Effective behavior of nonlinear microperiodic composites with imperfect contact via the asymptotic homogenization method

ABSTRACT

The asymptotic homogenization method is applied here to one-dimensional boundary-value problems for nonlinear differential equations with rapidly oscillating piecewise-constant coefficients which model the behavior of nonlinear microperiodic composites, in order to assess the influence of interfacial imperfect contact on the effective behavior. In particular, a nonlinear power-law flux on the gradient of the unknown was considered. Several calculations were performed and are discussed at the end of this work, including a comparison of some results with variational bounds, which is also an important approach of this work.

Keywords:
nonlinear composites; asymptotic homogenization method; imperfect contact