This is a copy of the slides presented at the meeting but not formally written up for the volume.

The development of different concepts for a two-materials system consisting of symmetric and asymmetric layers has been demonstrated. Flexural stiffness domains governed by flexural modulus, density, and layer geometry have been visualized on efficiency maps. It is demonstrated that although a bi-material system can evolve in several symmetric and asymmetric multilayers, the flexural properties of all the possible configurations fall into a region. This is bounded by two curves describing three symmetric layers sandwiches. The characterization of the flexural properties is based on a method recently introduced to model the mass-efficiency of monolithic structures [1]. The scheme is based on shape parameters, called Shape Transformers, which govern the geometric properties of the planar shape of a cross-section. These factors can classify shapes into families and classes with respect to the cross-section figure, and regardless size. Such a model is applied here to a bi-material laminate composite to take into account position and arrangement of layers. It can be used at the meso- as well as micro scale to predict the flexural stiffness of design alternatives for a multilayers bi-material. The rationale of the method hinges on the decoupling of material, shape and size, such that the design variables can be optimized separately. This feature is exploited to develop properties charts. When families and classes of shapes are visualised, domains of properties emerge with respect to the Shape classification. The domains are bounded by optimization paths, which identify the rules of mixture of a shape concept. In a case study, the efficiency of monolithic shaped beams is compared to that of bi-material multilayers composites for different constraints applied to the cross-section size. The maps offer ways to exploit the potential of both material and cross-section geometry, especially for concept design. The maps ease the visual ranking, widen the spectrum of choices, and enable the contrast of design alternatives, in a glance.