scholarly journals Microcrack interaction with circular inclusion and interfacial zone

2019 ◽  
Vol 13 (48) ◽  
pp. 503-512
Author(s):  
Tomas Profant ◽  
Miroslav Hrstka ◽  
Jan Klusak
Keyword(s):  
Circular Inclusion ◽  
Interfacial Zone ◽  
Microcrack Interaction

scholarly journals A Circular Inclusion and Two Radial Coaxial Cracks with Contacting Faces in a Piecewise Homogeneous Isotropic Plate Under Bending

2020 ◽  
Vol 14 (1) ◽  
pp. 16-21
Author(s):  
Heorgij Sulym ◽  
Viktor Opanasovych ◽  
Ivan Zvizlo ◽  
Roman Seliverstov ◽  
Oksana Bilash
Keyword(s):  
Isotropic Plate ◽  
Singular Integral Equations ◽  
Circular Inclusion ◽  
Contact Forces ◽  
Interfacial Zone ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Radial Cracks ◽  
Crack Faces ◽  
Task Parameters

AbstractThe bending problem of an infinite, piecewise homogeneous, isotropic plate with circular interfacial zone and two coaxial radial cracks is solved on the assumption of crack closure along a line on the plate surface. Using the theory of functions of a complex variable, complex potentials and a superposition of plane problem of the elasticity theory and plate bending problem, the solution is obtained in the form of a system of singular integral equations, which is numerically solved after reducing to a system of linear algebraic equations by the mechanical quadrature method. Numerical results are presented for the forces and moments intensity factors, contact forces between crack faces and critical load for various geometrical and mechanical task parameters.

scholarly journals Sensitivity of the Second Order Homogenized Elasticity Tensor to Topological Microstructural Changes

2021 ◽  
Author(s):  
V. Calisti ◽  
A. Lebée ◽  
A. A. Novotny ◽  
J. Sokolowski
Keyword(s):  
Circular Inclusion ◽  
Elasticity Tensor ◽  
Second Order ◽  
Topological Derivative ◽  
Microstructural Changes ◽  
Topological Derivatives ◽  
Spatial Dimensions ◽  
Elasticity Tensors ◽  
Derivatives Of ◽  
Optimization Of Microstructures

AbstractThe multiscale elasticity model of solids with singular geometrical perturbations of microstructure is considered for the purposes, e.g., of optimum design. The homogenized linear elasticity tensors of first and second orders are considered in the framework of periodic Sobolev spaces. In particular, the sensitivity analysis of second order homogenized elasticity tensor to topological microstructural changes is performed. The derivation of the proposed sensitivities relies on the concept of topological derivative applied within a multiscale constitutive model. The microstructure is topologically perturbed by the nucleation of a small circular inclusion that allows for deriving the sensitivity in its closed form with the help of appropriate adjoint states. The resulting topological derivative is given by a sixth order tensor field over the microstructural domain, which measures how the second order homogenized elasticity tensor changes when a small circular inclusion is introduced at the microscopic level. As a result, the topological derivatives of functionals for multiscale models can be obtained and used in numerical methods of shape and topology optimization of microstructures, including synthesis and optimal design of metamaterials by taking into account the second order mechanical effects. The analysis is performed in two spatial dimensions however the results are valid in three spatial dimensions as well.

Edge dislocation inside a circular inclusion

1965 ◽  
Vol 13 (3) ◽  
pp. 141-147 ◽  
Author(s):  
J. Dundurs ◽  
G.P. Sendeckyj
Keyword(s):  
Edge Dislocation ◽  
Circular Inclusion
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