A modified novel implementation of asymptotic homogenization (NIAH) to model frame-like periodic materials

Abstract

Modern engineering increasingly requires materials that can meet multiple functional needs. Over the past few decades, structural optimization techniques have been used to design materials by shaping and arranging small building blocks, called representative volume elements (RVEs or unit cells), in a repeating pattern at the microscale. These unit cell designs are often complex and difficult to manufacture. However, with the development of metal additive manufacturing, producing these advanced materials has become feasible. This progress has led to increased research into methods for analyzing porous materials designed using optimization. This paper focuses on analyzing low-density porous metamaterials, where the base structure is modeled using bar or Euler–Bernoulli frame elements. While pinned bar elements are commonly used, they are only reliable for problems involving stretching forces. In real-world applications, additive manufacturing creates structures where joints transmit both moments and torque, making frame elements more suitable than bar elements. To evaluate the effective properties of these materials, asymptotic homogenization techniques are often used, particularly the NIAH variant, which allows commercial software to handle the necessary calculations. Although using rod elements in the NIAH framework is straightforward, using beam elements requires some adjustments, which are explained in this paper. Unlike many other studies, this work specifically addresses how to adapt NIAH for beam elements at the microscale while ensuring that the resulting macroscopic models only include translational movements. The paper also presents a method for defining the base cell geometry to improve accuracy. Finally, the paper compares the performance of bar and frame elements in 2D and 3D lattice periodic metamaterials.