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Cellular solids whose ligaments are made of two distinct materials are constructed for studying their auxeticity and negative thermal expansion via 2D models with the methodology of finite‐element numerical analysis. Three bimaterial cellular models with various radii of ligament curvature (Rc = 5, 8, 11 cm) are analyzed. It is found that when the ligaments comprise aluminum and titanium alloy with Rc = 5 cm, the cellular solid exhibits simultaneous negative effective Poisson's ratio (−0.418) and negative thermal expansion coefficient (−20.82 × 10−6 K−1). When the radius of ligament curvature increases, auxeticity is less pronounced. Positive and negative thermal expansion can be tuned solely by the coefficients of thermal expansion of ligaments' constituents. Furthermore, smaller radii of curvature give rise to larger negative thermal expansion. In addition, modulus mismatch in the bimaterial ligament can be used to tune overall properties. Our findings herein may serve as foundations for the future quantitative design of such cellular materials. In addition, effective Poisson's ratio and coefficient of thermal expansion can be positively or negatively enhanced due to the interplay between the positive and negative phases. Interactions between negative stiffness and larger curvatures may make the system less unstable. [ABSTRACT FROM AUTHOR]