TPMS-based metamaterials with tuneable elastic anisotropy and mechanical coupling

• A novel metamaterial based on shape transformed triply periodic minimal surfaces. • TMPS-based unit cells with normal-shear and shear-shear coupling. • Metamaterials with tailorable elastic symmetry and anisotropy. • Stiffness tensors with monoclinic, orthorhombic, tetragonal, and cubic symmetries. • Coupling parameters and elastic anisotropy numerically and experimentally quantified. Architectured metamaterials typically comprise of unit cells with cubic stiffness tensors and this cubic symmetry greatly restricts the available design space of mechanical properties than can be attained. In this paper, this conventional design approach is challenged by creating metamaterials that have monoclinic, orthorhombic, and tetragonal symmetries, to provide additional design freedoms. The building block to these symmetry classes is a novel monoclinic unit cell, which is generated via the shape transformation of triply periodic minimal surfaces (TPMS). The monoclinic TPMS-based unit cell exhibits the most extreme stiffness anisotropy of the four symmetry classes in addition to possessing normal−shear and shear−shear mechanical coupling. Although the monoclinic cells only have one internal plane of symmetry, the faces of the unit cells remain periodic, which enables periodic boundary conditions to be applied in finite element analysis (FEA) and the characterisation of the unit cell homogenised stiffness tensors. Next, a wide range of these TPMS-based metamaterials were additively manufactured in polylactic acid and tested under quasi-static compression. Both the FEA and experimental test results confirm that stiffness anisotropy and mechanical coupling can be controlled, revealing an expanded design space for the stiffness tailoring of additively manufactured metamaterials.