scholarly journals Subdifferential Calculus Rules in Convex Analysis: A Unifying Approach Via Pointwise Supremum Functions

2008 ◽  
Vol 19 (2) ◽  
pp. 863-882 ◽  
Author(s):  
A. Hantoute ◽  
M. A. López ◽  
C. Zălinescu
Keyword(s):  
Convex Analysis ◽  
Subdifferential Calculus ◽  
Calculus Rules

Extensions Of Subdifferential Calculus Rules in Banach Spaces

1996 ◽  
Vol 48 (4) ◽  
pp. 834-848 ◽  
Author(s):  
A. Jourani ◽  
L. Thibault
Keyword(s):  
Banach Spaces ◽  
Clarke Subdifferential ◽  
Subdifferential Calculus ◽  
Finite Dimensional ◽  
Calculus Rules ◽  
Approximate Subdifferential ◽  
The Clarke Subdifferential

AbstractThis paper is devoted to extending formulas for the geometric approximate subdifferential and the Clarke subdifferential of extended-real-valued functions on Banach spaces. The results are strong enough to include completely the finite dimensional setting.

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.

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.

Subdifferential Calculus Rules for Possibly Nonconvex Integral Functions

2020 ◽  
Vol 58 (1) ◽  
pp. 462-484 ◽  
Author(s):  
Rafael Correa ◽  
Abderrahim Hantoute ◽  
Pedro Pérez-Aros
Keyword(s):  
Subdifferential Calculus ◽  
Calculus Rules
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