Celigueta et al 2019a - Revision history

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2020-07-10T10:23:48Z

Cinmemj at 08:43, 19 September 2019

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Cinmemj: Cinmemj moved page Draft Samper 925977240 to Celigueta et al 2019a

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Cinmemj moved page Draft Samper 925977240 to Celigueta et al 2019a

Cinmemj at 10:38, 17 July 2019

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Cinmemj at 12:07, 5 February 2019

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← Older revision		Revision as of 10:23, 10 July 2020
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−	~~Accepted for publication~~ in ''Computational Particle Mechanics'', pp. ~~1-11~~, ~~2019~~<br />	+	Published in ''Computational Particle Mechanics'', Vol. 7, pp. 543–553, 2020<br />
	DOI: 10.1007/s40571-019-00278-5		DOI: 10.1007/s40571-019-00278-5

← Older revision		Revision as of 08:43, 19 September 2019
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−	Accepted for publication in ''Computational Particle Mechanics'', pp. 1-11, 10.1007/s40571-019-00278-5	+	Accepted for publication in ''Computational Particle Mechanics'', pp. 1-11, 2019<br />
		+	DOI: 10.1007/s40571-019-00278-5

	==Abstract==		==Abstract==

← Older revision		Revision as of 08:16, 19 September 2019
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		+	Accepted for publication in ''Computational Particle Mechanics'', pp. 1-11, 10.1007/s40571-019-00278-5
		+
	==Abstract==		==Abstract==

← Older revision		Revision as of 10:38, 17 July 2019
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	The authors thank Prof. Juan Miquel and Dr. Francisco Zárate for their suggestions during the development of this work.		The authors thank Prof. Juan Miquel and Dr. Francisco Zárate for their suggestions during the development of this work.
−
−	~~==Conflict of Interest==~~
−
−	~~On behalf of all authors, the corresponding author states that there is no conflict of interest.~~

	==REFERENCES==		==REFERENCES==

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 On behalf of all authors, the corresponding author states that there is no conflict of interest.
-==8 REFERENCES==
+==REFERENCES==
-−
-===BIBLIOGRAPHY===
 <div id="cite-1"></div>

← Older revision	Revision as of 10:39, 17 July 2019
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 ==Abstract==
 We present a numerical procedure for elastic and non linear analysis (including fracture situations) of solid materials and structures using the Discrete Element Method (DEM). It can be applied to strongly cohesive frictional materials such as concrete and rocks. The method consists on defining non-local constitutive equations at the contact interfaces between discrete particles using the information provided by the stress tensor over the neighbour particles. The method can be used with different yield surfaces and in the paper it is applied to the analysis of fracture of concrete samples. Good comparison with experimental results is obtained.
-'''keywords'''
+'''Keywords''': Discrete Element Method, DEM, concrete, elasticity, non linearity, geomaterials, yield surface
-−
 Discrete Element Method, DEM, concrete, elasticity, non linearity, geomaterials, yield surface
 ==1 INTRODUCTION==

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 |}
-where <math display="inline">\tau _{z'x',i}</math> and <math display="inline">\tau _{z'y',i}</math> are the tangential components of the local stress tensor at the <math display="inline">i</math>th contact point, <math display="inline">{\boldsymbol{\sigma }'}_{i}</math> (Eq.[[#eq-4|4]]). Sub-index <math display="inline">step</math> in Eqs.[[#eq-6|6]] denotes the time step at which the different terms are approximated. For an explicit dynamic solution schemes, ''step'' refers to the previous time step. For implicit schemes, ''step'' refers to the current time step and the term is updated iteratively. Note that both <math display="inline">\tau _{z'x',i}</math> and <math display="inline">\tau _{z'y',i}</math> depend on the stress tensor for each particle (computed by Eq.[[#eq-1|1]]).  Therefore, their value has to be used either from the previous time step or the previous iteration. Otherwise, the forces would never be updated according to the relative displacements. The sub-index <math display="inline">step</math> in Eq.[[#eq-6|6]] avoids the substitution of <math display="inline">A_{i}G\left(\frac{\delta _{x'i}}{L_{i}}\right)_{step}</math> by <math display="inline">k_{ti}\delta _{x'i}</math>, which would cancel terms and make the expression independent from the relative displacements between the particles.
+where <math display="inline">\tau _{z'x',i}</math> and <math display="inline">\tau _{z'y',i}</math> are the tangential components of the local stress tensor at the <math display="inline">i</math>th contact point, <math display="inline">{\boldsymbol{\sigma }'}_{i}</math> (Eq.[[#eq-4|4]]). Sub-index <math display="inline">step</math> in Eqs.[[#eq-6|6]] denotes the time step at which the different terms are approximated. For an explicit dynamic solution schemes, <math>step</math> refers to the previous time step. For implicit schemes, <math>step</math> refers to the current time step and the term is updated iteratively. Note that both <math display="inline">\tau _{z'x',i}</math> and <math display="inline">\tau _{z'y',i}</math> depend on the stress tensor for each particle (computed by Eq.[[#eq-1|1]]).  Therefore, their value has to be used either from the previous time step or the previous iteration. Otherwise, the forces would never be updated according to the relative displacements. The sub-index <math display="inline">step</math> in Eq.[[#eq-6|6]] avoids the substitution of <math display="inline">A_{i}G\left(\frac{\delta _{x'i}}{L_{i}}\right)_{step}</math> by <math display="inline">k_{ti}\delta _{x'i}</math>, which would cancel terms and make the expression independent from the relative displacements between the particles.
 We highlight that both the normal and tangential forces make use of the averaged stress tensor <math display="inline">\boldsymbol{\sigma }_{i}</math> at each contact point. This  increases the stencil of neighboring spheres considered for computing the forces at each contact point.

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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_925977240-Rankine.png|480px|Rankine yield surface in the space of principal stresses]]
+|[[Image:Draft_Samper_925977240-Rankine.png|400px|Rankine yield surface in the space of principal stresses]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" | '''Figure 8:''' Rankine yield surface in the space of principal stresses