Handbook of Mechanics, Materials, and Structures

We describe a new technique for three-dimensional lithospheric-scale modeling of solid state deformation including strain localization processes. The new code, SLIM3D, includes a coupled thermo-mechanical treatment of deformation processes and allows for an elasto-visco-plastic rheology with diffusion, dislocation and Peierls creep mechanisms and Mohr-Coulomb plasticity. The code incorporates an Arbitrary Lagrangian Eulerian formulation with free surface and Winkler boundary conditions. SLIM3D is developed and implemented using the C++ objectoriented programming language. We describe aspects of physical models as well as details of the numerical implementation, including the Newton-Raphson solver, the stress update procedure, and the tangent operator. The applicability of the code to lithospheric-scale modeling is demonstrated by a number of benchmark problems that include: (i) the bending of an elastic plate, (ii) the sinking of a rigid cylinder into a viscous fluid, (iii) the initiation of shear bands in the brittle crust, (iv) triaxial compression test, and (v) lithospheric transpressional deformation. Finally, we discuss possible directions of further development.

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“…Normal stress related to bending in the cross-section is generally computed using the following formula (see e.g. Blake, 1985):…”

Section: Appendix C Cantilever Beammentioning

confidence: 99%

SLIM3D: A tool for three-dimensional thermomechanical modeling of lithospheric deformation with elasto-visco-plastic rheology

Popov

Sobolev

2008

Physics of the Earth and Planetary Interiors

187

159

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“…Removal of the load at the time t = 0 results in a creep recovery [2][3][4]: (3) where: η -coefficient of viscous damping of normal strain.…”

Section: Energy Dissipated After Removal and Application Of Multiaxiamentioning

confidence: 99%

“…According to the Kelvin-Voigt's model of a viscoelastic material [3][4][5], the internal restoring force, F, and the counteracting resistance force, R, can be expressed by: (4) where the dot denotes differentiation with respect to t. Consequently, the dissipation energy can be calculated as the work, W, of the restoring force. If at the time t the rod length is l + Δl, where l is its length prior to load, then:…”

Section: Energy Dissipated After Removal and Application Of Multiaxiamentioning

confidence: 99%

“…For example, if an axial load is applied at t = 0 to a viscoelastic rod and the resulting stress σ x0 is maintained constant, then a timedependent strain response will occur [2][3][4] (26)…”

Section: The Case Of Harmonic In-phase Stressmentioning

confidence: 99%

“…Of course, the amount of dissipated energy depends also on the amplitudes of the stress components and their number, on the load duration and frequency as well as on two parameters of the Kelvin-Voigt's model and Poisson's ratio. The Reader interested in application of three-parameter models of viscoelastic materials is referred, e.g., to [4,8].…”

Section: The Case Of Harmonic Out-of-phase Stressmentioning

confidence: 99%

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