Differentiation of the energy functional in the equilibrium problem for a Timoshenko plate with a crack on the boundary of an elastic inclusion

2017 ◽  
Vol 11 (2) ◽  
pp. 252-262 ◽  
Author(s):  
N. V. Neustroeva ◽  
N. P. Lazarev
Keyword(s):  
Equilibrium Problem ◽  
Elastic Inclusion ◽  
Energy Functional

Adhesion of lipid tubules in an assembly

1998 ◽  
Vol 9 (5) ◽  
pp. 485-506 ◽  
Author(s):  
RICCARDO ROSSO ◽  
EPIFIANO G. VIRGA
Keyword(s):  
Surface Tension ◽  
External Field ◽  
Equilibrium Problem ◽  
Biological Systems ◽  
Critical Value ◽  
Stability Diagram ◽  
Energy Functional ◽  
Highly Nonlinear ◽  
The Stability ◽  
Lipid Tubules

We study a unilateral equilibrium problem for the energy functional of a lipid tubule subject to an external field. These tubules, which constitute many biological systems, may form assemblies when they are brought in contact, and so made to adhere to one another along at interstices. The contact energy is taken to be proportional to the area of contact through a constant, which is called the adhesion potential. This competes against the external field in determining the stability of patterns with flat interstices. Though the equilibrium problem is highly nonlinear, we determine explicitly the stability diagram for the adhesion between tubules. We conclude that the higher the field, the lower the adhesion potential needed to make at interstices energetically favourable, though its critical value depends also on the surface tension of the interface between the tubules and the isotropic fluid around them.

scholarly journals INVARIANT INTEGRALS IN EQUILIBRIUM PROBLEM FOR A TIMOSHENKO TYPE PLATE WITH THE SIGNORINI TYPE CONDITION ON THE CRACK

2017 ◽  
Vol 19 (6) ◽  
pp. 100-115
Author(s):  
N.P. Lazarev
Keyword(s):  
Equilibrium Problem ◽  
Perturbation Parameter ◽  
Energy Functional ◽  
Type Condition ◽  
Invariant Integrals ◽  
Timoshenko Type ◽  
Crack Faces ◽  
Inequality Type

The equilibrium problem for the elastic Timoshenko type plate with a crack is considered. On the crack faces, the non-penetration conditions of inequality type (Signorini type conditions) are given. It is proved that there exist invariant integrals that are equal to the derivative of the energy functional with respect to perturbation parameter.

scholarly journals Asymptotic Justification of Models of Plates Containing Inside Hard Thin Inclusions

2020 ◽  
Author(s):  
Evgeny Rudoy
Keyword(s):  
Small Parameter ◽  
Equilibrium Problem ◽  
Elastic Properties ◽  
Rigid Inclusion ◽  
Elastic Inclusion ◽  
Asymptotic Model ◽  
Hard Inclusion ◽  
Passage To The Limit

An equilibrium problem of the Kirchhoff-Love plate containing a nonhomogeneous inclusion is considered. It is assumed that elastic properties of the inclusion depend on a small parameter characterizing width of the inclusion $\varepsilon$ as $\varepsilon^N$ with $N<1$. The passage to the limit as the parameter $\varepsilon$ tends to zero is justified, and an asymptotic model of a plate containing a thin inhomogeneous hard inclusion is constructed. It is shown that there exists two types of thin inclusions: rigid inclusion ($N<-1$) and elastic inclusion ($N=-1$). The inhomogeneity disappears in the case of $N\in (-1,1)$.

scholarly journals Asymptotic Justification of Models of Plates Containing Inside Hard Thin Inclusions

Technologies ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 59
Author(s):  
Evgeny Rudoy
Keyword(s):  
Small Parameter ◽  
Equilibrium Problem ◽  
Elastic Properties ◽  
Rigid Inclusion ◽  
Elastic Inclusion ◽  
Asymptotic Model ◽  
Hard Inclusion ◽  
Passage To The Limit

An equilibrium problem of the Kirchhoff–Love plate containing a nonhomogeneous inclusion is considered. It is assumed that elastic properties of the inclusion depend on a small parameter characterizing the width of the inclusion ε as εN with N<1. The passage to the limit as the parameter ε tends to zero is justified, and an asymptotic model of a plate containing a thin inhomogeneous hard inclusion is constructed. It is shown that there exists two types of thin inclusions: rigid inclusion (N<−1) and elastic inclusion (N=−1). The inhomogeneity disappears in the case of N∈(−1,1).

A Combination of the Work Formalism for Exchange with an Optimized Correlation Energy Functional for Atoms

1995 ◽  
Vol 5 (9) ◽  
pp. 1277-1287 ◽  
Author(s):  
N. A. Cordero ◽  
K. D. Sen ◽  
J. A. Alonso ◽  
L. C. Balbás
Keyword(s):  
Correlation Energy ◽  
Energy Functional

Cosserat Modeling of Size Effects in Crystalline Solids

2000 ◽  
Vol 653 ◽  
Author(s):  
Samuel Forest
Keyword(s):  
Stress State ◽  
Size Effects ◽  
Elastic Inclusion ◽  
Characteristic Size ◽  
Infinite Matrix ◽  
Crystalline Solids ◽  
Generalized Continua ◽  
Absolute Size ◽  
Kink Bands ◽  
The Matrix

AbstractThe mechanics of generalized continua provides an efficient way of introducing intrinsic length scales into continuum models of materials. A Cosserat framework is presented here to descrine the mechanical behavior of crystalline solids. The first application deals with the problem of the stress field at a crak tip in Cosserat single crystals. It is shown that the strain localization patterns developping at the crack tip differ from the classical picture : the Cosserat continuum acts as a bifurcation mode selector, whereby kink bands arising in the classical framework disappear in generalized single crystal plasticity. The problem of a Cosserat elastic inclusion embedded in an infinite matrix is then considered to show that the stress state inside the inclusion depends on its absolute size lc. Two saturation regimes are observed : when the size R of the inclusion is much larger than a characteristic size of the medium, the classical Eshelby solution is recovered. When R is much small than the inclusion, a much higher stress is reached (for an inclusion stiffer than the matrix) that does not depend on the size any more. There is a transition regime for which the stress state is not homogeneous inside the inclusion. Similar regimes are obtained in the study of grain size effects in polycrystalline aggregates of Cosserat grains.

Reciprocal Polarizable Embedding with a Transferable H2O Potential Function I: Formulation & Tests on Dimer

2019 ◽  
Author(s):  
Elvar Jónsson ◽  
Asmus Ougaard Dohn ◽  
Hannes Jonsson
Keyword(s):  
Potential Function ◽  
Dft Method ◽  
Multipole Expansion ◽  
Energy Functional ◽  
Real Space ◽  
Functional Formulation ◽  
General Energy ◽  
Projector Augmented Wave ◽  
Grid Based ◽  
Polarizable Embedding

This work describes a general energy functional formulation of a polarizable embedding QM/MM scheme, as well as an implementation where a real-space Grid-based Projector Augmented Wave (GPAW) DFT method is coupled with a potential function for H<sub>2</sub>O based on a Single Center Multipole Expansion (SCME) of the electrostatics, including anisotropic dipole and quadrupole polarizability.

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