Three-dimensional phenomenological thermodynamic model of pseudoelasticity of shape memory alloys at finite strains

Zi�lkowski, A.
November 2007
Continuum Mechanics & Thermodynamics;Nov2007, Vol. 19 Issue 6, p379
Academic Journal
The familiar small strain thermodynamic 3D theory of isotropic pseudoelasticity proposed by Raniecki and Lexcellent is generalized to account for geometrical effects. The Mandel concept of mobile isoclinic, natural reference configurations is used in order to accomplish multiplicative decomposition of total deformation gradient into elastic and phase transformation (p.t.) parts, and resulting from it the additive decomposition of Eulerian strain rate tensor. The hypoelastic rate relations of elasticity involving elastic strain rate $$\underline{{{\mathbf{d}}}}^{\rm e}$$ are derived consistent with hyperelastic relations resulting from free energy potential. It is shown that use of Jaumann corotational rate of stress tensor in rate constitutive equations formulation proves to be convenient. The formal equation for p.t. strain rate $$\underline{{{\mathbf{d}}}}^{{\rm in}}$$ , describing p.t. deformation effects is proposed, based on experimental evidence. Phase transformation kinetics relations are presented in objective form. The field, coupled problem of thermomechanics is specified in rate weak form (rate principle of virtual work, and rate principle of heat transport). It is shown how information on the material behavior and motion inseparably enters the rate virtual work principle through the familiar bridging equation involving Eulerian rate of nominal stress tensor.


Related Articles

  • Landau parameter of elasticity. Merabtine, N.; Bousnane, Z.; Benslama, M.; Boussaad, F. // Semiconductor Physics, Quantum Electronics & Optoelectronics;2006, Vol. 9 Issue 3, p1 

    Based on the consideration given by the Ginzburg-Landau (GL) theory according to the variational principle, we assume that the microscopic Gibbs function density given by [1] ... must be stationary at the thermodynamical equilibrium. To describe the universal propagation of the order parameter,...

  • Stability of a rectangular plate under biaxial tension. Sheidakov, D. N. // Journal of Applied Mechanics & Technical Physics;Jul2007, Vol. 48 Issue 4, p547 

    The stability problem of a rectangular plate undergoing uniform biaxial in-plane tensile strain is solved using the three-dimensional equations of nonlinear elasticity. The surfaces of the plate are stress-free, and special boundary conditions that allow one to separate variables in the...

  • Equilibrium States of Stratified Two-Phase Media under Given Boundary Loads. Osmolovskii, V. G. // Journal of Mathematical Sciences;Oct2004, Vol. 123 Issue 6, p4597 

    An elastic medium with the classical double-well potential is considered. It is assumed that the hydrostatic pressure is given on the boundary of the medium and the surface-tension coefficient is equal to zero. It is shown that the equilibrium states describing the stratifield distribution of...

  • On the phase transition temperature in a variational problem of elasticity theory for two-phase media. Osmolovskii, V. // Journal of Mathematical Sciences;May2009, Vol. 159 Issue 2, p168 

    We obtain sufficient conditions for the noncoincidence of the phase transition temperatures and illustrate this result by examples of problems in two-phase elastic media. We also indicate some cases where equilibrium states exist or not depending on the values of the temperature lying between...

  • Methods for First-Principles Alloy Thermodynamics. Walle, Axel // JOM: The Journal of The Minerals, Metals & Materials Society (TM;Nov2013, Vol. 65 Issue 11, p1523 

    Traditional first-principles calculations excel at providing formation energies at absolute zero, but obtaining thermodynamic information at nonzero temperatures requires suitable sampling of all the excited states visited in thermodynamic equilibrium, which would be computationally prohibitive...

  • Compatibility of weak rigidity with some types of elastic schemes. del Olmo, V.; Olivert, J. // Journal of Mathematical Physics;Apr86, Vol. 27 Issue 4, p1048 

    The behavior of the hypoelastic-Synge, hypoelastic-Maugin, and hypoelastic-Carter and Quintana almost-thermodynamic material schemes, under weak rigidity hypotheses, is studied. In every case, the absence of principal transverse shock waves (or the vanishing of the corresponding speeds) is...

  • Short-time nonstationary character of correlation functions in classical equilibrium ensembles. Chatzidimitriou-Dreismann, C. A. // Journal of Mathematical Physics;Nov86, Vol. 27 Issue 11, p2770 

    Dynamical quantities b(t) are considered that depend on the canonical variables of a small number n of particles of a classical N-particle condensed system being in thermal equilibrium. It is proved that equalities like d2/dt2=- are in general violated, if the interparticle...

  • Structure, electronic and elastic properties of the NbRu shape memory alloys. Mousa, A. A.; Hamad, B. A.; Khalifeh, J. M. // European Physical Journal B -- Condensed Matter;Dec2009, Vol. 72 Issue 4, p575 

    The phase stability and electronic structure of NbRu shape memory alloys are studied by self-consistent full-potential linearized augmented plane wave method (FP-LAPW) on the basis of the density functional theory (DFT). The calculated equilibrium volumes are about 32 Ã…3 and 30 Ã…3 for...

  • Effect of porosity on elastic characteristics of TiC/TiNi hard alloys. Akimov, V. V.; Akimov, M. V.; Korytov, M. S.; Plastinina, M. V. // Journal of Applied Mechanics & Technical Physics;Jul2009, Vol. 50 Issue 4, p658 

    A substantial effect of porosity on elastic properties of TiC/TiNi hard alloys is found. It is demonstrated that application of these materials in various elements and devices of modern engineering is inspired by a combination of their properties, such as high strength, hardness, wear...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics