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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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