Cornejo et al 2020a - Revision history

Onate at 11:59, 20 August 2020

2020-08-20T11:59:09Z

Cinmemj: Cinmemj moved page Draft Samper 955847035 to Cornejo et al 2020a

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Cinmemj moved page Draft Samper 955847035 to Cornejo et al 2020a

Cinmemj at 11:46, 5 June 2020

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Cinmemj at 11:40, 5 June 2020

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2020-06-05T11:28:06Z

← Older revision		Revision as of 11:59, 20 August 2020
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−	Published in ''Computational Particle Mechanics'', ~~2019~~<br />	+	Published in ''Computational Particle Mechanics'', Vol. 7, pp. 735–752, 2020<br />
	doi: 10.1007/s40571-019-00306-4		doi: 10.1007/s40571-019-00306-4

← Older revision		Revision as of 11:46, 5 June 2020
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		+	Published in ''Computational Particle Mechanics'', 2019<br />
		+	doi: 10.1007/s40571-019-00306-4
		+
	==Abstract==		==Abstract==

@@ Line 1,054: / Line 1,054: @@
 <div id="cite-11"></div>
-[11]   Babuška I. and Rheinboldt C., A-posteriori error estimates for the finite element method, ''Int. J. Numer. Methods Eng'', 12,  pages 1597–1615 (1978)
+[[#citeF-11|[11]]]   Babuška I. and Rheinboldt C., A-posteriori error estimates for the finite element method, ''Int. J. Numer. Methods Eng'', 12,  pages 1597–1615 (1978)
 <div id="cite-12"></div>
@@ Line 1,093: / Line 1,093: @@
 <div id="cite-24"></div>
-[24]  Melenk J.M. and Babuška I., The partition of unity finite element method: basic theory and applications, ''Computer methods in applied mechanics and engineering'', 139, pages 289-314 (1996)
+[[#citeF-24|[24]]]  Melenk J.M. and Babuška I., The partition of unity finite element method: basic theory and applications, ''Computer methods in applied mechanics and engineering'', 139, pages 289-314 (1996)
 <div id="cite-25"></div>
-[25]  Griebel M. and Schweitzer M.A., A particle-partition of unity method for the solution of elliptic, parabolic, and hyperbolic pdes, ''SIAM Journal on Scientific Computing'', 22, pages 289-314 (2000)
+[[#citeF-25|[25]]]  Griebel M. and Schweitzer M.A., A particle-partition of unity method for the solution of elliptic, parabolic, and hyperbolic pdes, ''SIAM Journal on Scientific Computing'', 22, pages 289-314 (2000)
 <div id="cite-26"></div>
@@ Line 1,198: / Line 1,198: @@
 <div id="cite-59"></div>
-[59]   Tremblay P., 2-D, 3-D and 4-D Anisotropic Mesh Adaptation for the Time-Continuous Space-Time Finite Element Method with Applications to the Incompressible Navier-Stokes Equations. PhD thesis Ottawa-Carleton Institute for Mechanical and Aerospace Engineering, Department of Mechanical Engineering, University of Ottawa. 2007
+[[#citeF-59|[59]]]  Tremblay P., 2-D, 3-D and 4-D Anisotropic Mesh Adaptation for the Time-Continuous Space-Time Finite Element Method with Applications to the Incompressible Navier-Stokes Equations. PhD thesis Ottawa-Carleton Institute for Mechanical and Aerospace Engineering, Department of Mechanical Engineering, University of Ottawa. 2007
 <div id="cite-60"></div>
@@ Line 1,204: / Line 1,204: @@
 <div id="cite-61"></div>
-[61]   Frey P.J. and Alauzet F., Anisotropic mesh adaptation for transient flows simulations.
+[[#citeF-61|[61]]]   Frey P.J. and Alauzet F., Anisotropic mesh adaptation for transient flows simulations.
 <div id="cite-62"></div>
-[62]   Bellet M., Adaptive mesh technique for thermal–metallurgical numerical simulation of arc welding processes, ''International Journal for Numerical Methods in Engineering'' (2008)
+[[#citeF-62|[62]]]   Bellet M., Adaptive mesh technique for thermal–metallurgical numerical simulation of arc welding processes, ''International Journal for Numerical Methods in Engineering'' (2008)
 <div id="cite-63"></div>

@@ Line 869: / Line 869: @@
 |[[Image:Draft_Samper_955847035-test-skew6.png|240px|Adaptive FE meshes of 4-noded tetrahedra during calculation a) 15546 FE, b) 14436 FE, c) 16707 FE, d) 25811 FE, e) 27478 FE and  f) 29738 FE]]
 |- style="text-align: center; font-size: 75%;"
-| colspan="2" | '''Figure 23:''' Adaptive FE meshes of 4-noded tetrahedra during calculation a) 15546 FE, b) 14436 FE, c) 16707 FE, d) 25811 FE, e) 27478 FE and  f) 29738 FE
+| colspan="2" | '''Figure 23:''' Adaptive FE meshes of 4-noded tetrahedra during calculation a) 15546 FE, b) 14436 FE, c) 16707 FE, d) 25811 FE, e) 27478 FE,  f) 29738 FE
 |}

@@ Line 26: / Line 26: @@
 |[[Image:Draft_Samper_955847035-test-cervera.png|300px|Discontinuities in a continuum (a) strong discontinuity (b) continuum smeared approach. Image from <span id='citeF-18'></span>[[#cite-18|[18]]]]]
 |- style="text-align: center; font-size: 75%;"
-| colspan="1" | '''Figure 1:''' Discontinuities in a continuum (a) strong discontinuity (b) continuum smeared approach. Image from <span id='citeF-18'></span>[[#cite-18|[18]]]
+| colspan="1" | '''Figure 1:''' Discontinuities in a continuum a) strong discontinuity, b) continuum smeared approach. Image from <span id='citeF-18'></span>[[#cite-18|[18]]]
 |}
@@ Line 34: / Line 34: @@
 |[[Image:Draft_Samper_955847035-test-cervera2.png|300px|Discontinuities in a discrete medium (a) strong discontinuity (b) discrete smeared approach. Image from <span id='citeF-18'></span>[[#cite-18|[18]]]]]
 |- style="text-align: center; font-size: 75%;"
-| colspan="1" | '''Figure 2:''' Discontinuities in a discrete medium (a) strong discontinuity (b) discrete smeared approach. Image from <span id='citeF-18'></span>[[#cite-18|[18]]]
+| colspan="1" | '''Figure 2:''' Discontinuities in a discrete medium a) strong discontinuity, b) discrete smeared approach. Image from <span id='citeF-18'></span>[[#cite-18|[18]]]
 |}

← Older revision	Revision as of 11:49, 5 June 2020
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 |[[Image:Draft_Samper_955847035-test-bitmap.png|320px|FE meshes during calculation (a) 5388 FE, b) 6276 FE, c) 8985 FE, d) 8188 FE, e) 6252 FE and f) Final result without remeshing technique]]
 |- style="text-align: center; font-size: 75%;"
-| colspan="1" | '''Figure 12:''' FE meshes during calculation (a) 5388 FE, b) 6276 FE, c) 8985 FE, d) 8188 FE, e) 6252 FE and f) Final result without remeshing technique
+| colspan="1" | '''Figure 12:''' FE meshes during calculation. a) 5388 FE, b) 6276 FE, c) 8985 FE, d) 8188 FE, e) 6252 FE, f) Final result without remeshing technique
 |}

@@ Line 808: / Line 808: @@
 |[[Image:Draft_Samper_955847035-test-mesh3_tensile.png|200px|Tensile test FE meshes during the remeshed FEM-DEM calculation using 4-noded tetrahedra (a) 12000 FE, b) 8248 FE, c) 14092 FE and d) 70749 FE]]
 |- style="text-align: center; font-size: 75%;"
-| colspan="2" | '''Figure 17:''' Tensile test FE meshes during the remeshed FEM-DEM calculation using 4-noded tetrahedra (a) 12000 FE, b) 8248 FE, c) 14092 FE and d) 70749 FE
+| colspan="2" | '''Figure 17:''' Tensile test FE meshes during the remeshed FEM-DEM calculation using 4-noded tetrahedra. a) 12000 FE, b) 8248 FE, c) 14092 FE,  d) 70749 FE
 |}
@@ Line 832: / Line 832: @@
 |[[Image:Draft_Samper_955847035-test-tensilev2.png|440px|Tensile test comparison of the crack pattern between the solution with (a) or without (b) the remeshing technique]]
 |- style="text-align: center; font-size: 75%;"
-| colspan="1" | '''Figure 20:''' Tensile test comparison of the crack pattern between the solution with (a) or without (b) the remeshing technique
+| colspan="1" | '''Figure 20:''' Tensile test comparison of the crack pattern between the solution with a) or without b) the remeshing technique
 |}

@@ Line 666: / Line 666: @@
 |[[Image:Draft_Samper_955847035-test-internal.png|377px|Transfer operators: a) Closest Point Transfer b) Shape Function Projection Transfer c) Least-Square Projection Transfer . Image from <span id='citeF-56'></span>[[#cite-56|[56]]]]]
 |- style="text-align: center; font-size: 75%;"
-| colspan="1" | '''Figure 9:''' Transfer operators: a) Closest Point Transfer b) Shape Function Projection Transfer c) Least-Square Projection Transfer . Image from <span id='citeF-56'></span>[[#cite-56|[56]]]
+| colspan="1" | '''Figure 9:''' Transfer operators. a) Closest Point Transfer. b) Shape Function Projection Transfer. c) Least-Square Projection Transfer. Image from <span id='citeF-56'></span>[[#cite-56|[56]]]
 |}

@@ Line 83: / Line 83: @@
 The coupled FEM-DEM formulation was developed by Zárate and Oñate <span id='citeF-2'></span>[[#cite-2|[2]]] as an effective procedure for predicting the onset and propagation of cracks in concrete and rocks.  Zárate, Cornejo and Oñate <span id='citeF-3'></span>[[#cite-3|[3]]] extended the formulation to 3D problems.
-Initially the continuum is modelled with simplex FE (3-noded triangles in 2D and 4-noded tetrahedra in 3D). The FE solution is obtained by reaching the dynamic equilibrium via an implicit transient dynamic solution scheme. An isotropic damage constitutive law is chosen in order to verify failure at the edges of the FE (using the SPR technique <span id='citeF-9'></span>[[#cite-9|[9]]]). Once one of the failure modes of the FE is achieved, this FE is removed from the mesh and DE are placed at the nodes of the removed FE (see Fig. [[#img-3|3]] and <span id='citeF-2'></span><span id='citeF-3'></span>[[#cite-2|[2,3]]].
+Initially the continuum is modelled with simplex FE (3-noded triangles in 2D and 4-noded tetrahedra in 3D). The FE solution is obtained by reaching the dynamic equilibrium via an implicit transient dynamic solution scheme. An isotropic damage constitutive law is chosen in order to verify failure at the edges of the FE (using the SPR technique <span id='citeF-9'></span>[[#cite-9|[9]]]). Once one of the failure modes of the FE is achieved, this FE is removed from the mesh and DE are placed at the nodes of the removed FE (see Fig. [[#img-3|3]] and <span id='citeF-2'></span><span id='citeF-3'></span>[[#cite-2|[2,3]]]).
 Some important aspects inherent to the FEM-DEM formulation guarantee the good results obtained, such as a smoothed stress field, mass conservation and the use of a simple algorithm to ensure the post-fracture contact between the fractured edge and the adjacent FE and DE in the mesh <span id='citeF-2'></span><span id='citeF-3'></span>[[#cite-2|[2,3]]].