Asymptotic Expansions and Domain Decomposition

Mathematics and Mechanics of Solids

2017

This paper describes the mechanical behavior of two linear micropolar solids, bonded together by a thin plate-like layer, constituted of a linear micropolar material, determined by means of an asymptotic analysis. 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 two different limit models and their associated limit problems, the so-called weak and strong micropolar interface models, respectively. Moreover, we identify the nonclassical transmission conditions at the interface between the two three-dimensional bodies in terms of the increases in the stresses, coupling stresses, displacements, and microrotations. Finally, we prove that the solution of the original problems strongly converges toward the solution of the limit problems, as ε tends to zero.

Section: Discussionmentioning

confidence: 99%

On modeling interfaces in linear micropolar composites

Mathematics and Mechanics of Solids

2017

“…Moreover we are numerically implementing the model by adapting the domain decomposition algorithm, presented in [14], to the piezoelectric case.…”

Section: Discussionmentioning

confidence: 99%

Mathematical Modeling of Weak and Strong Piezoelectric Interfaces

2015

J Elast

We study the electromechanical behavior of a thin interphase, constituted by a piezoelectric anisotropic thin layer, embedded between two generic three-dimensional piezoelectric bodies by means of the asymptotic analysis. After defining a small real dimensionless parameter ε, which will tend to zero, we characterize two different limit models and their associated limit problems, the so-called weak and strong interface models, respectively. Moreover, we identify the non classical electromechanical transmission conditions at the interface between the two three-dimensional bodies.

“…which can be written After an integration by parts, the variational formulation states as follows denotes the load on the lateral boundary of the interface, which can be evaluated with an analogous procedure of Section 6, using (17) and 6…”

Section: Accepted Manuscriptmentioning

confidence: 99%

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

International Journal of Solids and Structures

Rizzoni²,

Lebon³

et al. 2019

Self Cite

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 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 multiphysics interface law which comprises the above aforementioned models.