An asymptotic plate model for magneto-electro-thermo-elastic sensors and actuators

International audienceWe present an asymptotic two-dimensional plate model for linear magneto-electro-thermo-elastic sensors and actuators, under the hypotheses of anisotropy and homogeneity. Four different boundary conditions pertaining to electromagnetic quantities are considered, leading to four different models: the sensor-actuator model, the actuator-sensor model, the actuator model and the sensor model. We validate the obtained two-dimensional models by proving weak convergence results. Each of the four plate problems turns out to be decoupled into a flexural problem, involving the transversal displacement of the plate, and a certain partially or totally coupled membrane problem

Numerical Validation of Multiphysic Imperfect Interfaces Models

none4We investigate some mathematical and numerical methods based on asymptotic expansions for the modeling of bonding interfaces in the presence of linear coupled multiphysic phenomena. After reviewing new recently proposed imperfect contact conditions (Serpilli et al., 2019), we present some numerical examples designed to show the efficiency of the proposed methodology. The examples are framed within two different multiphysic theories, piezoelectricity and thermo-mechanical coupling. The numerical investigations are based on a finite element approach generalizing to multiphysic problems the procedure developed in Dumont et al. (2018).openDumont S.; Serpilli M.; Rizzoni R.; Lebon F.C.Dumont, S.; Serpilli, M.; Rizzoni, R.; Lebon, F. C

An asymptotic derivation of a general imperfect interface law for linear multiphysics composites

The paper is concerned with the derivation of a general imperfect interface law in a linear multiphysics framework for a composite, constituted by two solids, separated by a thin adhesive layer. The analysis is performed by means of the asymptotic expansions technique. After defining a small parameter epsilon, which will tend to zero, associated with the thickness and the constitutive coefficients of the intermediate layer, we characterize three different limit models and their associated limit problems: the soft interface model, in which the constitutive coefficients depend linearly on epsilon; the hard interface model, in which the constitutive properties are independent of epsilon; the rigid interface model, in which they depend on 1/epsilon. The asymptotic expansion method is reviewed by taking into account the effect of higher order terms and by defining a general multiphysics interface law which comprises the above aforementioned models. (C) 2019 Elsevier Ltd. All rights reserved

The Kinematics of Plate Models: A Geometrical Deduction

We present a deduction of the Kirchhoff-Love and Reissner-Mindlin kinematics of a simply- connected plate by using the formal asymptotic developments method applied to the compatibility conditions of Saint-Venant and the formula of Cesàro-Volterra. This formal deduction is purely geometrical because we do not use any information coming from the loading or the constitutive behavior

Interface laws for multi-physic composites

International audienc

An asymptotic plate model for magneto-electro-thermo-elastic sensors and actuators

We present an asymptotic two-dimensional plate model for linear magneto-electro-thermo-elastic sensors and actuators, under the hypotheses of anisotropy and homogeneity. Four different boundary conditions pertaining to electromagnetic quantities are considered, leading to four different models: the sensor–actuator model, the actuator–sensor model, the actuator model and the sensor model. We validate the obtained two-dimensional models by proving weak convergence results. Each of the four plate problems turns out to be decoupled into a flexural problem, involving the transversal displacement of the plate, and a certain partially or totally coupled membrane problem

Interface Laws for Multi-physic Composites

The paper describes the mechanical behavior of a composite constituted by two solids, bonded by a thin adhesive layer in a general multi-physic framework, by employing the asymptotic expansion technique. After defining a small parameter ε, which will tend to zero, associated with the thickness and the constitutive coefficients of the intermediate layer, we characterize three different limit models and their associated limit problems: the soft interface model, in which the constitutive coefficients depend linearly on ε; the hard interface model, in which the constitutive properties are independent of ε; the rigid interface model, in which they depend on 1/ε. The asymptotic expansion method is reviewed by taking into account the effect of higher order terms and by defining a general multi-physic interface law which comprises the above aforementioned models. Moreover, the FEM implementation of the transmission model is presented through a numerical example

Hard interfaces with microstructure: The cases of strain gradient elasticity and micropolar elasticity

As the size of a layered structure scales down, the adhesive layer thickness correspondingly decreases from macro- to micro-scale. The influence of the material microstructure of the adhesive becomes more pronounced, and possible size effect phenomena can appear. This paper describes the mechanical behaviour of composites made of two solids, bonded together by a thin layer, in the framework of strain gradient and micropolar elasticity. The adhesive layer is assumed to have the same stiffness properties as the adherents. By means of the asymptotic methods, the contact laws are derived at order 0 and order 1. These conditions represent a formal generalization of the hard elastic interface conditions. A simple benchmark equilibrium problem (a three-layer composite micro-bar subjected to an axial load) is developed to numerically assess the asymptotic model. Size effects and non-local phenomena, owing to high strain concentrations at the edges, are highlighted. The example proves the efficiency of the proposed approach in designing micro-scale-layered devices. This article is part of the theme issue 'Non-smooth variational problems with applications in mechanics'