Effective thermo-magneto-electro-elastic properties of laminates with non-uniform imperfect contact: delamination and product properties

• Published in: Acta mechanica 2022, Vol.233 (1), p.137-155
• Main Authors: Caballero-Pérez, Rogelio Oscar, Bravo-Castillero, Julián, López-Ríos, Luis Fernando
• Format: Article
• Language: English
• Subjects: Anisotropy; Asymptotic properties; Chemical reactions; Classical and Continuum Physics; Composite materials; Control; Delamination; Differential equations; Dynamical Systems; Elastic properties; Engineering; Engineering Fluid Dynamics; Engineering Thermodynamics; Heat and Mass Transfer; Laminated materials; Laminates; Magnetic properties; Mathematical models; Nonuniformity; Ordinary differential equations; Original Paper; Solid Mechanics; Theoretical and Applied Mechanics; Vibration
• ISSN: 0001-5970; 1619-6937
• DOI: 10.1007/s00707-021-03102-5

Non-uniform contact on the interphases of composites can model a wide variety of situations, ranging from delamination patterns with “islands” of contact to variable surface capacitance due to chemical reactions with the environment. In this work, the non-uniformity is modeled via spring-type imperfect contact conditions whose proportionality constants are functions of the position over the surface of contact. The effective thermo-magneto-electro-elastic coefficients of such a composite are studied via asymptotic homogenization. A modification of the ansatz of Bakhvalov is introduced on the global elliptic problem and the contact conditions in order to separate the global and local scales. This modification allows us to obtain families of local problems that are analytically solvable systems of ordinary differential equations whose solutions depend parametrically on the position variables of the contact surfaces. By integrating the local problems, analytical formulae for the functionally graded-like effective coefficients are obtained. The multiple coupled fields and associated moduli are organized through a matrix notation that facilitates the application of the asymptotic formalism and the derivation of the analytical formulae. The formulae are valid for any finite number of layers and anisotropies. Finally, some numerical examples are provided for composites with crystal symmetry 6 mm. One is related to the effective stiffnesses with a rectangular zone of delamination on the interphase. The second example shows the influence of some ideal non-uniform imperfect contact cases over the product properties of a thermopiezoelectric/thermopiezomagnetic two-phase composite.