Onate Rojek 2004a - Revision history

Move page script: Move page script moved page Draft Samper 102318540 to Onate Rojek 2004a

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Move page script moved page Draft Samper 102318540 to Onate Rojek 2004a

Cinmemj at 13:22, 31 October 2018

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Cinmemj at 13:19, 31 October 2018

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Cinmemj at 13:09, 31 October 2018

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Cinmemj at 13:08, 31 October 2018

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Cinmemj at 13:06, 31 October 2018

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Cinmemj at 13:05, 31 October 2018

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Cinmemj at 13:01, 31 October 2018

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+Published in ''Comput. Methods Appl. Mech. Engrg.'', Vol 193, 3087-3128, 2004<br />
-==COMBINATION OF DISCRETE ELEMENT AND FINITE ELEMENT METHODS FOR DYNAMIC ANALYSIS OF GEOMECHANICS PROBLEMS==
+doi: 10.1016/j.cma.2003.12.056
-−
-'''E. Oñate<math>^\dagger </math> and J. Rojek<math>^{\dagger \ddagger }</math>'''
-−
-{|
-|-
-|<math>^\dagger </math>International Centre for Numerical Methods in Engineering
-|-
-| Universidad Politécnica de Cataluña
-|-
-| Gran Capitán s/n, 08034 Barcelona, Spain
-|-
-| E&#8211;mail: [mailto:onate@cimne.upc.es onate@cimne.upc.es]
-|-
-| Web page: [http://www.cimne.upc.es www.cimne.upc.es]
-|-
-| <math>^{\ddagger }</math>Institute of Fundamental Technological Research
-|-
-| Polish Academy of Sciences
-|-
-| Swietokrzyska 21, 00-049 Warsaw, Poland
-|-
-| E&#8211;mail: [mailto:jrojek@ippt.gov.pl jrojek@ippt.gov.pl]
-|-
-−
-|}

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-<!-- metadata commented in wiki content
 ==COMBINATION OF DISCRETE ELEMENT AND FINITE ELEMENT METHODS FOR DYNAMIC ANALYSIS OF GEOMECHANICS PROBLEMS==
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+|
 |}
--->
 ==Abstract==
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 where <math display="inline">H</math>  is  the plastic softening modulus (assumed to be positive) and <math display="inline">\alpha </math>  is  the softening  parameter represented by the plastic part of the relative displacement <math display="inline">u^p</math>.
-An elasto-plastic contact law with linear softening is assumed for the shear and normal tensile contact forces, cf. Figs. [[#img-8|8]] and [[#img-9|9]]. An elastic linear law is assumed for compression.
+An elasto-plastic contact law with linear softening is assumed for the shear and normal tensile contact forces (Figs. [[#img-8|8]] and [[#img-9|9]]). An elastic linear law is assumed for compression.
 Dependence of the tangential force on the normal force is expressed by the application of the 2D failure criterion shown in Fig. [[#img-10|10]].  Yielding of contact bonds can occur under a combined tension and shear  action (if the normal contact force is tensile) or due to shear only (if the normal contact force is compressive). After the contact bonds are broken due to yielding, standard frictional contact can occur between the spherical elements.
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 |}
-with <math display="inline">H</math> being the hardness of worn surface and <math display="inline">k</math> being a dimensionless parameter. The Archard law was derived originally for adhesive wear, the same form of law, however, can be obtained for abrasive wear, cf. <span id='citeF-16'></span>[[#cite-16|[16]]]. Values of adhesive and abrasive wear constants <math display="inline">k</math>  for different combinations of materials can be found in  <span id='citeF-16'></span>[[#cite-16|[16]]]. It is commonly accepted that wear is related to friction and thus friction coefficients are often introduced into Eq. ([[#eq-61|61]]). If the Coulomb friction law ([[#eq-58|58]]) holds,  the Archard wear law can be written in the following equivalent form:
+with <math display="inline">H</math> being the hardness of worn surface and <math display="inline">k</math> being a dimensionless parameter. The Archard law was derived originally for adhesive wear, the same form of law, however, can be obtained for abrasive wear <span id='citeF-16'></span>[[#cite-16|[16]]]. Values of adhesive and abrasive wear constants <math display="inline">k</math>  for different combinations of materials can be found in  <span id='citeF-16'></span>[[#cite-16|[16]]]. It is commonly accepted that wear is related to friction and thus friction coefficients are often introduced into Eq. ([[#eq-61|61]]). If the Coulomb friction law ([[#eq-58|58]]) holds,  the Archard wear law can be written in the following equivalent form:
 <span id="eq-62"></span>

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 '''[[#citeF-44|[44]]]'''  E.&nbsp;Oñate, C.&nbsp;Recarey, F.&nbsp;Zarate, J.&nbsp;Miquel, and J.&nbsp;Rojek. Characterization of micro-macro parameters in discrete element   formulation. (to be published).
-==8 APPENDIX==
+==APPENDIX A==
-===8.1 Matrices and vectors in FEM equations of motion using the FIC formulation===
+===A.1 Matrices and vectors in FEM equations of motion using the FIC formulation===
 In FEM equations of motion using the FIC formulation ([[#eq-94|94]])&#8211;([[#eq-96|96]]) the following vectors and matrices have been used:

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 The combination of spherical rigid elements and  finite elements is a promising approach for simulation of geomechanical problems involving fracture, penetration and wear. The transient dynamic formulation presented allows to model the motion of discrete and finite elements using a unified algorithm. Frictional contact effects between the rigid spheres and between the spheres and finite elements can be simply accounted for. FIC stabilization procedure allows to use low order triangles and tetrahedra elements with equal order interpolation of the displacement and pressure variables free of the volumetric locking problem. This allows us to apply the presented formulation to problems where large plastic deformation occur in the continuum part of the domain. The discrete formulation can be used to model tools in rock cutting operations. This allows to reproduce tool wear simply by removing the worn particles from the tool surface, thus reproducing the material loss in a realistic manner. Further applications of this approach to the prediction of wear of rock cutting process can be found in <span id='citeF-17'></span><span id='citeF-44'></span>[[#cite-17|[17,44]]].
-===BIBLIOGRAPHY===
+==References==
 <div id="cite-1"></div>

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 |[[Image:Draft_Samper_102318540-pipeovaln3s-wd-eps-02.png|230px|]]
 |-
-|[[Image:Draft_Samper_102318540-pipeovaln3s-wd-eps-04.png|240px|]]
+|[[Image:Draft_Samper_102318540-pipeovaln3s-wd-eps-04.png|270px|]]
 |[[Image:Draft_Samper_102318540-pipeovaln3s-wd-eps-06.png|306px|Pipe ovalization &#8211; deformed configuration]]
 |- style="text-align: center; font-size: 75%;"

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-|[[Image:Draft_Samper_102318540-pipeovaln3s-wd-eps-0.png|206px|]]
+|[[Image:Draft_Samper_102318540-pipeovaln3s-wd-eps-0.png|180px|]]
 |[[Image:Draft_Samper_102318540-pipeovaln3s-wd-eps-02.png|230px|]]
 |-
-|[[Image:Draft_Samper_102318540-pipeovaln3s-wd-eps-04.png|206px|]]
+|[[Image:Draft_Samper_102318540-pipeovaln3s-wd-eps-04.png|226px|]]
 |[[Image:Draft_Samper_102318540-pipeovaln3s-wd-eps-06.png|306px|Pipe ovalization &#8211; deformed configuration]]
 |- style="text-align: center; font-size: 75%;"

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 {| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 100%;max-width: 100%;"
 |-
-|[[Image:Draft_Samper_102318540-pipeoval.png|492px|Pipe ovalization &#8211; geometry definition]]
+|[[Image:Draft_Samper_102318540-pipeoval.png|452px|Pipe ovalization &#8211; geometry definition]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" | '''Figure 38:''' Pipe ovalization &#8211; geometry definition
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 {| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 100%;max-width: 100%;"
 |-
-|[[Image:Draft_Samper_102318540-pipeovaln3s-wd-eps-0.png|246px|]]
+|[[Image:Draft_Samper_102318540-pipeovaln3s-wd-eps-0.png|226px|]]
-|[[Image:Draft_Samper_102318540-pipeovaln3s-wd-eps-02.png|330px|]]
+|[[Image:Draft_Samper_102318540-pipeovaln3s-wd-eps-02.png|230px|]]
 |-
-|[[Image:Draft_Samper_102318540-pipeovaln3s-wd-eps-04.png|348px|]]
+|[[Image:Draft_Samper_102318540-pipeovaln3s-wd-eps-04.png|308px|]]
-|[[Image:Draft_Samper_102318540-pipeovaln3s-wd-eps-06.png|366px|Pipe ovalization &#8211; deformed configuration]]
+|[[Image:Draft_Samper_102318540-pipeovaln3s-wd-eps-06.png|306px|Pipe ovalization &#8211; deformed configuration]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="2" | '''Figure 40:''' Pipe ovalization &#8211; deformed configuration