Microinertia and internal variables

The origin of microinertia of micromorphic theories is investigated from the point of view of non-equilibrium thermodynamics. In the framework of dual internal variables microinertia stems from a thermodynamic equation of state related to the internal variable with the properties of mechanical momentum.Comment: 14 pages, no figure

Thermoelastic Waves in Microstructured Solids

Thermoelastic wave propagation suggests a coupling between elastic deformation and heat conduction in a body. Microstructure of the body influences the both processes. Since energy is conserved in elastic deformation and heat conduction is always dissipative, the generalization of classical elasticity theory and classical heat conduction is performed differently. It is shown in the paper that a hyperbolic evolution equation for microtemperature can be obtained in the framework of the dual internal variables approach keeping the parabolic equation for the macrotemperature. The microtemperature is considered as a macrotemperature fluctuation. Numerical simulations demonstrate the formation and propagation of thermoelastic waves in microstructured solids under thermal loading

Pattern Formation of Elastic Waves and Energy Localization Due to Elastic Gratings

Elastic wave propagation through diffraction gratings is studied numerically in the plane strain setting. The interaction of the waves with periodically ordered elastic inclusions leads to a self-imaging Talbot effect for the wavelength equal or close to the grating size. The energy localization is observed at the vicinity of inclusions in the case of elastic gratings. Such a localization is absent in the case of rigid gratings

Dispersive Wave Equations for Solids with Microstructure

The dispersive wave motion in solids with microstructure is considered in the one-dimensional setting in order to understand better the mechanism of dispersion. It is shown that the variety of dispersive wave propagation models derived by homogenization, continualisation, and generalization of continuum mechanics can be unified in the framework of dual internal variables theory

Numerical Simulation of Waves and Fronts in Inhomogeneous Solids

Dynamic response of inhomogeneous materials exhibits new effects, which often do not exist in homogeneous media. It is quite natural that most of studies of wave and front propagation in inhomogeneous materials are associated with numerical simulations. To develop a numerical algorithm and to perform the numerical simulations of moving fronts we need to formulate a kinetic law of progress relating the driving force and the velocity of the discontinuity. The velocity of discontinuity is determined by means of the non-equilibrium jump relations at the front. The obtained numerical method generalizes the wave-propagation algorithm to the case of moving discontinuities in thermoelastic solids

Entropy production in phase field theories

Allen-Cahn (Ginzburg-Landau) dynamics for scalar fields with heat conduction is treated in rigid bodies using a non-equilibrium thermodynamic framework with weakly nonlocal internal variables. The entropy production and entropy flux is calculated with the classical method of irreversible thermodynamics by separating full divergences.Comment: 5 pages, no figure

Full Field Computing for Elastic Pulse Dispersion in Inhomogeneous Bars

In the paper, the finite element method and the finite volume method are used in parallel for the simulation of a pulse propagation in periodically layered composites beyond the validity of homogenization methods. The direct numerical integration of a pulse propagation demonstrates dispersion effects and dynamic stress redistribution in physical space on example of a one-dimensional layered bar. Results of numerical simulations are compared with analytical solution constructed specifically for the considered problem. Analytical solution as well as numerical computations show the strong influence of the composition of constituents on the dispersion of a pulse in a heterogeneous bar and the equivalence of results obtained by two numerical methods

Thermodynamics of Discrete Systems and Martensitic Phase Transition Simulation

A thermomechanical approach for the modelling of the phase-transition front propagation in solids is described for the class of thermoelastic phases. This description is based on the balance laws of  continuum mechanics in the reference configuration and the thermodynamics of discrete systems. Contact quantities are introduced following the basic concepts of the thermodynamics of discrete systems. The values of the contact quantities are determined within a finite-volume numerical scheme based on a modification of the known wave-propagation algorithm. No explicit expression is used for the kinetic relation governing the phase transition front propagation. All the needed information is extracted from the thermodynamic consistency conditions for adjacent discrete elements. It is shown that the developed model captures the experimentally observed velocity difference which appears because of impact-induced phase transformation