Materials under complex loading develop large strains and often phase transformation via an elastic instability, as observed in both simple and complex systems. Here, we represent a material (exemplified for Si I) under large Lagrangian strains within a continuum description by a 5th-order elastic energy found by minimizing error relative to density functional theory (DFT) results. The Cauchy stress—Lagrangian strain curves for arbitrary complex loadings are in excellent correspondence with DFT results, including the elastic instability driving the Si I → II phase transformation (PT) and the shear instabilities. PT conditions for Si I → II under action of cubic axial stresses are linear in Cauchy stresses in agreement with DFT predictions. Such continuum elastic energy permits study of elastic instabilities and orientational dependence leading to different PTs, slip, twinning, or fracture, providing a fundamental basis for continuum physics simulations of crystal behavior under extreme loading.
When a continuum is subjected to an induced stress, the equations that govern seismic wave propagation are modified in two ways. First, the equation of conservation of linear momentum gains terms related to the induced deviatoric stress, and, second, the elastic constitutive relationship acquires terms linear in the induced stress. This continuum mechanics theory makes testable predictions with regard to stress‐induced changes in the elastic tensor. Specifically, it predicts that induced compression linearly affects the prestressed moduli with a slope determined by their local adiabatic pressure derivatives and that induced deviatoric stress produces anisotropic compressional and shear wave speeds. In this article we successfully compare such predictions against ab initio mineral physics calculations for NaCl and MgO.
more » « less- NSF-PAR ID:
- 10370689
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Journal of Geophysical Research: Solid Earth
- Volume:
- 124
- Issue:
- 1
- ISSN:
- 2169-9313
- Page Range / eLocation ID:
- p. 729-741
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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A novel computational strategy is presented to calculate from first principles the coefficient of thermal expansion and the elastic constants of a material over meaningful intervals of temperature and pressure. This strategy combines a novel implementation of the quasiharmonic approximation to calculate the isothermal-isochoric linear and nonlinear elastic constants of a material, with elementary equations of nonlinear continuum mechanics. Our implementation of the quasiharmonic approximation relies on finite deformations, the use of nonprimitive supercells to describe a material, a recently proposed technique to calculate generalized mode Grüneisen parameters, and the numerical differentiation of the stress tensor to calculate both second- and third-order elastic constants. The combination of this method with nonlinear continuum mechanics is shown to yield accurate predictions of lattice parameters and linear elastic constants of a material over finite intervals of temperature and pressure, at the cost of calculating isothermal second- and third-order elastic constants for a single reference state. Here, the validity and limits of our novel methods are assessed by carrying out calculations of MgO based on classical interatomic potentials. To demonstrate potential, our methods are then used in conjunction with a density functional theory approach to calculate thermal expansion and elastic properties of silicon, lithium hydrate, and graphite.more » « less
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Abstract Rapid retreat of the Larsen A and B ice shelves has provided important clues about the ice shelf destabilization processes. The Larsen C Ice Shelf, the largest remaining ice shelf on the Antarctic Peninsula, may also be vulnerable to future collapse in a warming climate. Here, we utilize multisource satellite images collected over 1963–2020 to derive multidecadal time series of ice front, flow velocities, and critical rift features over Larsen C, with the aim of understanding the controls on its retreat. We complement these observations with modeling experiments using the Ice‐sheet and Sea‐level System Model to examine how front geometry conditions and mechanical weakening due to rifts affect ice shelf dynamics. Over the past six decades, Larsen C lost over 20% of its area, dominated by rift‐induced tabular iceberg calving. The Bawden Ice Rise and Gipps Ice Rise are critical areas for rift formation, through their impact on the longitudinal deviatoric stress field. Mechanical weakening around Gipps Ice Rise is found to be an important control on localized flow acceleration and the propagation of two rifts that caused a major calving event in 2017. Capturing the time‐varying effects of rifts on ice rigidity in ice shelf models is essential for making realistic predictions of ice shelf flow dynamics and instability. In the context of the Larsen A and Larsen B collapses, we infer a chronology of destabilization processes for embayment‐confined ice shelves, which provides a useful framework for understanding the historical and future destabilization of Antarctic ice shelves.
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Abstract Mineral inclusions are ubiquitous in metamorphic rocks and elastic models for host‐inclusion pairs have become frequently used tools for investigating pressure–temperature (
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