Tuning local anisotropy for macroscopic auxeticity: Design auxetic meta-laminae via systematic finite element simulations and machine learning approach

• A patch-wise meta -lamina system with tunable local anisotropy. • Systematic Finite element simulations on meta -lamina with random local anisotropy. • ML methods to predict mechanical properties from patch patterns. • Bayesian optimization for inverse design. This paper aims to design meta -lamina for desired properties including overall auxeticity via tuning local anisotropy of each discretized meta -patch. As an example, material system, meta -lamina with square patches is explored. By tuning the local anisotropy in each patch, desired overall elastic material constants, including the effective stiffnesses and effective Poisson’s ratios can be achieved. Interestingly, a large design pool for negative in-plane Poisson’s ratio are discovered and identified via systematic Finite Element (FE) simulations. This investigation delves into patch pattern-property relationships, machine learning methods, and inverse design approaches tailored for specific properties. Thorough investigations are conducted into the relationship between patch patterns, local anisotropy, and overall elastic properties, with concrete summaries provided for several typical patched metamaterial designs exhibiting varying properties. Four machine learning methods are used to train datasets from systematic finite element simulations. In addition, Bayesian optimization method is used to solve the inverse problem. Validation of the proposed designs is substantiated through finite element simulation, affirming the accuracy of both the design methodologies and the associated machine learning techniques. The design method proposed, alongside the developed machine learning techniques, offers an effective approach for the design of patch-wise meta -laminae.