Gradient flows as a selection procedure for equilibria of nonconvex energies

For atomistic material models, global minimization gives the wrong qualitative behavior; a theory of equilibrium solutions needs to be defined in different terms. In this paper, a concept based on gradient flow evolutions, to describe local minimization for simple atomistic models based on the Lennard–Jones potential, is presented. As an application of this technique, it is shown that an atomistic gradient flow evolution converges to a gradient flow of a continuum energy as the spacing between the atoms tends to zero. In addition, the convergence of the resulting equilibria is investigated in the case of elastic deformation and a simple damaged state

Breakdown of Burton-Prim-Slichter approach and lateral solute segregation in radially converging flows

A theoretical study is presented of the effect of a radially converging melt flow, which is directed away from the solidification front, on the radial solute segregation in simple solidification models. We show that the classical Burton-Prim-Slichter (BPS) solution describing the effect of a diverging flow on the solute incorporation into the solidifying material breaks down for the flows converging along the solidification front. The breakdown is caused by a divergence of the integral defining the effective boundary layer thickness which is the basic concept of the BPS theory. Although such a divergence can formally be avoided by restricting the axial extension of the melt to a layer of finite height, radially uniform solute distributions are possible only for weak melt flows with an axial velocity away from the solidification front comparable to the growth rate. There is a critical melt velocity for each growth rate at which the solution passes through a singularity and becomes physically inconsistent for stronger melt flows. To resolve these inconsistencies we consider a solidification front presented by a disk of finite radius $R_0$ subject to a strong converging melt flow and obtain an analytic solution showing that the radial solute concentration depends on the radius $r$ as $\sim\ln^{1/3}(R_0/r)$ and $\sim\ln(R_0/r)$ close to the rim and at large distances from it. The logarithmic increase of concentration is limited in the vicinity of the symmetry axis by the diffusion becoming effective at a distance comparable to the characteristic thickness of the solute boundary layer. The converging flow causes a solute pile-up forming a logarithmic concentration peak at the symmetry axis which might be an undesirable feature for crystal growth processes.Comment: 15 pages, 5 figure

Energetic and Entropic Elasticity of Nonisothermal Flowing Polymers: Experiment, Theory, and Simulation

The thermodynamical aspects of polymeric liquids subjected to nonisothermal flow are examined from the complementary perspectives of theory, experiment, and simulation. In particular, attention is paid to the energetic effects, in addition to the entropic ones, that occur under conditions of extreme deformation. Comparisons of experimental measurements of the temperature rise generated under elongational flow at high strain rates with macroscopic finite element simulations offer clear evidence of the persistence and importance of energetic effects under severe deformation. The performance of various forms of the temperature equation are evaluated with regard to experiment, and it is concluded that the standard form of this evolution equation, arising from the concept of purely entropic elasticity, is inadequate for describing nonisothermal flow processes of polymeric liquids under high deformation. Complete temperature equations, in the sense that they possess a direct and explicit dependence on the energetics of the microstructure of the material, provide excellent agreement with experimental data

A digital computer program for studying elasto-plastic structural behavior due to cyclic loading

A computer program has been developed to study the behavior of plane stress structures under cyclic loading. Such phenomena as thermal ratcheting, alternate plasticity, shake-down and the Bauschinger effect may be considered. The incremental theory of plasticity has been used. The program deals with realistic conditions such as nonlinear strain hardening, nonlinear temperature distribution and occurrence of both compressive and tensile plastic flow. The concept of an average material property has been used. Thermal ratcheting of a beam subjected to a constant bending moment and a temperature cycle has been studied in detail. The analysis shows analytically that the rate of plastic strain growth reduces with an increase in the number of loading cycles. Applications of the computer program have been discussed. Further, the thermal ratcheting of a two bar model has been discussed considering the simplifying assumptions of linear strain hardening and the absence of compressive plastic flow --Abstract, page ii

Self-powered kit for lighting system

Conventional portable light source which normally call a flashlight usually use conventional batteries as a power source. This batteries need to be replace each time the power from the batteries is fully drain. This will lead to excessive production of batteries if the batteries not be recycled. Excess manufacturing and poor disposal management of conventional type batteries will lead to serious issue such as the toxic material in the batteries will absorb in the soil and flow to the water supply and will be absorbed by the plant and end to the fruit. This wills then harmful to the human. Thus, the conventional method to power up portable light source needs to be replace with self-powered light source to prevent excessive use of conventional batteries. Renewable energy concept can be used in the design of self-powered light source and some method can be introduce such as solar, heat thermal, and cranking using dynamo. This study is aim to investigate and experiment another renewable energy which is by using electromagnetic theory to power up a portable light source. Expected deliverable of this project for is up to testing and experimenting some of the concept of electromagnetic theory to come out with the best design as a self-powered generator to the flashlight