Inhomogeneous shearing deformation of a rubber-like slab within the context of finite thermoelasticity with entropic origin for the stress

This paper deals with inhomogeneous shearing deformation of an infinite rub ber-like slab under a temperature difference across its thickness. The defo rmation is analyzed within the context of finite thermoelasticity with entr opic origin for the stress. The isothermal strain energy functions of Moone y and of Yeoh are generalized by incorporating them into the thermoelastic model. The energy balance equation, which is decoupled from the linear mome ntum balance equations, is solved For the temperature field using the Fouri er's law of heat conduction. The derived linear temperature field and the e quations of the thermoelastic model are inserted into the linear momentum b alance equations, thus yielding an ordinary differential equation for the s hear strain. The shear strain, the degree of inhomogeneity in the shear str ain, the stress field, and the principal stresses are then determined using a finite difference method. The Mooney slab undergoes markedly greater she ar strain near the colder boundary, thus exhibiting a boundary layer-like s tructure at higher temperature differences across the thickness. However, t he Yeoh slab exhibits a relatively smaller variation of the shear strain ev en at the highest temperature difference. This difference in the behavior o f the two slabs is attributed to the shear stiffening of the Yeoh slab, whi ch counteracts the formation of a boundary layer-like structure. Both slabs experience constant shear stresses across the thickness, whereas they expe rience much greater normal stress differences varying across the thickness. The values of the major principal stress turn out to be close to those of the first normal stress difference. The presence of a large normal stress d ifference compared with a relatively smaller shear stress in the slabs crea tes the possibility for Mode I type fracture propagation. (C) 2001 Elsevier Science Ltd. All rights reserved.