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Rocks exhibit beyond-Hookean, delayed and damped elastic, behaviour (creep, relaxation etc.). In many cases, the Poynting-Thomson-Zener (PTZ) rheological model proves to describe these phenomena successfully. A forecast of the PTZ model is that the dynamic elasticity coefficients are larger than the static (slow-limit) counterparts. This prediction has recently been confirmed on a large variety of rock types. Correspondingly, according to the model, the speed of wave propagation depends on frequency, the high-frequency limit being larger than the low-frequency limit. This frequency dependence can have a considerable influence on the evaluation of various wave-based measurement methods of rock mechanics. As experience shows, commercial finite element softwares are not able to properly describe wave propagation, even for the Hooke model and simple specimen geometries, the seminal numerical artefacts being instability, dissipation error and dispersion error, respectively. This has motivated research on developing reliable numerical methods, which amalgamate beneficial properties of symplectic schemes, their thermodynamically consistent generalization (including contact geometry), and spacetime aspects. The present work reports on new results obtained by such a numerical scheme, on wave propagation according to the PTZ model, in one space dimension. The simulation outcomes coincide nicely with the theoretically obtained phase velocity prediction. [ABSTRACT FROM AUTHOR]

Rocks are important examples for solid materials where, in various engineering situations, elastic, thermal expansion, rheological /viscoelastic and plastic phenomena each may play a remarkable role. Nonequilibrium continuum thermodynamics provides a consistent way to describe all these aspects in a unified framework. This we present here in a formulation where the kinematic quantities allow arbitrary nonzero initial (e.g., in situ) stresses and such initial configurations which - as a consequence of thermal or remanent stresses - do not satisfy the kinematic compatibility condition. The various characteristic effects accounted by the obtained theory are illustrated via experimental results where loaded solid samples undergo elastic, thermal expansion and plastic deformation and exhibit rheological behaviour. From the experimental data, the rheological coefficients are determined, and the measured temperature changes are also explained by the theory. Dedicated to the memory of Zoltán Szarka (1927-2015). [ABSTRACT FROM AUTHOR]