Tesi di diploma di 1° livello per la Classe delle Scienze Sperimentali Diploma di 1° livello Scuola Superiore di Catania, Catania, Italy 2014 A.A. 2012/2013

Includes bibliographical references (50-54 p.) and index.

1 Introduction.
2 Foundations of Continuum Mechanics.
2.1 Notation.
2.2 Kinematics.
2.3 Objective time derivatives.
2.4 Principle of Virtual Power for First Gradient materials.
2.5 Isotropy.
2.5.1 Symmetry of Mandel tensor.
3 Dissipation.
3.1 Principle of Maximum Dissipation.
3.2 Rate independent plasticity and yeld criterion.
3.3 Principle of Maximum Plastic Dissipation.
4 Analytic determination of the KKT-multiplier.
4.1 KKT multiplier.
4.2 Tensors A and Bp for isotropic hyperelastic materials.
4.3 Materials independent on I2.
5 Conclusions.
A Tensorial products.
Bibliography.

The aim of this thesis is to formulate an analytical expression of the lagrangian multiplier associated with the problem of maximizing ther dissipation of a continuum system: under appropriate hypotheses, the validity of the dissipation inequality defines the limits of the possible constitutive relations for a material. In the case of elastoplasticity, this leads to a constrained optimization problem, in which a lagrangian multiplier and the Karush-Kuhn-Ticker conditions are introduced.