On modeling interfaces in linear micropolar composites

Abstract

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.

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

“…Remark 5. The rigid multiphysics interface problems show the same features of the rigid interface asymptotic models obtained in different frameworks in [9][10][11][44][45][46]. Concerning the order 0 model, we obtain a continuity of the multiphysics state at the interface level, while the traction vector is discontinuous and depends on the divergence of a generalized membrane stress vector (N 0 α ), defined as follows…”

“…Moreover, the variational formulation for the general multiphysics interface problem is obtained: this is a key step to the numerical implementation of the interface conditions and to study the well-posedness of the limit problem. It is worth mentioning the unifying character of the general imperfect interface conditions, which leads to a straight-forward generalization of some previous works by the authors, see, e.g., [33,41,[44][45][46].…”

“…Remark 2. The transmission problems for a soft multiphysics interface at order 0 and order 1 represent a formal generalization of the soft interface models obtained by means of the asymptotic methods in linear elasticity [33,41] and in other multifield frameworks, such as piezoelectricity [44], magneto-electro-thermo-elasticity [45] and micropolar elasticity [46]. The soft interface model presents the same structure at both order 0 and 1 as, for instance, in linear elastic asymptotic models.…”

“…Within the framework of a higher-order theory, assuming the interphase elastic constants independent of the small thickness (p = 0), the asymptotic analysis yields to a general stiff imperfect interface condition, prescribing both the jumps of the displacement and traction vector fields and recovering as a particular case the perfect contact conditions at the zero-th order [1,14,31,32,41,43]. Using asymptotic analysis and strong convergence methods, M. Serpilli generalized the soft and rigid interface conditions to some particular multiphysics and multifield composites, having piezoelectric and magneto-electro-thermo-elastic couplings [44,45] or presenting an internal microstructure (micropolar elasticity, [46]).…”

“…It is interesting to notice that the bilinear form A(•, •), related to the interface energy, takes into account simultaneously two different behaviours with some coupling terms: the first one, depending on the jump of the multiphysics state A spring (s, r) := S [s]] • [[r]]dx,is classically associated with a soft interface, corresponding to spring-type conditions; the second one, depending on the mean value of the state A membrane (s, r) := S εK αβ s ,α • r ,β dx, corresponds to a membrane interface energy and it appears usually in hard and rigid interface problems[44][45][46].8 Applications to multiphysics materials8.1 The elastic caseA linear elastic material represents the simplest choice of multiphysics material in which the only order parameter is given by the displacement field u, i.e., s = u. The corresponding constitutive law is classically defined by: σ = Ce(u),…”