LAUSR

Abstract Topology optimization is nowadays used in several fields, namely in Engineering and Design, and is gradually finding its way into widespread use and commercial applications. This numerical procedure is used to search for the optimal material distribution for a structure within a given design space, subjected to a set of loads and boundary conditions. Topology optimization combines the Finite Element Method with mathematical optimization to provide the best solution. However, most topology optimization applications on structural mechanics aim only to increase the stiffness of the structure for a given volume or weight restriction, far from the true potential of this structural optimization sub-field. In this work, the authors aim for a more counter-intuitive application and use topology optimization to develop a novel test specimen subject to tensile load that presents a strain field with the broadest heterogeneous nature. This allows for the development of range of strain (and stress) states as wide as possible within a single test, the holy grail for material testing and behavior model calibration. This specimen provides a much greater wealth of information than classic and homogeneous experimental specimens (such as tensile, shear, etc.). The authors show results from different formulations and numerical strategies to solve this challenge, from more traditional stiffness-based objective functions to multi-objective approaches mixing mechanical stability with functions intended to spread the specimen response nature and provide a larger set of strain states in the same topology. One of these functions is also used as a new heterogeneity indicator, tested and validated both over the results of this work and the evaluation of other test specimens.