A Topology-optimized Ultrastiff Mechanical Metamaterial Exhibiting Stiffness beyond Hashin-Shtrikman Upper Bound

Description

The attached STL and STEP files are the lattices that correspond to a topology-optimized ultrastiff isotropic lattice structure whose stiffness exceeds the Hashin–Shtrikman upper (HSU) bound. This topology-optimized lattice, referred to as TO-SCO-HC, is provided at relative densities of 30% and 40% (STL file names: TO-SCO-HC_30RD and TO-SCO-HC_40RD). Due to the highly irregular surfaces of the topology-optimized lattices, CAD models were created by replacing these irregular regions to enable finite element simulations. The corresponding CAD versions are named SCO-HC lattices with relative densities of 30% and 40% (STEP file names: SCO-HC_30RD and SCO-HC_40RD). In addition, Figure 1 represents the new loading conditions used in Abaqus to generate ultrastiff topology optimized lattice.

Steps to reproduce

This study used the Tosca optimization module integrated with Abaqus software to optimize the topology of the lattice structures. The process involves specifying a design domain with loads, boundaries, and material constraints. The Tosca module enables the setting of objective functions such as maximizing stiffness or minimizing von Mises stress, along with material constraints such as relative density or stress limits. The Tosca module iteratively optimizes the design by redistributing material, resulting in lightweight and efficient geometries. Unit cells of the lattice were generated from a cube of 7.5 mm ×7.5 mm ×7.5 mm using FE simulation in Abaqus with an integrated Tosca topology optimization module. Elastic properties obtained from ASTM D638 tensile samples were considered, and the cube was discretized with 20 node hexahedral elements. Figure 1 shows that the normal stress of 22 MPa was applied to specific regions known as freezing regions, where the material remains intact after optimization. This normal stress value of 22 MPa, equal to the yield strength of the parent material PA12, served as a realistic upper limit that ensured that the material of the lattice would not undergo plastic deformation. The same normal stresses were applied in all three axial directions to ensure structural symmetry of the topology-optimized unit cell in 3D space. Load conditions were crucial in determining the architecture and performance of the lattice structure. To achieve a high elastic modulus through optimization, the freezing regions were rationally chosen to generate thick members that aligned with the loading direction to significantly improve the load-bearing performance. The remaining parts of the cube, excluding the freezing regions, constitute the design region from which the material will be removed. This selective removal of material reduced the weight of the structure while ensuring that the remaining material was distributed for effective load bearing. Two separate objective functions were used for the finite element simulation: minimizing von Mises stress and minimizing compliance, i.e., maximizing the stiffness. Volume constraints were applied to produce target relative densities (RDs) of 10%, 20%, 30%, and 40%. The topology optimization algorithm determines an optimal design based on the imposed structural loading conditions by minimizing the objective functions while maintaining the target relative densities

Institutions

• Indian Institute of Technology Guwahati

  Assam, Guwahati

Categories

Funders

• Science and Engineering Research Board

  Department of Science and Technology

  Delhi, India

  Grant ID: Project No. CRG/2022/007441

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