Mixed- and crack-type dynamical problems of electro-magneto-elasticity theory

Abstract

We investigate the solvability of three-dimensional dynamical mixed boundary value problems of electro-magneto-elasticity theory for homogeneous anisotropic bodies with interior cracks. Using the Laplace transform technique, the potential method, and the theory of pseudodifferential equations, we prove the existence and uniqueness theorems and analyze asymptotic properties of solutions near the crack edges and near the lines where the different boundary conditions collide.

Mixed boundary–transmission problems for composite layered elastic structures

“…Proof. The proof of the theorem is quite similar to the proof of Theorem 8.1 in Buchukuri et al 53 Throughout the paper, we assume that condition (13) holds.…”

“…Using Green's first identity, we can correctly determine a generalized trace of the stress vector{ ( x , n, 6 by the following duality relation (cf. McLean 56 and Buchukuri et al 53 )…”

“…The basic linear system of pseudo-oscillation equations for the thermo-electro-magneto-elasticity theory associated with Green-Lindsay's model for homogeneous solids in matrix form reads as (see Buchukuri et al 53 )…”

“…In our study, the main tools are the generalized potential method and the theory of pseudodifferential equations on manifolds with boundary. By the same approach, similar problems for simpler piezoelastic models were considered in Buchukuri et al [49][50][51] The basic boundary-transmission problems in the case of the composed layered space R 3 for the system of thermo-electro-magneto-elasticity theory are studied in Buchukuri et al 52,53 There are considered also the interfacial crack problems for composite body occupying the whole space consisting of a bounded component and its unbounded complement with one simply connected interface surface.…”

“…It should be mentioned that in the case of bounded layered structures with interfacial cracks, the investigation of the corresponding mixed boundary-transmission problems with potential method becomes more complicated theoretically and technically in comparison with the case of unbounded composite structure with one simply connected interface surface considered in Buchukuri et al 53 The paper is organized as follows.…”