Showing papers by "Kumbakonam R. Rajagopal published in 1997"
TL;DR: In this article, a thermomechanical framework for the study of deformation twinning of polycrystals under the assumption that the process is isothermal is proposed, and a criterion based on energetics is proposed for the initiation and propagation of twinning.
62 citations
TL;DR: In this article, the authors considered a hollow circular cylinder composed of such a material, also assumed to be incompressible and isotropic, and found that microstructural scission can lead to higher levels of shear deformation near the inner surface of the cylinder than in the case of purely elastic response.
Abstract: A constitutive theory for elastomeric materials has recently been developed according to which stress is generated by different micromechanisms at different levels of deformation. When the deformation is small, the stress is given by the usual theory of rubber elasticity. As the deformation increases, some junctions of the macromolecular microstructure rupture. Junctions then re-form to generate a new microstructure. The constitutive equation allows for continuous scission of the original junctions and formation of new ones as deformation increases. The macromolecular scission causes stress reduction. The formation of new microstructures results in permanent set on release of external load. The present work considers a hollow circular cylinder composed of such a material, also assumed to be incompressible and isotropic. The cylinder is fixed rigidly at its inner surface and undergoes axisymmetric deformation due to a uniform axial moment applied at the outer surface. There develops an outer zone of material with the original microstructure and an inner zone of material having undergone macromolecular scission, separated by a cylindrical interface, the radius of which increases with the rotation of the outer surface. The shear deformation distribution, moment-rotation response and permanent set on release of moment are determined. It is found that microstructural scission can lead to higher levels of shear deformation near the inner surface of the cylinder than in the case of purely elastic response. It is also seen that a residual state of high shear deformation can arise in a thin layer of material at the inner boundary of the cylinder.
40 citations
TL;DR: In this article, the slow motion of a body in an incompressible homogeneous fluid of second grade was studied and it was shown that there exists an unique solution to the equations of motion for the fluid, wherein the inertial terms are ignored.
23 citations
TL;DR: In this article, it was shown that if on the other hand the driving force is not small (of O(1)), but the departure of the cylinder from circular symmetry is small, then secondary deformations appear at first order, the parameter for perturbance being the divergence from the circular symmetry.
Abstract: Fosdick and Kao [1] extended a conjecture of Ericksen's [2] for non-linear fluids, to non-linear elastic solids, and showed that unless the material moduli of an isotropic elastic material satisfied certain special relations, axial shearing of cylinders would be necessarily accompanied by secondary deformations if the cross-section were not a circle or the annular region between two concentric circles. Further, they used the driving force as the small parameter for a perturbation analysis and showed that the secondary deformation will occur at fourth order, much in common with what is known for non-linear fluids. Here, we show that if on the other hand the driving force is not small (of O(1)), but the departure of the cylinder from circular symmetry is small, then secondary deformations appear at first order, the parameter for perturbance being the divergence from circular symmetry.
17 citations
TL;DR: In this article, a new theoretical framework for inferring thermoelastic constitutive relations directly from biaxial data is presented, which considers an experimentally natural decomposition of the motion into two parts due to traction-free uniform heating and one due to isothermal mechanical loading and imposes a mechanical incompressibility constraint on each motion.
Abstract: Well accepted descriptors of the thermoelastic behavior of elastomers undergoing finite strain remain elusive largely due to the continuing lack of appropriate multiaxial data. In this paper we present a new theoretical framework for inferring thermoelastic constitutive relations directly from biaxial data. In particular, we consider an experimentally natural decomposition of the motion into two parts – one due to traction-free uniform heating and one due to isothermal mechanical loading – and impose a mechanical incompressibility constraint on each motion. It is shown that, regardless of the order of the motions, one obtains a thermoelastic generalization of the classical result of Rivlin and Saunders for identifying response functions from (isothermal) biaxial data.
16 citations
TL;DR: In this article, a general theory for the phenomenon of solidification is presented in which the coupling between the thermal and kinematical fields is fully taken into account, and the resulting model describes the liquid region as an ordinary Newtonian liquid and the solid phase as an elastic material.
Abstract: A general theory for the phenomenon of solidification is presented in which the coupling between the thermal and kinematical fields is fully taken into account. The resulting model descsribes the liquid region as an ordinary Newtonian liquid and the solid phase as an elastic material. In the case of multi-component solidification it allows for the existence of a mixed region separating the pure phases whose behavior is modeled as a non-linear viscoelastic material. After a preliminary analysis of the jump conditions across the singular surface separating the two phases, the strong interdependence between the thermomechanical field, the geometry of the singular surface and the freezing temperature θf is examined in detail. A simple one-dimensional problem (Boussinesq problem) has been discussed to show how only a dynamical theory can predict with reasonable accuracy the final shape of the solid.
12 citations
5 citations