WGM Resonator with Transient Circular Inclusion

2012 ◽  
pp. 577-583
Keyword(s):  
Circular Inclusion

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

GPU-based pseudo-transient finite difference solution for power-law viscous flow in cartesian, polar and spherical coordinates

2021 ◽  
Author(s):  
Emilie Macherel ◽  
Yuri Podladchikov ◽  
Ludovic Räss ◽  
Stefan M. Schmalholz
Keyword(s):  
High Resolution ◽  
Finite Difference ◽  
Viscous Flow ◽  
Power Law ◽  
High Performance ◽  
Viscoelastic Behavior ◽  
Iterative Solution ◽  
Circular Inclusion ◽  
Lithospheric Flexure ◽  
Gpu Architectures

<p>Power-law viscous flow describes well the first-order features of long-term lithosphere deformation. Due to the ellipticity of the Earth, the lithosphere is mechanically analogous to a shell, characterized by a double curvature. The mechanical characteristics of a shell are fundamentally different to the characteristics of plates, having no curvature in their undeformed state. The systematic quantification of the magnitude and the spatiotemporal distribution of strain, strain-rate and stress inside a deforming lithospheric shell is thus of major importance: stress is for example a key physical quantity that controls geodynamic processes such as metamorphic reactions, decompression melting, lithospheric flexure, subduction initiation or earthquakes.</p><p>Stress calculations in a geometrically and mechanically heterogeneous 3-D lithospheric shell require high-resolution and high-performance computing. The pseudo-transient finite difference (PTFD) method recently enabled efficient simulations of high-resolution 3-D deformation processes, implementing an iterative implicit solution strategy of the governing equations for power-law viscous flow. Main challenges for the PTFD method is to guarantee convergence, minimize the required iteration count and speed-up the iterations.</p><p>Here, we present PTFD simulations for simple mechanically heterogeneous (weak circular inclusion) incompressible 2-D power-law viscous flow in cartesian and cylindrical coordinates. The flow laws employ a pseudo-viscoelastic behavior to optimize the iterative solution by exploiting the fundamental characteristics of viscoelastic wave propagation.</p><p>The developed PTFD algorithm executes in parallel on CPUs and GPUs. The development was done in Matlab (mathworks.com), then translated into the Julia language (julialang.org), and finally made compatible for parallel GPU architectures using the ParallelStencil.jl package (https://github.com/omlins/ParallelStencil.jl). We may unveil preliminary results for 3-D spherical configurations including gravity-controlled lithospheric stress distributions around continental plateaus.</p>

scholarly journals CRACKING DUE TO EIGEN STRAINS OF A CIRCULAR INCLUSION IN CERAMIC MATERIALS

1986 ◽  
Vol 35 (6) ◽  
pp. 750
Author(s):  
CAO BAO-HONG ◽  
ZHANG HONG-TU
Keyword(s):  
Ceramic Materials ◽  
Circular Inclusion

Interaction between an edge dislocation and a circular inclusion with interfacial rigid lines

2005 ◽  
Vol 180 (1-4) ◽  
pp. 157-174 ◽  
Author(s):  
Y. W. Liu ◽  
Q. H. Fang ◽  
C. P. Jiang
Keyword(s):  
Edge Dislocation ◽  
Circular Inclusion
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