Search results for "Elastic energy"
showing 8 items of 38 documents
On the thermodynamics of listric faults
2004
We investigate a novel fully coupled thermal-mechanical numerical model of the crust in order to trace the physics of interaction of its brittle and ductile layers. In a unified approach these layers develop in a natural transition as a function of the state variables pressure, deviatoric stress, temperature and strain-rate. We find that the main storage of elastic energy lies in the domain where brittle and ductile strain-rates overlap so that shear zones are attracted to this zone of maximum energy dissipation. This dissipation appears as a local heat source (shear heating). The brittle-ductile transition zone evolves through extreme weakening by thermo-mechanical feedback. The physics of…
The effect of elastic strain on the microstructure of free surfaces of stressed minerals in contact with an aqueous solution
2001
The influence of gradients in bulk elastic strain energy on the dissolution and growth behaviour of minerals in rocks is commonly considered negligible. We experimentally observed, however, that regular arrays of macroscopically visible etch grooves may develop on the originally smooth free surfaces of soluble crystals held in an undersaturated aqueous solution if the crystals are only elastically stressed. These grooves are oriented perpendicular to the compressive stress. They disappear soon after the stress is taken off. The formation of the grooves is well explained by recent theories on the instability of the surface of stressed solids. Development of such instabilities could significa…
A numerical assessment of the free energy function for fractional-order relaxation
2014
In this paper a novel method based on complex eigenanalysis in the state variables domain is proposed to uncouple the set of rational order fractional differential equations governing the dynamics of multi-degree-of-freedom system. The traditional complex eigenanalysis is appropriately modified to be applicable to the coupled fractional differential equations. This is done by expanding the dimension of the problem and solving the system in the state variable domain. Examples of applications are given pertaining to multi-degree-of-freedom systems under both deterministic and stochastic loads.
A mechanically based approach to non-local beam theories
2011
A mechanically based non-local beam theory is proposed. The key idea is that the equilibrium of each beam volume element is attained due to contact forces and long-range body forces exerted, respectively, by adjacent and non-adjacent volume elements. The contact forces result in the classical Cauchy stress tensor while the long-range forces are modeled as depending on the product of the interacting volume elements, their relative displacement and a material-dependent distance-decaying function. To derive the beam equilibrium equations and the pertinent mechanical boundary conditions, the total elastic potential energy functional is used based on the Timoshenko beam theory. In this manner, t…
Pressure-induced cooperative spin transition in ironII 2D coordination polymers: room-temperature visible spectroscopic study.
2011
For the 2D coordination polymers [Fe(3-Fpy)(2)M(II)(CN)(4)] (M(II) = Ni, Pd, Pt), the pressure-induced spin crossover behavior has been investigated at 298 K by monitoring the distinct optical properties associated with each spin state. Cooperative first-order spin transition characterized by a piezohysteresis loop ca. 0.1 GPa wide was observed for the three derivatives. Application of the mean field regular solution theory has enabled estimation of the cooperative parameter, Γ(p), and the enthalpy, ΔH(HL)(p), associated with the spin transition for each derivative. These values, found in the intervals 6.8-7.9 and 18.6-20.8 kJ mol(-1), respectively, are consistent with those previously repo…
Rapid conversion of elastic energy into plastic shear heating during incipient necking of the lithosphere
1998
An important and novel mechanism for ductile failure of the lithosphere is identified here, which is intrinsic to the thermal-mechanical feedback in a temperature dependent plastic body with coupled elastic fields. Both a temperature-dependent power-law visco-elasto-plastic rheology and a temperature-dependent elasto-plastic rheology are employed to study in a self-consistent fashion the deformation of the lithosphere subject to extension by means of a two-dimensional, finite-element code. A structural perturbation initially localizes elasto-plastic deformation only in its immediate vicinity. However, after 800,000 years have elapsed the localized zone of deformation takes off in a ‘crack-l…
Deterministic folding in stiff elastic membranes.
2008
Crumpled membranes have been found to be characterized by complex patterns of spatially seemingly random facets separated by narrow ridges of high elastic energy. We demonstrate by numerical simulations that compression of stiff elastic membranes with small randomness in their initial configurations leads to either random ridge configurations (high entropy) or nearly deterministic folds (low elastic energy). For folding with symmetric ridge configurations to appear in part of the crumpling processes, the crumpling rate must be slow enough. Folding stops when the thickness of the folded structure becomes important, and crumpling continues thereafter as a random process.
Radial symmetry of p-harmonic minimizers
2017
"It is still not known if the radial cavitating minimizers obtained by Ball [J.M. Ball, Discontinuous equilibrium solutions and cavitation in nonlinear elasticity, Phil. Trans. R. Soc. Lond. A 306 (1982) 557--611] (and subsequently by many others) are global minimizers of any physically reasonable nonlinearly elastic energy". The quotation is from [J. Sivaloganathan and S. J. Spector, Necessary conditions for a minimum at a radial cavitating singularity in nonlinear elasticity, Ann. Inst. H. Poincare Anal. Non Lineaire 25 (2008), no. 1, 201--213] and seems to be still accurate. The model case of the $p$-harmonic energy is considered here. We prove that the planar radial minimizers are indee…