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• W98110668 abstract "Realistic simulations of earth processes such as faulting, shearing, magma flow, subduction and convection often require the consideration of non-Newtonian Effects such as elasticity and power law creep. As the deformations involved in geological deformation are often large the constitutive relationships must maintain certain geometric terms to ensure that the tensor properties of the model are conserved. A model with such properties is termed as objective. There are a wide range of objective, visco-elastioplastic models to choose from. The main structural difference between these models consists in the choice of the objective stress rate, e.g. Jaumann, Oldroyd, Truesdell etc rates (see Kolymbas and Herle, 2003, for a recent discussion). In this paper we give an outline of a thermo-visco-elastic model including a discussion of numerical aspects such as the derivation of a consistent incremental form. The viscous part of the deformation involves a combination of both Newtonian and power law creep. The temperature sensitivity of the viscous deformation is considered by means of an Arrhenius relation involving a pressure dependent reference (melting) temperature. The salient features of the model are first explored by means of analytical and numerical solutions of a simple shear problem for an infinite strip with fixed and prescribed shear velocities on the bottom and top of the layer respectively. The model was implemented into the finite element code FINLEY consisting of two main parts: 1. a Python powered scripting facility (EScript) for the formulation of the governing equations and 2. a parallelized matrix assembly and solution engine. The relative role and importance of elasticity, Newtonian creep, power law creep and temperature dependence of the rheological parameters are explored by means of 2D finite element simulations of natural convection. We consider a quadratic domain with zero normal velocities on the boundaries, fixed temperatures on top and bottom and zero heat flux on the sides. The different cases are compared in terms of the time histories of the Nusselt number and the histories of fractions of the elasticand viscous mechanical powers. For instance ) 1 /( ) ( 1 2 − ∫ Nu dV V V N η τ is the average power fraction of the Newtonian part of the deformation;τ is the second deviatoric invariant of the stress tensor. In the case considered here Nu-1 is the total mechanical power. In the simple shear study we compare the shear stressshear strain curves for a constant applied shear strain rate, assuming infinitesimal theory (i.e. no co-rotational stress terms), Jaumann and Naghdi models respectively. It turns out that for a Jaumann model combined with Newtonian creep (Maxwell model) at relatively high values of the Weissenberg number (Wei=applied strain rate times viscosiy/shear modulus) the stress strain curve has a peak followed by strain softening until under increasing strain a steady state is reached. This behavior is observed at Wei> 1. This kind of geometric softening is also present if Truesdell’s definition of the co-rotational terms is used. This softening behavior is the reason why Maxwell models are still considered a challenge in the CFG community in connection with polymer flow simulations. Geometric softening is not present in the Naghdi and the infinitesimal deformation model. An important conclusion of this study is that geometric softening disappears in all models if a stress limiter in the form of power law creep or a yield criterion is included in the model. Provided, of course, that the transition stress or yield stress is low enough to prevent the stress entering the softening regime. The latter is the case in rocks and metals but not necessarily the case in polymers. In natural convection with temperature and pressure insensitive parameters, including elasticity and combined Newtonian and power law creep it turns out that elasticity is unimportant for realistic values of the Weissenberg number. The Weissenberg number is defined as ) /( μ η hermal t Wei > = <η is the average effective viscosity at steady state and μ is the shear modulus. For mantle convection conditions, Wei<10. However elasticity does have an effect if the creep parameters are strongly temperature dependent. The speed and efficiency of the solution scheme is determined crucially by the way in which the constitutive nonlinearities and handled. The presence of nonlinearities requires sub-iterations within each time step. There are two possible formulations: The secant and the tangent method. The tangent method is more complex and requires the derivation of a consistent incremental form of the constitutive relationships. We have compared three cases for an effective Rayleigh number of Ra= 10: 1. Secant method with iterations, 2. Tangent method with iteration, 3. Tangent method without iterations. The secant method requires about 4-5 sub-iterations per step; the tangent iteration require 1-4 iterations whereby more then one iteration was only necessary around the first few time steps. Thereafter there was virtually no difference between the tangent methods with or without iterations. The CPU time for the tangent method without iterations was about three times less than the CPU time of the secant method with iterations." @default.
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• W98110668 date "2004-01-01" @default.
• W98110668 modified "2023-09-27" @default.
• W98110668 title "The influence of elasticity and temperature dependence on geological flows." @default.
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