Journal of Elasticity 75: 69–89, 2004. © 2004 Kluwer Academic Publishers. Printed in the Netherlands. 69 Swelling Induced Finite Strain Flexure in a Rectangular Block of an Isotropic Elastic Material HUNGYU TSAI 1 , THOMAS J. PENCE 1 and ELEFTHERIOS KIRKINIS 2 1 Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824-1226, U.S.A. 2 Department of Applied Mathematics, University of Washington, Seattle, WA 98195-2420, U.S.A. Received 24 May 2004; in revised form 14 July 2004 Abstract. The deformation of a rectangular block into an annular wedge is studied with respect to the state of swelling interior to the block. Nonuniform swelling fields are shown to generate these flexure deformations in the absence of resultant forces and bending moments. Analytical expressions for the deformation fields demonstrate these effects for both incompressible and compressible gener- alizations of conventional hyperelastic materials. Existing results in the absence of a swelling agent are recovered as special cases. Mathematics Subject Classifications (2000): 74A50, 74B20, 74F10. Key words: swelling, elastic materials, constitutive theory, exact solutions, flexure. 1. Introduction In recent articles [8, 9], the issue of localized volume change was studied in the context of hyperelasticity for the purpose of investigating boundary value problems involving spherical and cylindrical symmetry. The general framework for treating this volume change is compatible with the thermodynamics and statistical mechan- ics of swelling in vulcanized rubber as summarized in [11]. This framework was utilized in [8] to study cavity nucleation within an elastic incompressible solid in the absence of external load and body forces. Specifically, the focus was on a non- uniform swelling field involving a spherical interface separating zones of different constant swelling value. Such swelling interfaces, i.e., surfaces of swelling field discontinuity, are observed in certain hydrogels and models have recently been proposed for describing the kinetic features of their motion [4]. The study in [8] focuses on mechanical effects and so describes the swelling as a prescribed field that is compatible with the spherical symmetry of the original geometry. The external zone then acts as an effective loading device on the inner core, with relatively greater external swelling providing an effective tensile loading on the core. Conditions were determined in [8] such that this effective loading was sufficient to induce cavitation. More generally, the motion of the swelling interface from the external surface of a spherical body to its center was shown