Material Formulation of Finite-Strain Thermoelasticity and Applications (original) (raw)
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Communications in Numerical Methods in Engineering, 2001
We present a theoretical formulation of ÿnite strain thermoelasticity in the general setting of manifolds and a very e cient computational framework for its ÿnite element implementation, obtained by generalizing Hill's principal axis methodology. The proposed formulation is further illustrated by a detailed presentation of a 4-node axisymmetric ÿnite element and numerical simulations. Copyright ? 2001 John Wiley & Sons, Ltd.
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Zeitschrift für angewandte Mathematik und Mechanik, 1993
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Relative Lagrangian Formulation of Finite Thermoelasticity
2017
Besides the Lagrangian and the Eulerian descriptions, the motion of a body can also be expressed relative to the present configuration of the body, known as the relative motion description. It is interesting to consider such a relative motion description in general to formulate the basic system of field equations for solid bodies. In doing so, when the time increment from the present state is small enough, the nonlinear constitutive equations can be linearized relative to the present state so that the resulting system becomes linear. This will be done for thermoelastic materials with a brief comment on the exploitation of entropy principle in general. Relative Lagrangian formulation is based on the well-known ``small-on-large'' idea, and can be implemented for solving problems with large deformation in successive incremental manner. Some applications of such a formulation in numerical simulations are briefly reviewed.
International Journal of Engineering Science, 2017
A set of six, independent, stress/strain, conjugate pairs are derived: One for dilation, two for squeeze, and three for shear. They follow from a Gram-Schmidt factorization of the deformation gradient. Theories for elastic solids are derived in terms of these conjugate pairs. Anisotropy is introduced through bijective maps between tensor components and constituents of the basis. The boundary value problems of simple tension and uniform pressure are used to illustrate the effects of anisotropy, as predicted by a Hooke-like material model.
Efficient Boundary Element Formulation of Thermoelasticity
Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016), 2016
The problem of thermoelasticity is present in many different areas of solid mechanics. It describes the effects of thermal as well as mechanical loads on an elastic structure. We use the uncoupled quasistatic formulation of thermoelasticity (UQT), in a linear model and apply the Boundary Element Method. The UQT formulation is applicable in most cases, where the mechanical load is constant or slowly varying in time. Here, the influence of the elastic deformations on the heat distribution is neglected. This leaves us with a decoupled system of differential equations, consisting of the heat equation and an elastic equation, which accounts for thermal and mechanical loads. In the elastic equation the thermal field variables are introduced via convolutions. We apply three different methods for the calculation of these convolutions to find the elastic field variables and compare their computation times.
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Scientific Reports
A 2D first order linear system of partial differential equations of plane strain thermoelasticity within the frame of extended thermodynamics is presented and analyzed. The system is composed of the equations of classical thermoelasticity in which displacements are replaced with velocities, complemented with Cattaneo evolution equation for heat flux. For a particular choice of the characteristic quantities and for positive thermal conductivity, it is shown that this system may be cast in a form that is symmetric t-hyperbolic without further recurrence to entropy principle. While hyperbolicity means a finite speed of propagation of heat waves, it is known that symmetric hyperbolic systems have the desirable property of well-posedness of Cauchy problems. A study of the characteristics of this system is carried out, and an energy integral is derived, that can be used to prove uniqueness of solution under some boundary conditions. A numerical application for a finite slab is considered ...
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International Journal of Plasticity, 1998
A~traet-With the use of rate-type constitutive equations in a strain-temperature space setting, a thermomechanical development of plasticity is presented in Lagrangian form. Particular attention is giw:n to the construction of an entropy function, and constitutive results due to thermodynamical considerations are discussed.
Thermomechanical constraints and constitutive formulations in thermoelasticity
Mathematical Problems in Engineering, 2003
We investigate three classes of constraints in a thermoelastic body: (i) a deformationtemperature constraint, (ii) a deformation-entropy constraint, and (iii) a deformationenergy constraint. These constraints are obtained as limits of unconstrained thermoelastic materials and we show that constraints (ii) and (iii) are equivalent. By using a limiting procedure, we show that for the constraint (i), the entropy plays the role of a Lagrange multiplier while for (ii) and (iii), the absolute temperature plays the role of Lagrange multiplier. We further demonstrate that the governing equations for materials subject to constraint (i) are identical to those of an unconstrained material whose internal energy is an affine function of the entropy, while those for materials subject to constraints (ii) and (iii) are identical to those of an unstrained material whose Helmholtz potential is affine in the absolute temperature. Finally, we model the thermoelastic response of a peroxidecured vulcanizate of natural rubber and show that imposing the constraint in which the volume change depends only on the internal energy leads to very good predictions (compared to experimental results) of the stress and temperature response under isothermal and isentropic conditions.