We use transfer matrix and state-space methods to derive exact solutions for the
time-dependent and plane strain deformations of simply supported multilayered
orthotropic elastic strips with simultaneous interfacial diffusion and rate-dependent
sliding. Our analysis considers the corresponding interfacial tractions as the
fundamental state variables. As a result, a homogeneous state-space equation can be
obtained by enforcing the interfacial diffusion and sliding conditions. The relaxation
times of the multilayered orthotropic strip and the evolution of the interfacial
tractions can then be determined from the derived state-space equation. Once
the transient interfacial tractions are known, all of the field variables at
any time and at any position of the multilayered strip can be conveniently
obtained.
Keywords
multilayered orthotropic strip, interfacial diffusion and
sliding, transfer matrix, state-space equation, relaxation
time
