Design of thin micro-architectured panels with extension–bending coupling effects using topology optimization

Abstract

We design the micro-architecture of thin elastic panels to control their macroscopic behavior, accounting simultaneously for in-plane stiffness, out-of-plane stiffness and the extension-bending coupling effects. Our topology optimization method combines inverse homogenization, the Hadamard shape derivative and a level set method in the diffuse interface context to systematically capture within the unit cell the optimal micro-architecture. The efficiency of the solution method is illustrated through four numerical examples where the designed shape yields an important extension-bending coupling. The deformation responses under tensile loading is assessed numerically both on the complete periodic panel and on its homogenised twin plate. The results demonstrate that the simultaneous control of the inplane, out-of-plane and their coupled behavior enables to shift a flat panel into a dome or a saddle shaped structure. Moreover, the obtained unit cells are elementary blocks to create directly 3D printable objects with shape-morphing capabilities.

Effective medium theory for second-gradient elasticity with chirality

“…Macroscopically, materials with a hierarchical microstructure may have vastly different characteristic properties than those of the underlying microstructure. Hence, by exploiting sophisticated microstructures we can design and produce, programmable macroscopic material behavior, e.g., low weight to strength ratio of panels, desired buckling modes of beams, programmable negative Poisson's ratio materials, etc..; see for instance the examples reported in [1], [2], [3], [4].…”

Effective medium theory for second-gradient nonlinear elasticity with chirality

“…low weight to strength ratio of panels, desired buckling modes of beams, programmable negative Poisson's ratio materials, etc. ; see for instance the examples reported in [BSDH17], [SBR + 15], [NVar], [ANC22], [ACN20].…”