Normalized Ratcheting Diagram Under Sinusoidal Vibration Waves

Ratcheting is a progressive incremental inelastic deformation or strain which can occur in a component that is subjected to variations of mechanical stress, thermal stress, or both. This study concentrated on the ratcheting occurrence of the piping model under the combined effect of constant external force and dynamic cyclic vibrations. Bent solid bars represented piping models, and sinusoidal acceleration waves were loaded. Characteristics of seismic loads between load-controlled and displacement-controlled properties were studied from the viewpoint of the frequency ratio of the forcing frequency to the natural frequency of the piping model. Besides, the ratcheting occurrence conditions of the beam and the piping model were compared in one normalized diagram to display the general mechanism of ratcheting with the consideration of the effect from the difference of shape and material. Results show that ratcheting occurs easily with a lower frequency ratio in both beam and piping models. In addition, it is meaningful to use beam models to understand the ratcheting mechanism of piping models. Describing the occurrence of ratcheting using the normalized ratcheting diagram for different components is feasible.

Nonlinear plane waves in saturated porous media with incompressible constituents

We consider the propagation of nonlinear plane waves in porous media within the framework of the Biot–Coussy biphasic mixture theory. The tortuosity effect is included in the model, and both constituents are assumed incompressible (Yeoh-type elastic skeleton, and saturating fluid). In this case, the linear dispersive waves governed by Biot’s theory are either of compression or shear-wave type, and nonlinear waves can be classified in a similar way. In the special case of a neo-Hookean skeleton, we derive the explicit expressions for the characteristic wave speeds, leading to the hyperbolicity condition. The sound speeds for a Yeoh skeleton are estimated using a perturbation approach. Then we arrive at the evolution equation for the amplitude of acceleration waves. In general, it is governed by a Bernoulli equation. With the present constitutive assumptions, we find that longitudinal jump amplitudes follow a nonlinear evolution, while transverse jump amplitudes evolve in an almost linearly degenerate fashion.

Cross-diffusion waves resulting from multiscale, multi-physics instabilities: theory

We propose a multiscale approach for coupling multi-physics processes across the scales. The physics is based on discrete phenomena, triggered by local thermo-hydro-mechano-chemical (THMC) instabilities, that cause cross-diffusion (quasi-soliton) acceleration waves. These waves nucleate when the overall stress field is incompatible with accelerations from local feedbacks of generalized THMC thermodynamic forces that trigger generalized thermodynamic fluxes of another kind. Cross-diffusion terms in the 4×4 THMC diffusion matrix are shown to lead to multiple diffusional P and S wave equations as coupled THMC solutions. Uncertainties in the location of meso-scale material instabilities are captured by a wave-scale correlation of probability amplitudes. Cross-diffusional waves have unusual dispersion patterns and, although they assume a solitary state, do not behave like solitons but show complex interactions when they collide. Their characteristic wavenumber and constant speed define mesoscopic internal material time–space relations entirely defined by the coefficients of the coupled THMC reaction–cross-diffusion equations. A companion paper proposes an application of the theory to earthquakes showing that excitation waves triggered by local reactions can, through an extreme effect of a cross-diffusional wave operator, lead to an energy cascade connecting large and small scales and cause solid-state turbulence.

Acceleration Waves in Rational Extended Thermodynamics of Rarefied Monatomic Gases

Rational Extended Thermodynamics theories with different number of moments are usually introduced to study non-equilibrium phenomena in rarefied gases. Here, we use them to describe one-dimensional acceleration waves in a rarefied monatomic gas. In particular, we focus on the degeneracy of the acceleration wave to a shock wave, in order to test the validity of the models and the role played by an increasing number of moments. As a byproduct, some peculiarities of the characteristic velocities at equilibrium are analyzed as well.

Cross-Diffusion Waves as a trigger for Multiscale, Multi-Physics Instabilities: Theory

We propose a non-local, meso-scale approach for coupling multiphysics processes across scale. The physics is based on discrete phenomena, triggered by local Thermo-Hydro-Mechano-Chemical (THMC) instabilities, that cause cross-diffusion (quasi-soliton) acceleration waves. These waves nucleate when the overall stress field is incompatible with accelerations from local feedbacks of generalized THMC thermodynamic forces that trigger generalized thermodynamic fluxes of another kind. Cross-diffusion terms in the 4 × 4 THMC diffusion matrix are shown to lead to multiple diffusional P- and S-wave equations as coupled THMC solutions. Uncertainties in the location of meso-scale material instabilities are captured by a wave-scale correlation of probability amplitudes. Cross-diffusional waves have unusual dispersion patterns and, although they assume a solitary state, do not behave like solitons but show complex interactions when they collide. Their characteristic wavenumber and constant speed define mesoscopic internal material time-space relations entirely defined by the coefficients of the coupled THMC reaction-cross-diffusion equations. For extreme conditions, cross-diffusion waves can lead to an energy cascade connecting large and small-scales and cause solid-state turbulence.

Influence of the composition gradient on the propagation of heat pulses in functionally graded nanomaterials

A theoretical model to describe heat transport in functionally graded nanomaterials is developed in the framework of extended thermodynamics. The heat-transport equation used in our theoretical model is of the Maxwell–Cattaneo type. We study the propagation of acceleration waves in functionally graded materials (FGMs). In the special case of functionally graded Si 1− c Ge c thin layers, we point out the influence of the composition gradient on the propagation of heat pulses. A possible use of heat pulses as exploring tool to infer the inner composition of FGMs is suggested.