Modelagem e otimização de compósitos termo-ativados

Abstract

Advancements in 3D printing technology are generating a revolution in terms of manufacture, allowing the printing of objects in complex geometries that can be generated through the use of technical criteria that were previously impractical to execute. On that aspect, one application that has gained popularity is of termo-activated composites, on which the presence of one or more materials with shape-memory properties allows the programed deformation of the composites after printing, as long as they are previously trained with a specific set of thermo-mechanical stimuli. The capacity of a class of polymers to deform over time motivates the interest in controlling precisely the geometry prescribed for their deformed configuration. With in that context, this work details the development of mathematical equations, numerical strategies and a computational base for the topology optimization of the inclusion region in termo-activated composites, aiming to allow the printing and treatment of pieces that deform to prescribed configurations based on the shape-memory effect that some polymers present. It intends to allow the optimum design of polymeric composite pieces in order to make then viable for applications on several industries. On top of the computational base, an analytical example is constructed to check the developed formulations and shows good agreement between the exact solution and numerical results based on such equations. Illustrative examples are also presented where several parameters are varied and the effect they have on the optimization algorithm are discussed. This also shows results that considered good and physically coherent. The success of the simpli_ed mathematical formulation and its associated computational implementation and numerical strategies can serve as a base upon which new assumptions and better approximations can be made in futures works. Those expansions, supported for the theoretical base here presented, can allow the application of the proposed problem within the context of several industries.