Samuel Amstutz

ANALYSIS OF THE INCOMPATIBILITY OPERATOR AND APPLICATION IN INTRINSIC ELASTICITY WITH DISLOCATIONS

The incompatibility operator arises in the modeling of elastic materials with disloca- tions and in the intrinsic approach to elasticity, where it is related to the Riemannian curvature of the elastic metric. It consists of applying successively the curl to the rows and the columns of a second- rank tensor, usually chosen symmetric and divergence-free. This paper presents a systematic analysis of boundary value problems associated with the incompatibility operator. It provides answers to such questions as existence and uniqueness of solutions, boundary trace lifting, and transmission condi- tions. Physical interpretations in dislocation models are also discussed, but the application range of these results far exceed any specific physical model.

Topology optimization methods with gradient-free perimeter approximation

1be incorporated within topology optimization algorithms. The required mathematical properties, 2 namely the -convergence and the compactness of sequences of minimizers, are first established. 3 Then we propose several methods for the solution of topology optimization problems with perimeter 4 penalization showing different features. We conclude by some numerical illustrations in the contexts 5 of least square problems and compliance minimization. 6

Incompatibility-governed elasto-plasticity for continua with dislocations

In this paper, a novel model for elasto-plastic continua is presented and developed from the ground up. It is based on the interdependence between plasticity, dislocation motion and strain incompatibility. A generalized form of the equilibrium equations is provided, with as additional variables, the strain incompatibility and an internal thermodynamic variable called incompatibility modulus, which drives the plastic behaviour of the continuum. The traditional equations of elasticity are recovered as this modulus tends to infinity, while perfect plasticity corresponds to the vanishing limit. The overall nonlinear scheme is determined by the solution of these equations together with the computation of the topological derivative of the dissipation, in order to comply with the second principle of thermodynamics.