Mechanics Research Communications 97 (2019) 52–56 Contents lists available at ScienceDirect Mechanics Research Communications journal homepage: www.elsevier.com/locate/mechrescom Bending device and anticlastic surface measurement of solids under large deformations and displacements F.O. Falope a,b,∗ , L. Lanzoni a,b , A.M. Tarantino a,b a University of Modena and Reggio Emilia, Department of Engineering Enzo Ferrari, DIEF, Via P. Vivarelli 10, Modena, 41125, Italy b CRICT, Centro Interdipartimentale di Ricerca e per i Servizi nel Settore delle Costruzioni, Via P. Vivarelli 10, Modena, 41125, Italy a r t i c l e i n f o Article history: Received 12 December 2018 Revised 11 April 2019 Accepted 13 April 2019 Available online 16 April 2019 Keywords: Finite bending Anticlastic surface Experimental elasticity Pure-bending device a b s t r a c t Large bending of elastic bodies gives rise to significant transverse effects. Based on a recent theoretical model in the context of finite elasticity, both the longitudinal and anticlastic curvatures in bent solids under large deformation and displacement can be accurately assessed. In order to experimentally inves- tigate the anticlastic deformation induced by large inflexion and corroborate the theoretical predictions, a properly designed mechanical bending device is here proposed. By imposing a rotation at the ends of the sample, both the longitudinal and anticlastic curvatures are measured by DIC (digital image corre- lation) monitoring instrumentation and compared with the theoretical results, finding good agreement. Compact analytical formulae for assessing the radii of curvature within the thickness of the sample are provided. Conversely to existing studies of the anticlastic surface induced by infinitesimal bending, the present analysis takes into account large through-to-thickness curvature variations, whose knowledg can plays a key role for a wide class of mechanical applications. © 2019 Elsevier Ltd. All rights reserved. 1. Introduction Bent crystals for realizing optical elements [1], MEMS exploiting channeling emissions [2,3] and spring-back of steel elements [4] or metallic sheets [5,6] for mechanical tasks are meaningful practical applications in which high bending deformations are needed. For these and many other duties the precise knowledge of the defor- mation field induced by bending is mandatory. Let us investigate here the deformation induced on an elastic prismatic H × B × L specimen by imparting opposite rotations to its cross sections in order to produce a pure-bending state. As an ex- ample, Fig. 1 shows the deformed configuration (black lines) of an elastic 10 × 15 × 130 mm 3 block provided by the theoretical anal- ysis reported in [7]. In that figure a rotation of α 0 = π /2 of the sample is imposed at the end cross sections. The imparted rotations induce two main effects: A principal longitudinal inflexion in the YZ planes coupled with a transverse bending in the XY planes, Fig. 1. Indeed, under the assumption of pure bending and neglecting end effects [3], a constant longitudi- nal radius of curvature R can be generally assumed and referred to the centroid line belonging to ZY plane which, accordingly, as- sumes the shape of an arc of circumference. However, owing to the ∗ Corresponding author. E-mail address: federicooyedeji.falope@unimore.it (F.O. Falope). Poisson effect, the longitudinal stress field produces deformation of fibers belonging to the XY planes also. This transverse deformation induces an opposite curvature with respect to the longitudinal in- flection. As a result, the sample assumes a saddle-like shape [8,9]. This phenomenon, known as anticlastic effect, arises in any bent solid and it has been widely investigated in the past [10–12]. In some circumstances, anisotropy can be exploited to emphasize the anticlastic effect [13]. Navier and de Saint Venant [10] investigated the bending of an isotropic beam with a rectangular cross section in the context of linearized elasticity, showing that the anticlastic profile has an ap- proximate radius of curvature r = R/ν, where ν is the Poisson co- efficient. Later, Lamb [11] found that a bent plate exhibits a trans- verse profile depending on the ratio  β = 4  3 4 (1 − ν 2 )B 4 R 2 H 2 ≈ B √ RH . (1) Searle [12] studied the role of the sample dimensions in the an- ticlastic deformation. Based on experimental tests [12], the Author observed that for a prismatic bent element with an aspect ratio closer to that of a plate (i.e. B and L with comparable size and {L, B} ≫ H), the anticlastic radius of curvature r varies considerably within its width, increasing in the neighborhood of the cross sec- tion corners. Such a phenomenon can be described through the Searle parameter β given in Eq. (1). In particular, for β > 20 the https://doi.org/10.1016/j.mechrescom.2019.04.011 0093-6413/© 2019 Elsevier Ltd. All rights reserved.