Nonlinear Thermomechanics Research Articles

Nonlinear thermomechanics for analysis of weak shock profile data in ductile polycrystals

Modeling of shock compression of isotropic, polycrystalline elastic-plastic solids that deform by dislocation glide is undertaken. Internal energy density of the material depends on a thermoelastic Eulerian strain tensor, entropy, and an internal state variable representative of dislocation density. Dislocation glide is incompressible, but inelastic volume changes arising from residual local strain fields and core effects of dislocations are captured. A semi-analytical method is advanced for extracting inelastic constitutive response information from particle velocity histories of polycrystalline samples under planar shock loading. The only parameters entering the procedure are fundamental thermoelastic properties and assumed bounds on the fraction of plastic work corresponding to energy storage of generated dislocations in the lattice. Densities of statistically stored and geometrically necessary dislocations, in addition to shear stress, plastic strain, plastic strain rate, and temperature, are outcomes of the analysis. The model is implemented for polycrystalline aluminum and copper. Certain results are compared with others in the literature obtained under different kinematic and thermodynamic assumptions. Effects of choices of nonlinear thermoelastic formulations and higher-order elastic constants on extracted deviatoric stress profiles can be substantial. Stored energy of dislocations and commensurate residual volume changes together can notably affect extracted shear stress. Stored energy significantly affects predicted entropy production and its contribution to temperature rise. The calculated density of geometrically necessary dislocations required to maintain compatibility of total strain across the structured steady plastic wave front is small relative to the line density of total dislocations.

An Eulerian formulation of nonlinear thermomechanics and electrodynamics of moving anisotropic elastic solids

In this paper, the formulation of nonlinear thermomechanics and electrodynamics of deformable materials proposed by Eringen and Maugin (1990) is restructured using the thermomechanical formulation of Green and Naghdi (1977, 1978). Constitutive equations for thermoelastic solids are typically proposed using Lagrangian forms of deformation variables. Consequently, previous developments of constitutive equations for thermoelastic electrodynamic materials proposed Lagrangian forms of electrodynamic quantities. In contrast, here, an Eulerian formulation is proposed which naturally unifies the constitutive modeling. In particular, the formulation does not use electrodynamic body force or body couple terms and the nonlinear constitutive equations for thermomechanical and electrodynamic variables are determined by derivatives of a single Helmholtz free energy function. Also, the constitutive equations for electrodynamic contributions to the stress tensor, the polarization and magnetization vectors depend naturally on the specific functional form of the Helmholtz free energy and need not be proposed independently.

Energy Approach to the Formulation of Boundary Problems of Nonlinear Thermomechanics for Elastic Systems

An energy approach is proposed to derive the physical constitutive equations of nonlinear thermomechanics for inertial elastic systems. A potential of local inertial thermodynamic state and a potential of thermoelastic energy dissipation are introduced. The variational formulation of nonlinear boundary problems of thermoelasticity is implemented on the basis of the Hamiltonian energy functional. Sufficient conditions for the convexity of the functional are formulated

Investigation of the nuclear explosion effect on asteroids

Impact of an asteroid on the Earth could be catastrophic. Deflection and fragmentation of such asteroids by surface and underground nuclear explosives has been proposed. The aim of this investigation is the optimization of explosive effects by varying of the explosive depth and charge. The study is based on nonlinear thermomechanics of an elastoviscoplastic damaged medium. For numerical simulation Godunov's type scheme on unstructured grid is used. The deflecting impulse depends on the power and depth of the charge, and the physical and strength properties of asteroid material. The process of dynamical vaporization and disintegration of asteroid material around the burst point as well as the generation of intensive jet is also investigated.

Continuous models in nonlinear thermomechanics of binary systems

We study some general problems connected with the construction of thermodynamic models in the mechanics of two-component elastic bodies. Principal relations of the model are established on the basis of fundamental concepts and approaches of nonlinear continuum mechanics and nonequilibrium thermodynamics. We also demonstrate that systems of this sort can be described without using chemical potentials in the explicit form.

Methods and results of an analysis of the nonlinear thermomechanics of crack development in a reactor vessel during accidents

Methods and results of an analysis of the nonlinear thermomechanics of crack development in a reactor vessel during accidents

An analysis of weld geometry in creep of welded tubes undergoing internal pressure

The purpose of this paper is to present the complex problems of creep in welded joints of steel tubes. The following sections are contained in this paper: formulation of the equations for nonlinear thermomechanics, discussions of the creep law and the flow rule as well as presentation of equations for the finite element method. A numerical algorithm for solution is explained. Theoretical considerations are supplemented by solving a practical engineering problem.

Irreversible (rational) thermodynamics of mixtures of a solid substance with chemically reacting fluids

The method of rational thermodynamics of Truesdell's school (non-linear thermomechanics of continuum) has been applied to mixtures of a solid substance with chemically reacting fluids. The kinematics, balances, and stoichiometry in such mixtures are formulated, and constitutive equations are proposed involving the effects of diffusion, heat conduction, and long-term memory expressed by internal parameters. The final form of the constitutive equations has been obtained by applying the constitutive entropic principle of Coleman and Noll. The equilibrium in the mixture is discussed.

Variational-Lagrangian irreversible thermodynamics of nonlinear thermorheology

A principle of virtual dissipation generalizing d’Alembert’s principle to nonlinear irreversible thermodynamics provides a unifying foundation which leads to an extremely general variational-Lagrangian analysis of dissipative phenomena. Thus a synthesis is achieved between thermodynamics and classical mechanics. The present paper applies this principle to the nonlinear thermomechanics of continua with dissipation and heat conduction. Field equations, constitutive equations and Lagrangian equations with generalized coordinates are derived for nonlinear thermoviscoelastcity, nonlinear thermoelasticity and heat conduction, plasticity, and compressible heat conducting fluids with Newtonian and non-Newtonian viscosity. The thermodynamics of instability is also analyzed from the same fundamental viewpoint.

Rational thermodynamics of a nonreacting binary linear fluid

The methods of nonlinear thermomechanics of continuous media are used for an analysis of transfer phenomena in binary fluid mixtures. From the derived relations, as a special case, are then deduced fundamental relations for the thermodynamics of irreversible processes to describe transfer phenomena in binary mixtures.