Plastic deformation of minerals at high pressure: Multiscale numerical modelling
Patrick Cordier, Fabrice Barbe, Julien Durinck, Andrea Tommasi, Andrew M. Walker, 2005. "Plastic deformation of minerals at high pressure: Multiscale numerical modelling", Mineral behaviour at extreme conditions, Ronald Miletich
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Multiscale modelling and computation is becoming one of the most active research areas in materials science. This evolution is driven by the rapid growth in available computing power and by the development of many innovative algorithms and techniques. In mineral physics, the issue of mantle rheology, controlled by the deformation of high-pressure mineral assemblages, can be addressed by this new approach. In contrast with thermodynamic properties like the equation of state, which are fully determined at the atomic length scale, mechanical properties are inherently multiscale: they depend on the interrelationship between processes operating at the scale of the atom, the crystal, the rock and the whole planet. Moreover, these different scales are often strongly coupled to each other, which makes the problem even more challenging.
Mechanical properties of real materials are controlled by crystal defects such as point defects, dislocations, stacking faults and grain boundaries. Taken individually, these defects can be described at the fundamental level through their atomic and electronic structures, which can be found by solving the Schrödinger equation. First-principles calculations and molecular dynamics are used to address such problems. At the scale of a grain, the mechanical properties are often the result of the collective behaviour of these defects in response to the loading conditions. Newly developed three-dimensional dislocation dyna-EMU Notes in Mineralogy, Vol. 7 (2005), Chapter 16, 389–415 mics simulation techniques are aimed to take these interactions between defects into account to provide insights about single-crystal plasticity. Constitutive laws for single-crystal plasticity can be ultimately transferred to the scale of the polycrystal. Polycrystal plasticity models and finite-element methods based on continuum mechanics examine how an aggregate (with possibly several phases) will deform in response to an applied stress.
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Extreme conditions and their effects on matter and materials are currently fashionable topics in modern science. Perhaps the fascination derives from the unimaginable dimensions that grab our attention and push the boundaries of our imagination. Imagine the pressures in extremely dense neutron stars where electrons and protons are fused together and atoms collapse to the density of an atomic nucleus; imagine temperatures of thousands of degrees Kelvin at the solar surface, or multimegabar and terapascal pressures deep within the interior of our planets. But even a simple droplet of water represents an extreme environment when it comes into contact with an otherwise stable crystal of rock salt, causing the crystal to dissolve as external conditions are drastically changed. We have an inherent desire to understand these diverse kinds of phenomena in nature, the mechanisms of the material changes involved, as well as the extreme conditions which are becoming increasingly demanded to achieve the extraordinary performance of new engineering materials. This rapidly evolving area of science is necessarily interdisciplinary, as it combines fundamental physics, chemistry and biology with geoplanetary and materials science, in addition to increasingly becoming one of the keys to engineering and technology aimed at process optimisation. Current experimental methods permit materials to be studied at pressures of several megabars, temperatures of tens of thousands of degrees Kelvin, and to achieve magnetic fields of several thousand teslas. Moreover, the rapid surge in computer technology has, in turn, permitted the solution of many previously intractable problems, and now even allows the behaviour of matter to be predicted far beyond the range of conditions currently accessible to experimentation. Previously unknown phenomena such as the formation of new phases, new forms of electronic and magnetic order, melting, atomic and electronic excitation, ionisation or the formation of a plasma state might result from exposing matter to extreme conditions well beyond those which were characteristic of the equilibria at the time of formation. With this volume of EMU Notes in Mineralogy we have endeavoured to provide up-to-date reviews of our understanding of the behaviour of minerals and geomaterials at exterior conditions that are sufficiently extreme to induce changes. In total 18 chapters reflect the diversity of this theme, but also demonstrate how strongly interdisciplinary this domain of modern mineralogy has become, bringing together physicists, chemists and geologists as well as experimentalists and computer scientists. The present volume contains the contributions of the lectures presented at the 7th EMU School, held at the University of Heidelberg from June 19 to June 25, 2005.