Modélisation du couplage magnéto-élastique dans les milieux solides à symétrie cubique

The performance of electrical machinesis largely related to the magnetic behavior of theferromagnetic materials they are made of. Takinginto account the magneto-mechanical coupling isone of the possible ways of progress in this field.The strongly non-linear evolution of magnetizationand magnetostriction is modeled by writing constitutivelaws that derive from thermodynamic potentials.However, current magneto-elastic constitutivelaws, written in a linear framework, are insufficientto describe the influence of stresses beyond acertain threshold. An extension of energy densitiesimplies the use of constitutive tensors of increasingorders as the degree of stress increases. One wayto circumvent this difficulty is to use polynomialsof invariants characteristic of a given symmetry.Thus, invariants are given for a material symmetrywhich is fixed a priori when the use of constitutivetensors implies assumptions on the symmetrya posteriori. This thesis first presents a generalmethod to determine a basis of fundamental invariants(or integrity basis) associated to a finitesymmetry group, here the cubic symmetry, allowingthe formulation of a Gibbs free energy densityat any order. This basis is composed of 30 invariantswritten in an intrinsic way. It can be reducedin the case of plane loading and with sheets thatexhibits strong crystallographic textures (fibers).The invariant basis was then used to reformulatein an equivalent way the energy densities initiallywritten using constitutive tensors. A new free enthalpy,quadratic in magnetization and nonlinear instress, has been proposed and allows, contrary tothe previous forms, to model the saturation of themagnetostriction while ensuring its sign change.