From point defects to plate tectonic faults

Understanding and explaining emergent constitutive laws in the multi-scale evolution from point defects, dislocations and two-dimensional defects to plate tectonic scales is an arduous challenge in condensed matter physics. The Earth appears to be the only planet known to have developed stable plate tectonics as a means to get rid of its heat. The emergence of plate tectonics out of mantle convection appears to rely intrinsically on the capacity to form extremely weak faults in the top 100 km of the planet. These faults have a memory of at least several hundred millions of years, yet they appear to rely on the effects of water on line defects. This important phenomenon was first discovered in laboratory and dubbed ``hydrolytic weakening''. At the large scale it explains cycles of co-located resurgence of plate generation and consumption (the Wilson cycle), but the exact physics underlying the process itself and the enormous spanning of scales still remains unclear. We present an attempt to use the multi-scale non-equilibrium thermodynamic energy evolution inside the deforming lithosphere to move phenomenological laws to laws derived from basic scaling quantities, develop self-consistent weakening laws at lithospheric scale and give a fully coupled deformation-weakening constitutive framework. At meso- to plate scale we encounter in a stepwise manner three basic domains governed by the diffusion/reaction time scales of grain growth, thermal diffusion and finally water mobility through point defects in the crystalline lattice. The latter process governs the planetary scale and controls the stability of its heat transfer mode.

Exact eigenvalue correspondences between laminated plate theories via membrane vibration

Based on Reddy's third-order theory, the first-order theory and the classical theory, exact explicit eigenvalues are found for compression buckling, thermal buckling and vibration of laminated plates via analogy with membrane vibration, These results apply to symmetrically laminated composite plates with transversely isotropic laminae and simply supported polygonal edges, Comprehensive consideration of a Winkler-Pasternak elastic foundation, a hydrostatic inplane force, an initial temperature increment and rotary inertias is incorporated. Bridged by the vibrating membrane, exact correspondences are readily established between any pairs of buckling and vibration eigenvalues associated with different theories. Positive definiteness of the critical hydrostatic pressure at buckling, the thermobukling temperature increment and, in the range of either tension loading or compression loading prior to occurrence of buckling, the natural vibration frequency is proved. (C) 2000 Elsevier Science Ltd. All rights reserved.

Punching shear of slab-column connection in flat plate construction

The flat plate system is currently widely used in construction. It permits architectural flexibility, more clear space, less building height, easier formwork, and shorter construction time. However, there remains the problem of brittle punching failure due to the transfer of shearing forces and unbalanced moments at the flat plate-column connection. It is the purpose of this paper to investigate the effects of various interdependent factors that govern the punching shear resistance and behaviour of the flat plate-column connection, as well as their inclusion in current Codes.

A semi- analytic finite element approach to the stress analysis of circular plate

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choose MyPlate : 10 tips to a great plate

Making food choices for a healthy lifestyle can be as simple as using these 10 Tips : balance calories, enjoy your food, but eat less, avoid oversized portions, foods to eat more often, make half your plate fruits and vegetables, switch to fat-free or low-fat (1%) milk, make half your grains whole grains, foods to eat less often, compare sodium in foods, drink water instead of sugary drinks.

Take Charge of Your Plate!

This sheet provides a list of the different foods and portion sizes you need for a healthy diet.