Layered materials

We propose a continuum model for bodies made of thin and thick layers of different elastic constituents. Assuming the thickness of subsequent layers are very different (as, e.g., in sedimentary rocks), we take a special assumption on the kinematic of thin beds and partly constrain their deformations to those of the neighboring thick courses. The kinematic of thin beds is thus described through the displacements of their middle surface (three fields depending on two coordinates) plus six parameters giving some average information on the displacement field within the bed (bending, torsion, shear, and elongation of normal fibers). The search for minimal potential energy, under imposed boundary traction, gives then the set of equilibrium field equations and boundary conditions for the displacements of the internally constrained body. homogeneous stress conditions, it is possible to integrate these equations and find the explicit expression of a global compliance tensor, which gives a Reuss approximation of the homogeneous behavior of the layered continuum.