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Prescribing Surface Strains to change Gauss curvature

Submitted by Narasimham on
research
differential geometry

Prescribing  Surface Strains to change Gauss curvature

To change Gauss curvature K of a surface we need to strain each differential shell element by virtue of Egregium theorem ( K is invariant if strain is zero in isometry mappings).

Can someone help with a geometrical problem where imposed strains are to be defined (at differential shell element level of a right circular cylinder) to obtain a surface of revolution with Gauss curvature +1 or -1 (sphere or pseudosphere) ? Or their isometric equivalents? Cylindrical coordinates may be used.

Nonlinear Mechanics of Surface Growth for Cylindrical and Spherical Elastic Bodies

Submitted by arash_yavari on
research
Surface growth; accretion mechanics; geometric mechanics; nonlinear elasticity
residual stress

This paper is dedicated to the memory of my friend Professor Bill Klug whose life was tragically cut short on June 1, 2016.

A Nobel Prize worthy paper, unifying Mechanics and Thermodynamics with a mathematical basis

Submitted by Cemal Basaran on
research
mechanics
thermodynamics
statistical mechanics
CDM continuum damage mechanics
evolution problem

I highly recommend this paper to any mechanician who is familiar with the scientific efforst in the last 150 years to unify mechanics and thermodynamics. Sosnoskiy and Sherbakov and several others from the Russian Academy of Sciences listed in the Acknowledgemnsts have achieved it. Congratulations.

Sosnovskiy, L. Sherbakov, S.,”Mechanothermodynamic Entropy and Analysis of Damage State of Complex Systems”, Entropy, 2016, 18, 268.

A Nobel prize worthy paper, unifying Mechanics and Thermodynamics with a Mathematical Basis

Submitted by Cemal Basaran on
research
mechanics
thermodynamics
statistical mechanics
CDM continuum damage mechanics

I highly recommend this paper to any mechanician who is familiar with the scientific efforst in the last 150 years to unify mechanics and thermodynamics. Sosnoskiy and Sherbakov and several others from the Russian Academy of Sciences listed in the Acknowledgemnsts have achieved it. Congratulations.

Sosnovskiy, L. Sherbakov, S.,”Mechanothermodynamic Entropy and Analysis of Damage State of Complex Systems”, Entropy, 2016, 18, 268.

Plasticity model in Abaqus to capture the continues plastic strain of granular material under triaxial cyclic loading?

Submitted by navaratnarajah on
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ABAQUS
Plasticity
granular material
Plastic Strain
cyclic load

I am working on modelling ballast aggregates under triaxial loading. Confining pressure applied in the intermediate and minor principal direction and cyclic compression load applied in the major principal axis direction. I wanted to capture the continues plastic strain (PS) with cycles (N). My test results show that the PS increase with N up to about 10,000 cycles and the rate of strain slowly diminish for later cycles and almost stay constant after N=100,000. What available model in Abaqus can be used to get this behaviour. I have to run my analysis at least for 10,000 cycles.

A Unification of the Concepts of Variational Iteration, Adomian Decomposition and Picard Iteration method; and a Local Variational Iteration Method

Submitted by Xuechuan Wang on
research
nonlinear dynamics; Variational Iteration; Adomian Decomposition; Picard Iteration method

This paper compares the variational iteration method (VIM), the Adomian decomposition method (ADM) and the Picard iteration method (PIM) for solving a system of first order nonlinear ordinary differential equations (ODEs). A unification of the concepts underlying these three methods is attempted by considering a very general iterative algorithm for VIM. It is found that all the three methods can be regarded as special cases of using a very general matrix of Lagrange multipliers in the iterative algorithm of VIM.

A Comparison of the Elastic Properties of Graphene- and Fullerene-Reinforced Polymer Composites: The Role of Filler Morphology and Size

Submitted by chang-tsan.lu on
research
Graphene-based composite material

A recently published paper in mechanical properties of graphene polymer nanocomposites via MD simulations, by Chang-Tsan Lu, Asanka Weerasinghe, Dimitrios Maroudas and Ashwin Ramasubramaniam.

Multiscale real-space quantum-mechanical tight-binding calculations of electronic structure in crystals with defects using perfectly matched layers

Submitted by pourmatin on
research
Schrodinger
Non-reflecting boundary condition
PML

<p>We consider the scattering of incident plane-wave electrons from a defect in a crystal modeled by the time-harmonic Schrödinger equation. While the defect potential is localized, the far-field potential is periodic, unlike standard free-space scattering problems. Previous work on the Schrödinger equation has been almost entirely in free-space conditions; a few works on crystals have been in one-dimension. We construct absorbing boundary conditions for this problem using perfectly matched layers in a tight-binding formulation.

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