Multiple Crack Propagation and Coalescence in Finite Elements with Minimal Local Remeshing Using the Subregion Generalized Variational Principle

2020 ◽  
Vol 146 (10) ◽  
pp. 04020111
Author(s):  
Minmao Liao ◽  
Pan Zhang
Keyword(s):  
Variational Principle ◽  
Finite Elements ◽  
Crack Propagation ◽  
Generalized Variational Principle ◽  
Multiple Crack

A GENERALIZED VARIATIONAL PRINCIPLE FOR TRANSPORT PHENOMENA

1958 ◽  
Vol 36 (10) ◽  
pp. 1308-1318 ◽  
Author(s):  
G. E. Tauber
Keyword(s):  
Magnetic Field ◽  
Variational Principle ◽  
Ritz Method ◽  
Transport Coefficients ◽  
Distribution Functions ◽  
Generalized Variational Principle ◽  
Lattice Vibrations ◽  
Arbitrary Direction ◽  
Energy Surfaces ◽  
Thermomagnetic Phenomena

A generalized variational principle has been formulated which takes the phonon distribution functions and the external magnetic field into account, is valid for an arbitrary direction of the electric field and polarization of the lattice vibrations, and does not depend on any special form of the energy surfaces. The various transport coefficients, for both thermoelectric and thermomagnetic phenomena, are obtained by the Ritz method in terms of infinite determinants without requiring an explicit solution of the transport equations.

scholarly journals On the semi-inverse method and variational principle

2013 ◽  
Vol 17 (5) ◽  
pp. 1565-1568 ◽  
Author(s):  
Xue-Wei Li ◽  
Ya Li ◽  
Ji-Huan He
Keyword(s):  
Heat Conduction ◽  
Variational Principle ◽  
Inverse Method ◽  
Generalized Variational Principle ◽  
Open Forum ◽  
One Dimensional ◽  
History Of

In this Open Forum, Liu et al. proved the equivalence between He-Lee 2009 variational principle and that by Tao and Chen (Tao, Z. L., Chen, G. H., Thermal Science, 17(2013), pp. 951-952) for one dimensional heat conduction. We confirm the correction of Liu et al.?s proof, and give a short remark on the history of the semi-inverse method for establishment of a generalized variational principle.

A Markov Chain Fracture Model for Intergranular Crack Propagation in Polycrystalline Materials

2010 ◽  
Vol 89-91 ◽  
pp. 29-34
Author(s):  
Muhammad A. Arafin ◽  
Jerzy A. Szpunar
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Crack Propagation ◽  
Intergranular Crack ◽  
Crack Nucleation ◽  
External Stress ◽  
Polycrystalline Materials ◽  
Multiple Crack ◽  
Stress Direction ◽  
Nucleation Sites

A model for intergranular damage propagation in polycrystalline materials is proposed, based on Markov Chain theory, Monte Carlo simulation and percolation concept. The model takes into account crack branching and coalescence, multiple crack nucleation sites, crack-turning etc., as well as the effect of grain boundary plane orientations with respect to the external stress direction. Both honeycomb and voronoi microstructures were utilized as the input microstructures. The effect of multiple crack nucleation sites has been found to have great influence on the crack propagation length. It has been observed that percolation threshold reported in the literature based on hexagonal microstructure is not applicable when the effect of external stress direction on the susceptibilities of grain boundaries is considered. The successful integration of voronoi algorithm with the Markov Chain and Monte Carlo simulations has opened up the possibilities of evaluating the intergranular crack propagation behaviour in a realistic manner.

On the Topology Update of the Numerical Manifold Method for Multiple Crack Propagation

2021 ◽  
pp. 2150030
Author(s):  
Jun He ◽  
Shuling Huang ◽  
Xiuli Ding ◽  
Yuting Zhang ◽  
Dengxue Liu
Keyword(s):  
Crack Initiation ◽  
Crack Propagation ◽  
Numerical Method ◽  
Crack Tip ◽  
Search Method ◽  
Numerical Manifold Method ◽  
Crack Initiation And Propagation ◽  
Multiple Crack ◽  
Initiation And Propagation ◽  
Numerical Manifold

Crack initiation and propagation are the two key issues of concern in the geotechnical engineering. In this study, the numerical manifold method (NMM) is applied to simulate crack propagation and the topology update of the NMM for multiple crack propagation is studied. The crack-tip asymptotic interpolation function is incorporated into the NMM to increase the accuracy of the crack-tip stress field. In addition, the Mohr-Coulomb criterion with tensile cut off is adopted to be the crack propagation criterion to judge the direction of crack initiation and propagation. Then a crack tip searching method is developed to automatically update the position of the crack tips. The inapplicability of the original loop search method in the NMM is also illustrated and a novel loop search method based on manifold elements is developed for physical loop updating. Moreover, methods for the manifold element updating and physical cover updating are provided. Based on the above study, the developed numerical method is capable to simulate multiple crack propagation. At last, typical rock rupture problems are numerically simulated to manifest the effectiveness of the developed numerical method.

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