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Homogenization of a poro-elasticity model coupled with diffusive transport and a first order reaction for concrete
Symmetry and positive definiteness of the tensor-valued spring constant derived from P1-FEM for the equations of linear elasticity
1. | Waseda Institute for Advanced Study, Waseda University, 3-4-1, Okubo, Shinjuku, Tokyo 169-8555, Japan |
2. | Institute of Science and Engineering, Kanazawa University, Kakuma, Kanazawa 920-1192, Japan |
References:
[1] |
T. Belytschko and T. Black, Elastic crack growth in finite elements with minimal remeshing, International Journal for Numerical Methods in Engineering, 45 (1999), 601-620.
doi: 10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S. |
[2] |
S. C. Brenner and L. R. Scott, The Mathematical Theory of Finite Element Methods, Springer, New York, 2002.
doi: 10.1007/978-1-4757-3658-8. |
[3] |
F. Camborde, C. Mariotti and F. V. Donzé, Numerical study of rock and concrete behaviour by discrete element modelling, Computers and Geotechnics, 27 (2000), 225-247.
doi: 10.1016/S0266-352X(00)00013-6. |
[4] |
H. Chen, L. Wijerathne, M. Hori and T. Ichimura, Stability of dynamic growth of two anti-symmetric cracks using PDS-FEM, Journal of Japan Society of Civil Engineers, Division A: Structural Engineering/Earthquake Engineering & Applied Mechanics, 68 (2012), 10-17.
doi: 10.2208/jscejam.68.10. |
[5] |
P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978. |
[6] |
J. M. Gere, Mechanics of Materials, Brooks/Cole-Thomson Learning, Belmont, CA, 2004. |
[7] |
M. Hori, K. Oguni and H. Sakaguchi, Proposal of FEM implemented with particle discretization for analysis of failure phenomena, Journal of the Mechanics and Physics of Solids, 53 (2005), 681-703.
doi: 10.1016/j.jmps.2004.08.005. |
[8] |
M. Kimura and H. Notsu, A mathematical model of fracture phenomena on a spring-block system, Kyoto University RIMS Kokyuroku, 1848 (2013), 171-186. |
[9] |
J. Karátson and S. Korotov, An algebraic discrete maximum principle in Hilbert space with applications to nonlinear cooperative elliptic systems, SIAM Journal on Numerical Analysis, 47 (2009), 2518-2549.
doi: 10.1137/080729566. |
[10] |
A. Munjiza, The Combined Finite-Discrete Element Method, John Wiley & Sons, Chichester, 2004.
doi: 10.1002/0470020180. |
[11] |
H. Notsu and M. Tabata, A single-step characteristic-curve finite element scheme of second order in time for the incompressible Navier-Stokes equations, Journal of Scientific Computing, 38 (2009), 1-14.
doi: 10.1007/s10915-008-9217-5. |
[12] |
A. Okabe, B. Boots, K. Sugihara and S.-N. Choi, Spatial Tessellation: Concepts and Applications of Voronoi Diagrams, John Wiley and Sons, Chichester, 1992. |
[13] |
G. Voronoi, Nouvelles applications des paramètres continus à la théorie des formes quadratiques, deuxième memoire, recherche sur les parallelloèdres primitifs, Journal für die Reine und Angewandte Mathematik, 134 (1908), 198-287. |
show all references
References:
[1] |
T. Belytschko and T. Black, Elastic crack growth in finite elements with minimal remeshing, International Journal for Numerical Methods in Engineering, 45 (1999), 601-620.
doi: 10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S. |
[2] |
S. C. Brenner and L. R. Scott, The Mathematical Theory of Finite Element Methods, Springer, New York, 2002.
doi: 10.1007/978-1-4757-3658-8. |
[3] |
F. Camborde, C. Mariotti and F. V. Donzé, Numerical study of rock and concrete behaviour by discrete element modelling, Computers and Geotechnics, 27 (2000), 225-247.
doi: 10.1016/S0266-352X(00)00013-6. |
[4] |
H. Chen, L. Wijerathne, M. Hori and T. Ichimura, Stability of dynamic growth of two anti-symmetric cracks using PDS-FEM, Journal of Japan Society of Civil Engineers, Division A: Structural Engineering/Earthquake Engineering & Applied Mechanics, 68 (2012), 10-17.
doi: 10.2208/jscejam.68.10. |
[5] |
P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978. |
[6] |
J. M. Gere, Mechanics of Materials, Brooks/Cole-Thomson Learning, Belmont, CA, 2004. |
[7] |
M. Hori, K. Oguni and H. Sakaguchi, Proposal of FEM implemented with particle discretization for analysis of failure phenomena, Journal of the Mechanics and Physics of Solids, 53 (2005), 681-703.
doi: 10.1016/j.jmps.2004.08.005. |
[8] |
M. Kimura and H. Notsu, A mathematical model of fracture phenomena on a spring-block system, Kyoto University RIMS Kokyuroku, 1848 (2013), 171-186. |
[9] |
J. Karátson and S. Korotov, An algebraic discrete maximum principle in Hilbert space with applications to nonlinear cooperative elliptic systems, SIAM Journal on Numerical Analysis, 47 (2009), 2518-2549.
doi: 10.1137/080729566. |
[10] |
A. Munjiza, The Combined Finite-Discrete Element Method, John Wiley & Sons, Chichester, 2004.
doi: 10.1002/0470020180. |
[11] |
H. Notsu and M. Tabata, A single-step characteristic-curve finite element scheme of second order in time for the incompressible Navier-Stokes equations, Journal of Scientific Computing, 38 (2009), 1-14.
doi: 10.1007/s10915-008-9217-5. |
[12] |
A. Okabe, B. Boots, K. Sugihara and S.-N. Choi, Spatial Tessellation: Concepts and Applications of Voronoi Diagrams, John Wiley and Sons, Chichester, 1992. |
[13] |
G. Voronoi, Nouvelles applications des paramètres continus à la théorie des formes quadratiques, deuxième memoire, recherche sur les parallelloèdres primitifs, Journal für die Reine und Angewandte Mathematik, 134 (1908), 198-287. |
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