Anticlastic Curvature and Material Freedom

The anticlastic curvature in bending of a rectangular section bar occurs due to the Poisson effect. The anticlastic curvature, which is transverse to the bending curve, is studied in the context of material freedom, including the range of Poisson's ratio, time dependence of properties, 3D effects, and the role of microstructure. Anticlastic (saddle shape) curvature occurs for positive Poisson's ratio; synclastic (convex shape) curvature occurs for negative Poisson's ratio. Some planar negative Poisson's ratio materials exhibit anticlastic saddle curvature rather than the expected convex curvature in bending due to effects of 3D structure. Materials with 3D microstructure or millistructure are predicted to exhibit a transverse curvature in bending, suggestive of a Poisson's ratio greater than the true value from tension or compression tests. The effect of microstructure is interpreted via the Cosserat continuum.