Generalized thermo-visco-elastic problem of a spherical shell with three-phase-lag effect

AbstractThis problem deals with the thermo-visco-elastic interaction due to step input of temperature on the stress free boundaries of a homogeneous visco-elastic isotropic spherical shell in the context of generalized theories of thermo-elasticity. Using the Laplace transformation the fundamental equations have been expressed in the form of vector–matrix differential equation which is then solved by eigen value approach. The inverse of the transformed solution is carried out by applying a method of Bellman et al. [R. Bellman, R.E. Kolaba, J.A. Lockette, Numerical Inversion of the Laplace Transform, American Elsevier Publishing Company, New York, 1966]. The stresses are computed numerically and presented graphically in a number of figures for copper material. A comparison of the results for different theories (TEWED (GN-III), three-phase-lag method) is presented. When the body is elastic and the outer radius of the shell tends to infinity, the corresponding results agree with the result of existing literature

Numerical thermo-elasto-plastic analysis of residual stresses on different scales during cooling of hot forming parts

In current research, more and more attention is paid to the understanding of residual stress states as well as the application of targeted residual stresses to extend e.g. life time or stiffness of a part. In course of that, the numerical simulation and analysis of the forming process of components, which goes along with the evolution of residual stresses, play an important role. In this contribution, we focus on the residual stresses arising from the austenite-to-martensite transformation at microscopic and mesoscopic level of a Cr-alloyed steel. A combination of a Multi-Phase-Field model and a two-scale Finite Element simulation is utilized for numerical analysis. A first microscopic simulation considers the lattice change, such that the results can be homogenized and applied on the mesoscale. Based on this result, a polycrystal consisting of a certain number of austenitic grains is built and the phase transformation from austenite to martensite is described with respect to the mesoscale. Afterwards, in a two-scale Finite Element simulation the plastic effects are considered and resulting residual stress states are computed

Reflection of Waves in Transversely Isotropic Thermoelastic Solid

The main objective of the present paper is to study the propagation of waves in the transversely isotropic medium in the context of thermoelasticity with GN theory of type-II and III. By imposing the boundary conditions on the components of displacement, stresses and temperature distribution, wave equation have been solved. Numerically simulated results have been plotted graphically with respect to frequency to evince the effect of anisotropy. Keywords: Thermoelasticity, transversely isotropic, reflection, plane wave AMS 2010 No.: 74JXX, 74F, 74B, 80A. 1. Introduction In last three decades, non-classical theories involving finite speed of heat transportation in elastic solids have been developed to remove the paradox obtained in classical theory. These generalized theories involve a hyperbolic-type heat transport equation, in contrast to the conventional coupled thermo-elasticity theory (1967), which involves a parabolic-type heat transport equation, and are supported by experiments exhibiting the actual occurrence of wavetype heat transport in solids, called second sound effect. The extended thermo-elasticity theory proposed b