scholarly journals Stability analysis of a nanopatterned bimaterial interface

2021 ◽  
Vol 17 (1) ◽  
pp. 97-104
Author(s):  
Gleb M. Shuvalov ◽  
◽  
Sergey A. Kostyrko ◽  
Keyword(s):  
Solid Mechanics ◽  
Chemical Potential ◽  
Plane Elasticity ◽  
Interface Roughness ◽  
Bimaterial Interface ◽  
Bulk Materials ◽  
Atom Flux ◽  
Interface Elasticity ◽  
Curved Interface ◽  
Plane Elasticity Problem

In the article it is shown that the nanopatterned interface of bimaterial is unstable due to the diffusion atom flux along the interface. The main goal of the research is to analyze the conditions of interface stability. The authors developed a model coupling thermodynamics and solid mechanics frameworks. In accordance with the Gurtin—Murdoch theory of surface/interface elasticity, the interphase between two materials is considered as a negligibly thin layer with the elastic properties differing from those of the bulk materials. The growth rate of interface roughness depends on the variation of the chemical potential at the curved interface, which is a function of interface and bulk stresses. The stress distribution along the interface is found from the solution of plane elasticity problem taking into account plane strain conditions. Following this, the linearized evolution equation is derived, which describes the amplitude change of interface perturbation with time.

scholarly journals Verifying Larché–Cahn elasticity, a milestone of 20th-century thermodynamics

2018 ◽  
Vol 115 (43) ◽  
pp. 10914-10919 ◽  
Author(s):  
Shan Shi ◽  
Jürgen Markmann ◽  
Jörg Weissmüller
Keyword(s):  
20Th Century ◽  
Open System ◽  
Solid Mechanics ◽  
Chemical Potential ◽  
Local Strain ◽  
Elastic Parameters ◽  
Dynamic Mechanical Analyzer ◽  
Strain Gradients ◽  
Alloy Chemistry ◽  
Diffusion Paths

Many materials phenomena are governed by the interaction between chemistry and mechanics. However, it was only in the second half of the 20th century that the theory of open system elasticity by Francis Larché and John W. Cahn concatenated the fields of solid mechanics and alloy chemistry. As the theory’s central materials descriptors, the open system elastic parameters describe how solids deform under stress when solute can rearrange at equilibrium while the chemical potential is held constant. Here, we report experiments verifying the predictions for these parameters. We study the elasticity of nanoporous Pd-H and Pd-Au-H during load cycles imposed by a dynamic mechanical analyzer. Short diffusion paths afford fast equilibration of H in the local strain gradients that carry the macroscopic elastic deformation. The experiment is in excellent agreement with the theory, confirming a central prediction of one of the key contributions to 20th-century thermodynamics.

scholarly journals On Symplectic Analysis for the Plane Elasticity Problem of Quasicrystals with Point Group 12 mm

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Hua Wang ◽  
Jianrui Chen ◽  
Xiaoyu Zhang
Keyword(s):  
Mixed Boundary ◽  
Separation Of Variables ◽  
Point Group ◽  
Mixed Boundary Conditions ◽  
Hamiltonian Operator ◽  
Plane Elasticity ◽  
Elasticity Problem ◽  
Operator Matrices ◽  
Group 12 ◽  
Plane Elasticity Problem

The symplectic approach, the separation of variables based on Hamiltonian systems, for the plane elasticity problem of quasicrystals with point group 12 mm is developed. By introducing appropriate transformations, the basic equations of the problem are converted to two independent Hamiltonian dual equations, and the associated Hamiltonian operator matrices are obtained. The study of the operator matrices shows the feasibility of the method. Without any assumptions, the general solution is presented for the problem with mixed boundary conditions.

An Exact Analytical Solution for Star-Shaped Cracks

2015 ◽  
Vol 1094 ◽  
pp. 458-463 ◽  
Author(s):  
Zhu Chen
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Analytical Solution ◽  
Complex Analysis ◽  
Exact Analytical Solution ◽  
Plane Elasticity ◽  
Type I ◽  
Griffith Crack ◽  
Shaped Crack ◽  
Plane Elasticity Problem

Using the method of complex analysis and by constructing conformal mapping, the study investigates the plane elasticity problem of star-shaped cracks and provides an analytical solution for the stress intensity factor (SIF) of crack-tip type I and II. Problems of the classic Griffith crack, the cross-shaped crack, concurrent uniformly distributed three-cracks and symmetrical eight-cracks are also simulated.

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