Equilibrium Shapes of Small Strained Islands

1995 ◽  
Vol 399 ◽  
Author(s):  
Brian J. Spencer ◽  
J. Tersoff
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Chemical Potential ◽  
Equilibrium Shape ◽  
Two Dimensional ◽  
Asymptotic Results ◽  
Island Size ◽  
Equilibrium Shapes ◽  
Equilibrium Morphology

ABSTRACTWe calculate the equilibrium morphology of a strained layer, for the case where it wets the substrate (Stranski-Krastonow growth). Assuming isotropic surface energy and equal elastic constants in the film and substrate, we are able to calculate two-dimensional equilibrium shapes as a function of the island size and spacing. We present asymptotic results for the equilibrium shape of a thin island where the island height is much smaller than the island width. We also present numerical results of the full equations to describe the island shape when the islands are widely separated. From these solutions we are able to determine the chemical potential of the island as a function of island volume and the strain energy density along the surface of the island for small to medium-sized islands.

The Strain Energy Density of Compressible, Rubber-Like Shells of Revolution

1996 ◽  
Vol 63 (2) ◽  
pp. 419-423 ◽  
Author(s):  
R. F. Yu¨kseler
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Density Functions ◽  
Two Dimensional ◽  
Circular Plates ◽  
Shells Of Revolution ◽  
Large Rotations ◽  
Shear Strains ◽  
Transverse Shear Strains

An approach for the derivation of two-dimensional strain energy density functions of compressible, rubber-like shells of revolution which undergo axisymmetric, arbitrarily large rotations and strains including transverse normal and transverse shear strains is proposed. The proposed method is applied to polyurethane rubber, circular plates and numerical results for the flexural buckling of polyurethane circular plates are obtained for an illustrative comparison with a method presented previously.

Cauchy–Born strain energy density for coupled incommensurate elastic chains

2018 ◽  
Vol 52 (2) ◽  
pp. 729-749 ◽  
Author(s):  
Paul Cazeaux ◽  
Mitchell Luskin
Keyword(s):  
Energy Density ◽  
Error Estimates ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Large Body ◽  
Two Dimensional ◽  
One Dimensional ◽  
Finite Samples ◽  
Weakly Interacting ◽  
Atomistic Systems

The recent fabrication of weakly interacting incommensurate two-dimensional layer stacks (A. Geim and I. Grigorieva, Nature 499 (2013) 419–425) requires an extension of the classical notion of the Cauchy–Born strain energy density since these atomistic systems are typically not periodic. In this paper, we rigorously formulate and analyze a Cauchy–Born strain energy density for weakly interacting incommensurate one-dimensional lattices (chains) as a large body limit and we give error estimates for its approximation by finite samples as well as the popular supercell method.

scholarly journals Volume free strain energy density method for applications to blunt V-notches

2020 ◽  
Vol 28 ◽  
pp. 734-742
Author(s):  
Pietro Foti ◽  
Seyed Mohammad Javad Razavi ◽  
Liviu Marsavina ◽  
Filippo Berto
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Density Method ◽  
Free Strain

scholarly journals On the application of the volume free strain energy density method to blunt V-notches under mixed mode condition

2021 ◽  
Vol 230 ◽  
pp. 111716
Author(s):  
Pietro Foti ◽  
Seyed Mohammad Javad Razavi ◽  
Majid Reza Ayatollahi ◽  
Liviu Marsavina ◽  
Filippo Berto
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Mixed Mode ◽  
Strain Energy ◽  
Density Method ◽  
Free Strain

scholarly journals Alternative derivation of the higher-order constitutive model for six-parameter elastic shells

2021 ◽  
Vol 72 (2) ◽  
Author(s):  
Mircea Bîrsan
Keyword(s):  
Energy Density ◽  
Constitutive Model ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Shell Theory ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Classical Shell Theory ◽  
Three Dimensional Elasticity ◽  
General Method

AbstractIn this paper, we present a general method to derive the explicit constitutive relations for isotropic elastic 6-parameter shells made from a Cosserat material. The dimensional reduction procedure extends the methods of the classical shell theory to the case of Cosserat shells. Starting from the three-dimensional Cosserat parent model, we perform the integration over the thickness and obtain a consistent shell model of order $$ O(h^5) $$ O ( h 5 ) with respect to the shell thickness h. We derive the explicit form of the strain energy density for 6-parameter (Cosserat) shells, in which the constitutive coefficients are expressed in terms of the three-dimensional elasticity constants and depend on the initial curvature of the shell. The obtained form of the shell strain energy density is compared with other previous variants from the literature, and the advantages of our constitutive model are discussed.

Storing Energy in the Mechanical Domain

2014 ◽  
Vol 1679 ◽  
Author(s):  
O.G. Súchil ◽  
G. Abadal ◽  
F. Torres
Keyword(s):  
Energy Source ◽  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Critical Strain ◽  
Substrate Surface ◽  
Maximum Load ◽  
Linear Buckling ◽  
Initial Ph ◽  
Self Powered

ABSTRACTSelf-powered microsystems as an alternative to standard systems powered by electrochemical batteries are taking a growing interest. In this work, we propose a different method to store the energy harvested from the ambient which is performed in the mechanical domain. Our mechanical storage concept is based on a spring which is loaded by the force associated to the energy source to be harvested [1]. The approach is based on pressing an array of fine wires (fws) grown vertically on a substrate surface. For the fine wires based battery, we have chosen ZnO fine wires due the fact that they could be grown using a simple and cheap process named hydrothermal method [2]. We have reported previous experiments changing temperature and initial pH of the solution in order to determine the best growth [3]. From new experiments done varying the compounds concentration the best results of fine wires were obtained. To characterize these fine wires we have considered that the maximum load we can apply to the system is limited by the linear buckling of the fine wires. From the best results we obtained a critical strain of εc = 3.72 % and a strain energy density of U = 11.26 MJ/m3, for a pinned-fixed configuration [4].

On the Crack Initiated from the Bi-Material Notch Tip

2010 ◽  
Vol 452-453 ◽  
pp. 441-444 ◽  
Author(s):  
Tomáš Profant ◽  
Jan Klusák ◽  
Michal Kotoul
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Local Minimum ◽  
Plane Elasticity ◽  
Mean Value ◽  
Tangential Stresses ◽  
Density Factor ◽  
The Mean ◽  
Energy Density Factor

The bi-material notch composed of two orthotropic parts is considered. The radial and tangential stresses and strain energy density is expressed using the Stroh-Eshelby-Lekhnitskii formalism for the plane elasticity. The potential direction of the crack initiation is determined from the maximum mean value of the tangential stresses and local minimum of the mean value of the generalized strain energy density factor in both materials. Matched asymptotic procedure is used to derive the change of potential energy for the debonding crack and the crack initiated in the determined direction.

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