Implementation aspects of the bridging scale method and application to intersonic crack propagation

2007 ◽  
Vol 71 (5) ◽  
pp. 583-605 ◽  
Author(s):  
David E. Farrell ◽  
Harold S. Park ◽  
Wing Kam Liu
Keyword(s):  
Crack Propagation ◽  
Scale Method ◽  
Intersonic Crack Propagation ◽  
Implementation Aspects ◽  
Bridging Scale Method

scholarly journals Mathematical models of supersonic and intersonic crack propagation in linear elastodynamics

2021 ◽  
Author(s):  
Javier Bonet ◽  
Antonio J. Gil
Keyword(s):  
Kinetic Energy ◽  
Crack Propagation ◽  
Mathematical Models ◽  
Linear Elasticity ◽  
Strain Energy ◽  
Equations Of Motion ◽  
Two Dimensions ◽  
Discontinuous Solutions ◽  
Linear Elasticity Theory ◽  
Intersonic Crack Propagation

AbstractThis paper presents mathematical models of supersonic and intersonic crack propagation exhibiting Mach type of shock wave patterns that closely resemble the growing body of experimental and computational evidence reported in recent years. The models are developed in the form of weak discontinuous solutions of the equations of motion for isotropic linear elasticity in two dimensions. Instead of the classical second order elastodynamics equations in terms of the displacement field, equivalent first order equations in terms of the evolution of velocity and displacement gradient fields are used together with their associated jump conditions across solution discontinuities. The paper postulates supersonic and intersonic steady-state crack propagation solutions consisting of regions of constant deformation and velocity separated by pressure and shear shock waves converging at the crack tip and obtains the necessary requirements for their existence. It shows that such mathematical solutions exist for significant ranges of material properties both in plane stress and plane strain. Both mode I and mode II fracture configurations are considered. In line with the linear elasticity theory used, the solutions obtained satisfy exact energy conservation, which implies that strain energy in the unfractured material is converted in its entirety into kinetic energy as the crack propagates. This neglects dissipation phenomena both in the material and in the creation of the new crack surface. This leads to the conclusion that fast crack propagation beyond the classical limit of the Rayleigh wave speed is a phenomenon dominated by the transfer of strain energy into kinetic energy rather than by the transfer into surface energy, which is the basis of Griffiths theory.

A Bridging Scale Method for Multi-scale Analysis of Granular Materials

2010 ◽  
Author(s):  
Xikui Li ◽  
Ke Wan ◽  
Jane W. Z. Lu ◽  
Andrew Y. T. Leung ◽  
Vai Pan Iu ◽  
...  
Keyword(s):  
Granular Materials ◽  
Scale Analysis ◽  
Multi Scale ◽  
Scale Method ◽  
Bridging Scale Method ◽  
Multi Scale Analysis

Algorithms for bridging scale method parameters

2007 ◽  
Vol 40 (6) ◽  
pp. 965-978 ◽  
Author(s):  
D. E. Farrell ◽  
E. G. Karpov ◽  
W. K. Liu
Keyword(s):  
Scale Method ◽  
Bridging Scale Method

Intersonic Crack Propagation—Part I: The Fundamental Solution

2000 ◽  
Vol 68 (2) ◽  
pp. 169-175 ◽  
Author(s):  
Y. Huang ◽  
H. Gao
Keyword(s):  
Fundamental Solution ◽  
Crack Propagation ◽  
Cohesive Zone Model ◽  
Shear Crack ◽  
Crack Tip ◽  
Zone Model ◽  
Shear Wave Speed ◽  
Numerical Studies ◽  
Intersonic Crack Propagation ◽  
Tip Velocity

Recent experiments of Rosakis et al. have clearly shown that the crack-tip velocity can exceed the shear wave speed for a crack tip propagating between two weakly bonded, identical and isotropic solids under shear-dominated loading. This has motivated recent theoretical and numerical studies on intersonic crack propagation. We have obtained analytically the fundamental solution for mode-II intersonic crack propagation in this paper. This fundamental solution can provide the general solutions for intersonic crack propagation under arbitrarily initial equilibrium fields. We have also developed a cohesive zone model to determine the crack-tip energy release for an intersonic shear crack.

Continuum and atomistic studies of intersonic crack propagation

2001 ◽  
Vol 49 (9) ◽  
pp. 2113-2132 ◽  
Author(s):  
Huajian Gao ◽  
Yonggang Huang ◽  
Farid F. Abraham
Keyword(s):  
Crack Propagation ◽  
Intersonic Crack Propagation

Intersonic crack propagation along interfaces: Experimental observations and analysis

1998 ◽  
Vol 38 (3) ◽  
pp. 218-225 ◽  
Author(s):  
M. Kavaturu ◽  
A. Shukla ◽  
A. J. Rosakis
Keyword(s):  
Crack Propagation ◽  
Intersonic Crack Propagation

scholarly journals A mathematical framework of the bridging scale method

2006 ◽  
Vol 65 (10) ◽  
pp. 1688-1713 ◽  
Author(s):  
Shaoqiang Tang ◽  
Thomas Y. Hou ◽  
Wing Kam Liu
Keyword(s):  
Mathematical Framework ◽  
Scale Method ◽  
Bridging Scale Method
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