  We determine the asymptotic behavior of the solutions to the linear
elastodynamic equations in a stratified medium comprising an alternation of
possibly very stiff layers with much softer ones, when the thickness of the
layers tends to zero. The limit equations may depend on higher order terms,
characterizing bending effects. A part of this work is set in the context of
non-periodic homogenization and an extension to stochastic homogenization is
presented.
