Filumena Marturano:

Abstract

Mathematical models related to some Josephson junctions are pointed out and attention is drawn to the solutions of certain initial boundary problems and to some of their estimates. In addition, results of rigorous analysis of the behaviour of these solutions when t → ∞ and when the small parameter ε tends to zero are cited. These analyses lead us to mention some of the open problems.

On the Relation between Two Constitutive Models Frequently Adopted in Viscoplasticity

“…Equation ( 6) 2 represents an equivalent form, see e.g. De Angelis [18], of the loading/unloading conditions in the well known complementarity form…”

“…The normality law (9) may be expressed in subdifferential form by observing, see e.g. De Angelis [18], that N C (σ) coincides with the subdifferential of the indicator function…”

“…The representation of the viscoplastic constitutive law in the form (18) 2 has also a more general significance. In fact if the function G(x) is assumed to be equal to the indicator function of the set of non-positive real numbers…”

“…and thus the viscoplastic flow law (18) 2 supplies at the limit the plastic flow law (12). The generalized viscoplastic flow law (18) 2 is therefore capable to be suitably specialized for representing different viscoplastic constitutive models and at the limit is capable of properly supplying the plastic flow law. Such generalized framework is useful for the derivation of variational formulations in plasticity and viscoplasticity which form the basis for the development of numerical algorithms in finite element applications, see e.g.…”

“…This result was originally presented by the author, see e.g. De Angelis [18]. For the proof of this result it is necessary to properly use the mathematical tools of convex analysis and notions about problems of projection on convex sets.…”