1,721,189 research outputs found
Trends in Applications of Mathematics to Mechanics
No full textTrends in applications of mathematics to mechanics proceedings of the XIVthInternational Symposium on Trends in Applications of Mathematics to Mechanics (STAMM'2004) Seeheim, Germany, 22-28 August 2004 Yongqi Wang, Kolumban Hutter (eds.)
On propagation of longitudinal and transverse waves in initially stressed linearly elastic media
No full textThe conditions of propagation of small-displacement longitudinal and transverse elastic waves are studied for an initially stressed bod
Thermo-mechanically coupled ice-sheet response — cold, polythermal, temperate
No full textAbstractClassical mixture concepts are the appropriate vehicle for describing the dynamics of ice masses containing some water. We review and derive, respectively, the theoretical formulations of cold, polythermal and temperate ice masses, emphasize the peculiarities of the model equations and point to difficulties that were encountered with the proposed models. The focus is both on the adequate physical motivation of the models and the consistency of their mathematical representation. The paper also has a tutorial character.As usual, cold ice is treated as a single-component incompressible heat-conducting viscous fluid, while two different models are presented for temperate ice. When it arises in a polythermal ice mass, the water content is small and a simple diffusive model for the moisture content suffices. This diffusive model is further simplified by taking its appropriate limit, when the moisture diffusivity tends to zero. Temperate ice in a wholly temperate — Alpine — glacier is treated as a two-phase flow problem, i.e. the momentum-balance laws of both constituents ice and water are properly accounted for. Such Darcy-type models are suggested because the water arises in a greater proportion; so its dynamic role can no longer be ignored.The constituent ice is treated as an incompressible non-linearly viscous isotropic body with constitutive properties similar to those of cold ice. The interstitial water is a density-preserving ideal or perfect fluid. The two interact with an interaction force that is proportional to the “porosity” and the seepage velocity. Internal melting that arises will lead to a generalization of the familiar Darcy law.When water is present, the boundary and transition conditions across internal singular surfaces take special, more complicated forms and involve statements on drainage to the base. These conditions are also discussed in detail.</jats:p
The Effect of Longitudinal Strain on the Shear Stress of an Ice Sheet: In Defence of Using Stretched Coordinates
No full textAbstract
Thickness changes of ice sheets are, except perhaps at the snout region, small as compared to unity. This suggests using a coordinate stretching so as to make the surface changes in the new coordinates of order one. The explicit occurrence of the smallness parameter in the governing equations then allows us to search for perturbation solutions in various problems. Here, it is shown that the classical formula for the basal shear stress follows easily from such a perturbation procedure. Furthermore it can be improved to account for longitudinal strain effects. As compared to previous work in this area, these formulae are explicit and allow us to take vertical variations of material properties into account in a straightforward manner.</jats:p
Time-Dependent Surface Elevation of an ice Slope
No full textAbstractBy introducing a coordinate stretching, the governing field equations of the creep flow of a non-Newtonian viscous medium down a uniform slope are solved to determine the differential equation describing the propagation of long surface waves caused by initial disturbances and/or time-dependent accumulation-rate The differential equation for the surface wave depends on the flow law of the non-Newtonian fluid, the boundary condition at the ice-bedrock interface, the bedrock topography and the thickness–wavelength ratio. For moderately long waves and small elevation above the mean thickness the results agree in their essentials with those of the kinematic wave theory and the forward wave equation with a diffusion term is derived, but when improving this by allowing higher elevations the Burger's equation and even more complex equations are obtained. To derive these results Glen’s flow law must be generalized to avoid infinitely fast changes in stress deviators close to zero Strain-rates, The range of applicability of the various equations is discussed.</jats:p
Ice–ocean dynamics and mechanics: a summary of the papers
No full textA subjective review and summary of the key ideas presented at the conference is given, with occasional indications as to which scientific steps might resolve specific queries that arose from the work. The intention is to encourage closer reading of the papers.</jats:p
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