations ◽  
First Order ◽  
Multiscale Systems ◽  
Compare And Contrast ◽  
Practical Implications

Abstract A dual-continuum model can offer a practical approach to understanding first-order behaviours of poromechanically coupled multiscale systems. To close the governing equations, constitutive equations with models to calculate effective constitutive coefficients are required. Several coefficient models have been proposed within the literature. However, a holistic overview of the different modelling concepts is still missing. To address this we first compare and contrast the dominant models existing within the literature. In terms of the constitutive relations themselves, early relations were indirectly postulated that implicitly neglected the effect of the mechanical interaction arising between continuum pressures. Further, recent users of complete constitutive systems that include inter-continuum pressure coupling have explicitly neglected these couplings as a means of providing direct relations between composite and constituent properties, and to simplify coefficient models. Within the framework of micromechanics, we show heuristically that these explicit decouplings are in fact coincident with bounds on the effective parameters themselves. Depending on the formulation, these bounds correspond to end-member states of isostress or isostrain. We show the impacts of using constitutive coefficient models, decoupling assumptions and parameter bounds on poromechanical behaviours using analytical solutions for a 2D model problem. Based on the findings herein, we offer recommendations for how and when to use different coefficient modelling concepts.

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