Inhomogeneous deformations in finite thermo-elasticity

First, we study the inhomogeneous extension or compression of non-linearly elastic materials within the context of finite thermoelasticity. We consider a generalization of the classical neo-Hookean model in which the shear modulus is allowed to depend on the temperature. This is an extension of the analysis of Rajagopal and Wineman ([23] int. J. Engng Sci. 23, 217 (1985)) on the isothermal inhomogeneous uniaxial extension of a slab of neo-Hookean or Mooney-Rivlin material, for which they were able to find explicit exact solutions. Permitting the shear modulus to depend on temperature allows ''boundary layer'' type of solutions, in that the deformation is inhomogeneous near the boundary and nearly homogeneous away from the boundary. It is found that the strains within the ''boundary layer'' are much higher than in the far field, which might justify calling these layers, regions of localized strain. Next, we study, within the context of finite thermoelasticity, the radial expansion and axial shearing of a hollow circular cylinder, an extension of the recent study of Haughton ([20] Int. J. Engng Sci. 30, 1027 (1992)) wherein he found ''boundary layer'' type solutions even in the isothermal case. Copyright (C) 1996 Elsevier Science Ltd