Rational Design of an Auxetic Architected Material Using a RBSM-based Approach
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A framework for the computational design of elastic isotropic two-dimensional metamaterials is presented. A rational (inverse) design philosophy is followed since the architected material is tailored to reach a target mechanical response. The proposed framework lies on a centro-symmetric heuristic molecule (HM) that constitutes the unit-cell of the periodic material. The modelling of the HM is described through a rigid body spring model (RBSM) with linearized kinematics. Rigid shaped atoms interact through centred and non-centred spring-based bonds. An ultra-soft auxetic elastic isotropic architected material is designed, with a target Poisson's ratio of $\nu=-1.0$ according to the rigid-body-spring model. Under the assumptions of a single material and a non-assembly approach for the additive manufacturing step, a periodic material was produced based on the auxetic HM as unit-cell. The 3d printed material demonstrates the feasibility of production, but an experimental validation regarding the real Poisson's ratio is not conducted in this study. Instead, a numerical investigation is conducted to assess the linear elastic limit anisotropy of the material under a uni-axial deformation mode with varying direction. For this exercise, the bonds are assumed to have a brittle, quasi-brittle and elastic-perfectly plastic constitutive law. A significant anisotropy is observed for the linear limit either in terms of onset of cracking deformation and peak force. Finally, it is demonstrated how the design of different bond lengths influence the mechanical response of the material.
