Nabla2:
You are looking for, talking about, several quite different things. Orthotropic usually refers to the use of the surface material (bridge deck plates, ship deck plates, airplane skin mat’l., and the like) as part of the spanning structural system. This usually leads to a less costly and lighter weight structural system for the bridge deck, or any other structural spanning system, since it uses all of the materials as an integral part of the structural system. There are books on this design and construction method, and most structural handbooks and text books cover the subject.
Anisotropic has to do with mechanical material properties not being the same in all directions. Isotropic means the material properties are the same (essentially the same) in all directions. We usually think of steel as an isotropic material, but in thicker rolled plates and sections the direction of rolling and the changes caused, through thickness, cause the through thickness properties to be somewhat lower than those parallel to the plate surfaces. And, for that matter some properties change in the plane of the plate too, as a function of the direction of rolling and perpendicular to that direction. These are related to work hardening and grain orientation caused by the process. In thicker plates and sections there is also a tendency for the process to cause slag inclusions and laminations to occur parallel to the plane of the plate or direction of rolling, and these cause physical weak planes or pipes. Extruding, drawing and forging can cause some of these same work hardening and grain orientation phenomenon. Look to metallurgy, and materials processing handbooks and texts. The steel industry, ASM, ASTM and AWS, and the like have some good literature on these subjects.
If what you are talking about is a plate like system made up of several different layers of different materials, then you are talking about a composite section. And, you must consider the mechanical properties of each material and how they interact within that whole plate element. That is; how do they bond together at their interfaces, how do they transmit stresses across these interfaces, how do they yield and strain w.r.t. each other. Theory of Elasticity and Strength of Materials books usually cover this topic.