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This study explores the interplay between wave propagation and damage in brittle materials. The damage models, based on micro-mechanical fracture dynamics, capture any possible unstable growth of micro-cracks, introducing a macroscopic loss of stability. After stating the non-dimensional mathematical problem describing the wave propagation with damage, we introduce a non-dimensional number, called the microscopic evolution index, which links the micro and macro scales and discriminates the microscopic scale behaviour. For large values of microscopic evolution index, corresponding to a microscopic quasi-static process coupled with a macroscopic dynamic one, the macroscopic dynamic system could lose its hyperbolicity or become very stiff and generate shock waves. A semi-analytical solution to the one-dimensional wave propagation problem with damage, which could be very useful in the accuracy evaluation of the numerical schemes, was constructed. Concerning the asymptotic behaviour of the dynamic exact solution on the microscopic evolution index (or on the strain rate), an important strain rate sensitivity was found the pulse loses its amplitude for decreasing strain rate and, starting with a critical value, the micro-scale model is rate independent. A possible regularization technique to smooth the shock waves at low and moderate strain rates is discussed. Finally, some numerical results analyse the role played by the the friction on the micro-cracks in the damage modelling of blast wave propagation. This article is part of the theme issue 'Fracture dynamics of solid materials from particles to the globe'.Dynamic earthquake rupture is one of the most extensive and devastating fracture phenomena on the Earth. It causes a sudden crustal deformation around a fault and generates seismic waves that induce bulk density variations propagating with them. Both processes constitute rock-mass redistribution, which is expected to induce simultaneous transient gravity perturbations at all distances before the arrival of P-waves. Interest in such pre-P gravity signals has increased both in terms of modelling and observations because of their potential for earthquake early warning. A simple forward model has pioneered the search for the so-called prompt elasto-gravity signals, which led to the first report of a signal from the 2011 Mw9.0 Tohoku-Oki earthquake using a single superconducting gravimeter record. The second report followed using hundreds of broadband seismometers with critical modification of the previous model to consider the pre-P ground acceleration in the measurement of gravity. Post-event analyses have identified prompt elasto-gravity signals from several large earthquakes, and state-of-the-art instruments are now being developed for real-time signal detection. This paper reviews recent progress in the cutting-edge subject of prompt elasto-gravity signals owing to large-scale earthquake rupture. This article is part of the theme issue 'Fracture dynamics of solid materials from particles to the globe'.This paper presents a numerical study on thermal jet drilling of granite rock that is based on a thermal spallation phenomenon. For this end, a numerical method based on finite elements and a damage-viscoplasticity model are developed for solving the underlying coupled thermo-mechanical problem. An explicit time-stepping scheme is applied in solving the global problem, which in the present case is amenable to extreme mass scaling. Rock heterogeneity is accounted for as random clusters of finite elements representing rock constituent minerals. The numerical approach is validated based on experiments on thermal shock weakening effect of granite in a dynamic Brazilian disc test. The validated model is applied in three-dimensional simulations of thermal jet drilling with a short duration (0.2 s) and high intensity (approx. 3 MW m-2) thermal flux. The present numerical approach predicts the spalling as highly (tensile) damaged rock. Finally, it was shown that thermal drilling exploiting heating-forced cooling cycles is a viable method when drilling in hot rock mass. This article is part of the theme issue 'Fracture dynamics of solid materials from particles to the globe'.Fast development of seismology and related disciplines like seismic prospecting observed in recent decades has its roots in efficient applications of ideas of continuum media mechanics to describe seismic wave propagation through the Earth. Using the same approach enhanced by fracture mechanics methods to describe physical processes leading to nucleation, development and finally arresting of earthquake ruptures has also advanced our understanding of earthquake physics. Selleckchem GSK-3 inhibitor However, in this case, we can talk only about a partial success since many aspects of earthquake processes are still very poorly understood if at all. We argue that to progress with seismic source analysis we need to turn our attention to a complementary approach, namely a 'discrete' one. We demonstrate here that taking into account discreteness of solid materials we are able not only to incorporate classical 'continuum' solutions but also reveal many details of fracture processes whose analysis is beyond the classical fracture mechanics. In this paper, we analyse tensional processes encountered in rock mechanics laboratory experiments, mining seismology and sometimes in realistic inter-plate seismic episodes. The 'discreteness' principle is implemented through the discrete element method-the numerical method entirely based on the discrete representation of the medium. Special attention is paid to energy accumulation and transformation during loading and relaxation phases of fragmentation processes. This article is part of the theme issue 'Fracture dynamics of solid materials from particles to the globe'.Fracture asperities interlock or break during stick slip and ride over each other during stable sliding. The evolution of fracture asperities during the transition between stick slip and stable sliding has attracted less attention, but is important to predict fracture behaviour. Here, we conduct a series of direct shear experiments on simulated fractures in homogeneous polycarbonate to examine the evolution of fracture asperities in the transition stage. Our results show that the transition stage occurs between the stick slip and stable sliding stages during the progressive reduction in normal stress on the smooth and rough fractures. Both the fractures exhibit the alternative occurrence of small and large shear stress drops followed by the deterministic chaos in the transition stage. Our data indicate that the asperity radius of curvature correlates linearly with the dimensionless contact area under a given normal stress. For the rough fracture, a bifurcation of acoustic energy release appears when the dimensionless contact area decreases in the transition stage. The evolution of fracture asperities is stress-dependent and velocity-dependent. This article is part of the theme issue 'Fracture dynamics of solid materials from particles to the globe'.Solid materials have been used extensively for various kinds of structural components in our surroundings. Stability of such solid structures, including not only machinery, architectural and civil structures but also our solid earth, is largely governed by fracture development in the solids. Especially, dynamic fracture, once occurring-quite often unexpectedly-evolves very rapidly and can lead to catastrophic structural failures and disasters like earthquakes. However, contrary to slowly enlarging fractures that can be recognized spatio-temporally in detail, it is extremely difficult to trace dynamically growing fractures even in controlled laboratory experimental conditions, and its physics still remains unexplored. This theme issue introduces and summarizes recent advancements in our understanding of the widespread topics of dynamic fracture of solids from well-assorted perspectives, involving laboratory experiments, simulations and analytical methods as well as field observations, with the common background of mechanics of fracture. Multi-scale subjects range from fracture of metals at atom or particle levels to disastrous rock bursts in deep gold mines and detection of unique signals before devastating fracture such as large, global-scale earthquakes. This article is part of the theme issue 'Fracture dynamics of solid materials from particles to the globe'.This contribution addresses what can be learnt from our recent experimental observations of dynamic fracture development in brittle solid materials with real three-dimensional configurations. It is pointed out that the three-dimensional dynamic behaviour of (quasi-)brittle solids is essentially different not only from the one-dimensional dynamic one but also from the three-dimensional static one. The experimental observations include those of cylindrical concrete columns pressurized by deflagration at the centre and ice spheres subjected to dynamic impact at the bottom. Surprisingly, plain fracture patterns can be found through these experiments, but it does not seem simple to describe or predict the involved physical process by conventional analytical treatment or numerical simulations. Indeed, our understanding of mechanical details of actual three-dimensional fracture is still limited, especially in dynamic cases where the length scale of fracture and relevant waves is of the order of the size of solids under consideration. Although a more sophisticated physical interpretation including the dynamic interaction of waves in a relatively high-frequency range is required, the discussed dynamics of three-dimensional fracture development will assist in generating precisely controlled dynamic fracture networks that can be used for practical purposes of dismantling solid structural components and mitigating risks of catastrophic failures. This article is part of the theme issue 'Fracture dynamics of solid materials from particles to the globe'.This paper presents a numerical investigation on the influence of the mining environment on seismic sources, with a focus on pillar failure mechanisms in tabular mining. We investigate the influence of the mining stope (underground excavation or void) on seismic inversions for the scalar moment, corner frequency, source radius, stress drop and moment tensor using synthetic events created within elastodynamic numerical modelling software, WAVE3D. The main objective is to determine whether the source parameters calculated from the recorded waveforms are due to a combination of the stope source and the pillar sources, rather than being related only to crushing of the pillar or shearing in the pillar footwall. The main finding is that the presence of stopes, and types of pillars, have a significant impact on the seismic moment and other source parameters. This is important since the moment is viewed as a robust parameter on which seismic magnitude is often based; however, this study indicates that moments calculated for pillar failure in a tabular stoping environments are less representative of the shearing or crushing source than originally thought. This article is part of the theme issue 'Fracture dynamics of solid materials from particles to the globe'.
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