Scale effects in the optimal design of a microstructured medium against buckling

Certain classes of problems in optimal structural design lead naturally to the introduction of periodic microstructured media as the basis material for the construction of a mechanical element. The unit cell size of these microstructures cannot be arbitrarily small, as suggested by the pertaining optimization analyses up to date, and has to be related to the structure's overall dimensions. One physically important mechanism that provides such microstructure size limitations is elastic buckling.An analytically tractable model of an infinite periodic rectangular planar frame with axially compressed beams is used to study the optimal buckling loads. For any given design, one can find a critical stress above which buckling instability occurs. In addition one can also find the region in the design space for which the optimal critical mode is a global one, i.e. its characteristic length is much larger than the unit cell size. In this region of the design space one can safely use the homogenized material properties to describe the medium, for they provide all the information needed to predict a global buckling instability. In addition to the detailed parametric study for the model problem investigated here, implications for the optimal design against buckling of more general structures are also briefly discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/28918/1/0000755.pd

Computational Homogenization of Architectured Materials

Architectured materials involve geometrically engineered distributions of microstructural phases at a scale comparable to the scale of the component, thus calling for new models in order to determine the effective properties of materials. The present chapter aims at providing such models, in the case of mechanical properties. As a matter of fact, one engineering challenge is to predict the effective properties of such materials; computational homogenization using finite element analysis is a powerful tool to do so. Homogenized behavior of architectured materials can thus be used in large structural computations, hence enabling the dissemination of architectured materials in the industry. Furthermore, computational homogenization is the basis for computational topology optimization which will give rise to the next generation of architectured materials. This chapter covers the computational homogenization of periodic architectured materials in elasticity and plasticity, as well as the homogenization and representativity of random architectured materials

Recent developments in topology design of materials and mechanisms

This paper gives a brief introduction to some of the methods used in topology design of continuum structures and to their use for the design of materials and mechanisms. This encompasses the use of topology design in design of materials with extreme properties, and the introduction of buckling criteria in such design problems. A topic is also the design of isotropic composites which realize certain popular interpolation schemes used in topology design (making the dog bite its tail). Finally, examples of the design of flexible mechanisms will be discussed