A thermodynamically consistent constitutive equation for describing the response exhibited by several alloys and the study of a meaningful physical problem. (1st March 2017)

• Record Type: Journal Article
• Authors: Devendiran, V.K.; Sandeep, R.K.; Kannan, K.; Rajagopal, K.R.
• Is Part Of: International journal of solids and structures. Volume 108(2017)
• Page Start: 1
• Page End: 10
• Publication Date: 2017-03-01
• Subjects: Gibbs potential -- Implicit elastic material -- Nonlinear elastic -- Generalization of linearized elastic model -- Plate with a hole; Mechanics, Applied -- Periodicals; Structural analysis (Engineering) -- Periodicals; Elastic solids -- Periodicals; Mécanique appliquée -- Périodiques; Constructions, Théorie des -- Périodiques; Solides élastiques -- Périodiques; Elastic solids; Mechanics, Applied; Structural analysis (Engineering); Periodicals; 624.18
• DOI: 10.1016/j.ijsolstr.2016.07.036
• Languages: English
• ISSNs: 0020-7683

Abstract

Abstract: There are many alloys used in orthopaedic applications that are nonlinear in the elastic regime even when the strains are 'small' (see Hao et al., 2005; Saito et al., 2003; Sakaguch et al., 2004). By using conventional theories of elasticity, either Cauchy or Green elasticity, it is impossible to systematically arrive at constitutive equations, which would be applicable in the elastic domain of such metals as such materials exhibit non-linear response for small strains 1 where the classical linearized response is supposed to hold in the sense that the norm of the squares of the displacement gradient are much smaller than the displacement gradient. We delineate a new framework for developing constitutive equations for a new class of elastic materials, termed as implicit elastic materials, which can be used to describe the response of such alloys. In addition to a fully implicit constitutive relation, we discuss a non-linear constitutive relation between the linearized strain and the stress that can be properly justified to describe the response of such alloys. By using the example of a rectangular plate with a hole subject to uniform loading, a classical problem, we illustrate the differences in the stress and strain fields when compared to that predicted by the classical linearized relation.