Fully coupled peridynamic thermomechanics

This study concerns the derivation of the coupled peridynamic (PD) thermomechanics equations based on thermodynamic considerations. The generalized peridynamic model for fully coupled thermomechanics is derived using the conservation of energy and the free-energy function. Subsequently, the bond-based coupled PD thermomechanics equations are obtained by reducing the generalized formulation. These equations are also cast into their nondimensional forms. After describing the numerical solution scheme, solutions to certain coupled thermomechanical problems with known previous solutions are presented

Entropic Limit Analysis Applied to Radial Cavity Expansion Problems

Analytical solutions of limit analysis design for the simple problem of plane strain expansion of a cylindrical cavity are derived and generalized into entropic extremum principles that allow a fundamental assessment of coupled thermal/hydro/mechanical/chemical (THMC) material instabilities and their effect on the upper and lower bounds of dissipation. The proposed approach integrates a thermodynamically based estimation of uncertainties in coupled deformation processes and an identification of the intrinsic material length/time scales that appear as energy eigenstates of the localization problem. Analytical limit analysis design solutions of the cavity expansion are obtained and upper and lower bound estimates are shown to coincide. This provides a robust framework for adding multiphysics feedbacks. Isothermal conditions are first relaxed and the feedback between shear heating, thermal weakening and thermal diffusion is analyzed. Then the analysis is extended to a full range of THMC localization phenomena which are described with a cascade of characteristic time/length scales derived from instabilities in the governing reaction-diffusion equations. Entropic uncertainties are estimated by alternating system constraints between thermodynamic flux and thermodynamic force on the boundaries

Partitioning of sulfur between solid and liquid iron under Earth's core conditions: Constraints from atomistic simulations with machine learning potentials

Partition coefficients of light elements between the solid and liquid iron phases are crucial for uncovering the state and dynamics of the Earth's core. As one of the major light element candidates, sulfur has attracted extensive interests for measuring its partitioning and phase behaviors over the last several decades, but the relevant experimental data under Earth's core conditions are still scarce. In this study, using a toolkit consisting of electronic structure theory, high-accuracy machine learning potentials and rigorous free energy calculations, we establish an efficient and extendible framework for predicting complex phase behaviors of iron alloys under extreme conditions. As a first application of this framework, we predict the partition coefficients of sulfur over wide range of temperatures and pressures (from 4000 K, 150 GPa to 6000 K, 330 GPa), which are demonstrated to be in good agreement with previous experiments and ab initio simulations. After a continuous increase below ∼250 GPa, the partition coefficient is found to be around 0.75 ± 0.07 at higher pressures and are essentially temperature-independent. Given these predictions, the partitioning of sulfur is confirmed to be insufficient to account for the observed density jump across the Earth's inner core boundary and its roles on the geodynamics of the Earth's core should be minor

Asymptotic analysis of surface waves at vacuum/porous medium and liquid/porous medium interfaces

Surface waves at a free interface of a saturated porous medium and at an interface between a porous medium and a liquid are investigated. Existence and peculiarities of such surface waves are revealed. At a free interface two types of surface waves are proved to be possible: the true Stoneley wave, propagating almost without attenuation, and the leaky generalized Rayleigh wave, which reradiates a part of its energy into interior of a medium. At a porous medium/liquid interface three types of surface waves are expected. These are the true Stoneley wave, the pseudo Stoneley wave, and the generalized Rayleigh wave

The static and time-dependent signature of ocean–continent and ocean–ocean subduction: the case studies of Sumatra and Mariana complexes

SUMMARY The anomalous density structure at subduction zones, both in the wedge and in the upper mantle, is analysed to shed light on the processes that are responsible for the characteristic gravity fingerprints of two types of subduction: ocean–continent and ocean–ocean. Our modelling is then performed within the frame of the EIGEN-6C4 gravitational disturbance pattern of two subductions representative of the above two types, the Sumatra and Mariana complexes, finally enabling the different characteristics of the two patterns to be observed and understood on a physical basis, including some small-scale details. A 2-D viscous modelling perpendicular to the trench accounts for the effects on the gravity pattern caused by a wide range of parameters in terms of convergence velocity, subduction dip angle and lateral variability of the crustal thickness of the overriding plate, as well as compositional differentiation, phase changes and hydration of the mantle. Plate coupling, modelled within a new scheme where the relative velocity at the plate contact results self-consistently from the thermomechanical evolution of the system, is shown to have an important impact on the gravity signature. Beyond the already understood general bipolar fingerprint of subduction, perpendicular to the trench, we obtain the density and gravity signatures of the processes occurring within the wedge and mantle that are responsible for the two different gravity patterns. To be compliant with the geodetic EIGEN-6C4 gravitational disturbance and to compare our predictions with the gravity at Sumatra and Mariana, we define a model normal Earth. Although the peak-to-peak gravitational disturbance is comparable for the two types of subductions, approximately 250 mGal, from both observations and modelling, encompassing the highest positive maximum on the overriding plates and the negative minimum on the trench, the trough is wider for the ocean–ocean subduction: approximately 300 km compared to approximately 180 km for the ocean–continent subduction. Furthermore, the gravitational disturbance pattern is more symmetric for the ocean–ocean subduction compared to the ocean–continent subduction in terms of the amplitudes of the two positive maxima over the overriding and subducting plates. Their difference is, for the ocean–ocean type, approximately one half of the ocean–continent one. These different characteristics of the two types of subductions are exploited herein in terms of the different crustal thicknesses of the overriding plate and of the different dynamics in the wedge and in the mantle for the two types of subduction, in close agreement with the gravity data

Qualitative study of a geodynamical rate-and-state model for elastoplastic shear flows in crustal faults

The Dieterich-Ruina rate-and-state friction model is transferred to a bulk variant and the state variable (aging) influencing the dissipation mechanism is here combined also with a damage influencing standardly the elastic response. As the aging has a separate dynamics, the overall model does not have a standard variational structure. A one-dimensional model is investigated as far as the steady-state existence, localization of the ataclastic core, and its time response, too. Computational experiments with a damage-free variant show stick-slip behavior (i.e. seismic cycles of tectonic faults) as well as stable slip under very large velocities