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61.
Gurtin recently proposed a strain-gradient theory for crystal plasticity in which the gradient effect originates from a defect energy that characterizes energy storage due to the presence of a net Burgers vector. Here we consider a number of different possibilities for this energy: specifically, working within a simple two-dimensional framework, we compare predictions of the theory with results of discrete-dislocation simulations of stress relaxation in thin films. Our objective is to investigate which specific defect energies are capable of capturing the size-dependent response of such systems for different crystal orientations. 相似文献
62.
A series of experiments has been conducted to determine the effect of loading variables such as cyclic frequency, load ratio, and material on acoustic emission from fatigue-crack propagation. It is shown that the applied-stress intensity range (ΔK) is the controlling parameter for all materials studied while the other parameters have lesser effects. Two potential methods for engineering application of acoustic emission during fatigue loading are described. 相似文献
63.
A theory of strain-gradient plasticity for isotropic, plastically irrotational materials. Part I: Small deformations 总被引:1,自引:0,他引:1
This study develops a small-deformation theory of strain-gradient plasticity for isotropic materials in the absence of plastic rotation. The theory is based on a system of microstresses consistent with a microforce balance; a mechanical version of the second law that includes, via microstresses, work performed during viscoplastic flow; a constitutive theory that allows:
- •
- the microstresses to depend on , the gradient of the plastic strain-rate, and
- •
- the free energy ψ to depend on the Burgers tensor .
64.
Morton E. Gurtin 《Journal of the mechanics and physics of solids》2004,52(11):2545-2568
This study develops a gradient theory of small-deformation viscoplasticity based on: a system of microforces consistent with its peculiar balance; a mechanical version of the second law that includes, via the microforces, work performed during viscoplastic flow; a constitutive theory that accounts for the Burgers vector through a free energy dependent on , with Hp the plastic part of the elastic-plastic decomposition of the displacement gradient. The microforce balance and the constitutive equations, restricted by the second law, are shown to be together equivalent to a nonlocal flow rule in the form of a coupled pair of second-order partial differential equations. The first of these is an equation for the plastic strain-rate in which the stress T plays a basic role; the second, which is independent of T, is an equation for the plastic spin. A consequence of this second equation is that the plastic spin vanishes identically when the free energy is independent of, but not generally otherwise. A formal discussion based on experience with other gradient theories suggests that sufficiently far from boundaries solutions should not differ appreciably from classical solutions, but close to microscopically hard boundaries, boundary layers characterized by a large Burgers vector and large plastic spin should form.Because of the nonlocal nature of the flow rule, the classical macroscopic boundary conditions need be supplemented by nonstandard boundary conditions associated with viscoplastic flow. As an aid to solution, a variational formulation of the flow rule is derived.Finally, we sketch a generalization of the theory that allows for isotropic hardening resulting from dissipative constitutive dependences on . 相似文献
65.
In this paper we present a new framework for identifying preferred solutions to multi-objective binary optimisation problems.
We develop the necessary theory which leads to new formulations that integrate the decision space with the space of criterion
weights. The advantage of this is that it allows for incorporating preferences directly within a unique binary optimisation
problem which identifies efficient solutions and associated weights simultaneously. We discuss how preferences can be incorporated
within the formulations and also describe how to accommodate the selection of weights when the identification of a unique
solution is required. Our results can be used for designing interactive procedures for the solution of multi-objective binary
optimisation problems. We describe one such procedure for the multi-objective multi-dimensional binary knapsack formulation
of the portfolio selection problem. 相似文献
66.
Patrick Morton 《The Ramanujan Journal》2011,25(2):247-275
The arithmetic on elliptic curves in Deuring normal form is shown to be related to solutions of the Fermat equation 27X 3+27Y 3=X 3 Y 3. This arithmetic is used to give conditions for the existence of multipliers μ on supersingular elliptic curves in characteristic p for which μ 2=?3p. Together with an explicit factorization of a certain class equation, these conditions imply that the number of irreducible binomial quadratic factors (mod p) of the Legendre polynomial P (p?e)/3(x) of degree (p?e)/3 is a simple linear function of the class number of the quadratic field \(\mathbb{Q}(\sqrt{-3p})\). 相似文献
67.
The Ramanujan Journal - In this paper, transformation formulas for the function $$\begin{aligned} A_{1}\left( z,s:\chi \right) =\sum \limits _{n=1}^{\infty }\sum \limits _{m=1} ^{\infty }\chi... 相似文献
68.
L. H. Bailey J. K. Morton Th. Umbach K. Löffl C. S. Robinson und Selma L. Bandemer 《Fresenius' Journal of Analytical Chemistry》1927,71(9):361-362
Ohne Zusammenfassung 相似文献
69.
70.