Mathematical modeling of piezomagnetoelectric thin plates

Abstract

Abstract. We present the outline of the rigorous mathematical derivation of linearized piezomagnetoelectric thin plate models and focus on the results it leads to. It is in particular shown how four different models emerge from theoretical tools. New mixed 'senso-actuator' and 'actuato-sensor' behaviors appear. Moreover, the influence of all the 45 crystal symmetry classes on our models is described. We point out the extremely important structural switch-off phenomenon for which the electromagnetoelastic coupling disappear for some specific crystal classes.

Mathematical Modeling of Weak and Strong Piezoelectric Interfaces

“…[10,12,21,22,24,25] has stimulated the research toward a rational simplification of the modeling of complex structures obtained joining elements of different dimensions and/or materials of highly contrasted properties. Thin interphases represent one of the most peculiar bonded joint between two media.…”

Asymptotic modeling of thin linearly quasicrystalline plates

“…We show that depending on the type of boundary conditions, 26 different models indexed by a triplet p = (p 1 , p 2 , p 3 ) ∈ {0, 1, 2} 3 appear at the limit. Comparing to our previous studies devoted to the mathematical modeling of thin plates in the framework of multi-physical couplings [6][7][8], we are here in front of a real 'explosion' of the number of limit models. This multiplication of models, however, has its roots in the very structure of QCs.…”

“…As explained in our previous papers [6][7][8][9], the signs of the various powers of ε in the components of k p (ε, ξ) induce an orthogonal decomposition of H in subspaces H p with ∈ {−, 0, +}, which allows a comprehensive description of our plate models in any theoretically admissible quasicrystallographic classes. We denote by h p the projection on H p of any element h of H. As an example, for p = (0, 1, 2), we have: H − p = (e, g) ∈ H; e αβ = 0, g 2α = 0, g 3i = 0 H 0 p = (e, g) ∈ H; e i3 = 0, g 1i = 0, g 23 = 0, g 3α = 0 H + p = (e, g) ∈ H; e ij = 0, g 1i = 0, g 2i = 0, g 33 = 0 Then, for a given triplet p, the operator Q can be decomposed in nine elements…”

Asymptotic piezoelectric plate models in microstretch elasticity

“…Looking at the piezoelectric counterpart of the problem, an extended literature has been consecrated to the derivation of asymptotic models for piezoelectric plates and assemblies, in quasi‐static and transient situations, see, e.g., , for the statics of thin isotropic and monoclinic piezoelectric plate models, the papers , taking into account magnetic effects, as well as pyroelectric, pyroelastic and pyromagnetic effects in and the works by Serpilli on interface models in piezoelectric/thermo‐electro‐magneto‐elastic composites. Furthermore, it has been formally proved in and pointed out from a mechanical point of view in , that two possible limit behaviors can arise for a piezoelectric plate: the sensor behavior and the actuator behavior.…”