Wu Cervera 2014a - Revision history

Cinmemj: Cinmemj moved page Draft Samper 728720684 to Wu Cervera 2014a

2017-10-25T09:54:39Z

Cinmemj moved page Draft Samper 728720684 to Wu Cervera 2014a

Cinmemj at 09:54, 25 October 2017

2017-10-25T09:54:01Z

Cinmemj at 13:35, 17 October 2017

2017-10-17T13:35:11Z

Cinmemj at 13:34, 17 October 2017

2017-10-17T13:34:40Z

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Cinmemj at 13:33, 17 October 2017

2017-10-17T13:33:48Z

Cinmemj at 13:33, 17 October 2017

2017-10-17T13:33:27Z

Cinmemj: Created page with "==1 Title, abstract and keywords== Your document should start with a concise and informative title. Titles are often used in information-retrieval systems. Avoid abbreviation..."

2017-10-17T13:32:18Z

Created page with "==1 Title, abstract and keywords== Your document should start with a concise and informative title. Titles are often used in information-retrieval systems. Avoid abbreviation..."

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{| style="margin: 1em auto 1em auto;border: 1pt solid black;border-collapse: collapse;"
|-
| style="text-align: center;"|Thickness
| style="text-align: center;"|3.175 mm
|-
| style="text-align: center;"|Young Modulus
| style="text-align: center;"|12.74 MPa
|-
| style="text-align: center;"|Poisson coefficient
| style="text-align: center;"|0.25
|-
| style="text-align: center;"|Density
| style="text-align: center;"|1107 kg/m<sup>3</sup>
|}
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<span style="text-align: center; font-size: 75%;">Table 1: Material properties</span></div>

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@@ Line 1: / Line 1: @@
 ==Abstract==
-This work investigates systematically strain localization and failure mechanics for elastoplastic damage solids. Two complementary methodologies, i.e., traction-based discontinuities localized in an elastic solid and strain localization of a stress-based inelastic softening solid, are addressed. In the former it is assumed a priori that the discontinuity (band) forms with a continuous stress field and along the known orientation. A traction-based failure criterion is introduced to characterize the discontinuity (band) and the orientation is determined from Mohr’s maximization postulate. If the (apparent) displacement jumps are retained as independent variables, the strong/regularized discontinuity approaches follow, requiring constitutive models for both the bulk and discontinuity (band). Elimination of the displacement jumps at the material point level results in the embedded/smeared discontinuity approaches in which an overall inelastic constitutive model fulfilling the static constraint suffices. The second methodology is then adopted to check whether the assumed strain localization can occur and identify its consequences on the resulting approaches. The kinematic constraint guaranteeing stress boundedness/continuity upon strain localization is established for general inelastic softening solids. Application to a unified elastoplastic damage model naturally yields all the ingredients of a localized model for the discontinuity (band), justifying the first methodology. Two dual but not necessarily equivalent approaches, i.e., the traction-based elastoplastic damage model and the stress-based projected discontinuity model, are identified. The former is equivalent to the embedded/smeared discontinuity approaches, whereas in the later the discontinuity orientation and associated failure criterion, not given a priori, are determined consistently from the kinematic constraint. The bi-directional connections and equivalence conditions between the traction- and stress-based approaches are classified. Closed-form 2D results under plane stress condition are also given, with the classical Rankine, Mohr-Coulomb, von Mises and Drucker-Prager criteria analyzed as the illustrative examples. A generic failure criterion of either elliptic, parabolic or hyperbolic type, is then considered in a unified manner, resulting in many failure criteria frequently employed in practice.
+This work investigates systematically strain localization and failure mechanics for elastoplastic damage solids. Two complementary methodologies, i.e., traction-based discontinuities localized in an elastic solid and strain localization of a stress-based inelastic softening solid, are addressed. In the former it is assumed a priori that the discontinuity (band) forms with a continuous stress field and along the known orientation. A traction-based failure criterion is introduced to characterize the discontinuity (band) and the orientation is determined from Mohr’s maximization postulate. If the (apparent) displacement jumps are retained as independent variables, the strong/regularized discontinuity approaches follow, requiring constitutive models for both the bulk and discontinuity (band). Elimination of the displacement jumps at the material point level results in the embedded/smeared discontinuity approaches in which an overall inelastic constitutive model fulfilling the static constraint suffices.
-[[Media:Draft_Samper_728720684_7141_M147.pdf|M147.pdf]]
+The second methodology is then adopted to check whether the assumed strain localization can occur and identify its consequences on the resulting approaches. The kinematic constraint guaranteeing stress boundedness/continuity upon strain localization is established for general inelastic softening solids. Application to a unified elastoplastic damage model naturally yields all the ingredients of a localized model for the discontinuity (band), justifying the first methodology.
 ==References==
 See pdf document

@@ Line 3: / Line 3: @@
 This work investigates systematically strain localization and failure mechanics for elastoplastic damage solids. Two complementary methodologies, i.e., traction-based discontinuities localized in an elastic solid and strain localization of a stress-based inelastic softening solid, are addressed. In the former it is assumed a priori that the discontinuity (band) forms with a continuous stress field and along the known orientation. A traction-based failure criterion is introduced to characterize the discontinuity (band) and the orientation is determined from Mohr’s maximization postulate. If the (apparent) displacement jumps are retained as independent variables, the strong/regularized discontinuity approaches follow, requiring constitutive models for both the bulk and discontinuity (band). Elimination of the displacement jumps at the material point level results in the embedded/smeared discontinuity approaches in which an overall inelastic constitutive model fulfilling the static constraint suffices. The second methodology is then adopted to check whether the assumed strain localization can occur and identify its consequences on the resulting approaches. The kinematic constraint guaranteeing stress boundedness/continuity upon strain localization is established for general inelastic softening solids. Application to a unified elastoplastic damage model naturally yields all the ingredients of a localized model for the discontinuity (band), justifying the first methodology. Two dual but not necessarily equivalent approaches, i.e., the traction-based elastoplastic damage model and the stress-based projected discontinuity model, are identified. The former is equivalent to the embedded/smeared discontinuity approaches, whereas in the later the discontinuity orientation and associated failure criterion, not given a priori, are determined consistently from the kinematic constraint. The bi-directional connections and equivalence conditions between the traction- and stress-based approaches are classified. Closed-form 2D results under plane stress condition are also given, with the classical Rankine, Mohr-Coulomb, von Mises and Drucker-Prager criteria analyzed as the illustrative examples. A generic failure criterion of either elliptic, parabolic or hyperbolic type, is then considered in a unified manner, resulting in many failure criteria frequently employed in practice.
-<pdf>Media:Draft_Samper_728720684_7287_M147.pdf</pdf>
+[[Media:Draft_Samper_728720684_7141_M147.pdf|M147.pdf]]
 ==References==
 See pdf document

← Older revision		Revision as of 13:33, 17 October 2017
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−	==~~1 Title, abstract and keywords~~==	+	==Abstract==

	Your document should start with a concise and informative title. Titles are often used in information-retrieval systems. Avoid abbreviations and formulae where possible. Capitalize the first word of the title.		Your document should start with a concise and informative title. Titles are often used in information-retrieval systems. Avoid abbreviations and formulae where possible. Capitalize the first word of the title.

← Older revision	Revision as of 09:54, 25 October 2017
(No difference)

@@ Line 1: / Line 1: @@
 ==Abstract==
-Your document should start with a concise and informative title. Titles are often used in information-retrieval systems. Avoid abbreviations and formulae where possible. Capitalize the first word of the title.
+This work investigates systematically strain localization and failure mechanics for elastoplastic damage solids. Two complementary methodologies, i.e., traction-based discontinuities localized in an elastic solid and strain localization of a stress-based inelastic softening solid, are addressed. In the former it is assumed a priori that the discontinuity (band) forms with a continuous stress field and along the known orientation. A traction-based failure criterion is introduced to characterize the discontinuity (band) and the orientation is determined from Mohr’s maximization postulate. If the (apparent) displacement jumps are retained as independent variables, the strong/regularized discontinuity approaches follow, requiring constitutive models for both the bulk and discontinuity (band). Elimination of the displacement jumps at the material point level results in the embedded/smeared discontinuity approaches in which an overall inelastic constitutive model fulfilling the static constraint suffices. The second methodology is then adopted to check whether the assumed strain localization can occur and identify its consequences on the resulting approaches. The kinematic constraint guaranteeing stress boundedness/continuity upon strain localization is established for general inelastic softening solids. Application to a unified elastoplastic damage model naturally yields all the ingredients of a localized model for the discontinuity (band), justifying the first methodology. Two dual but not necessarily equivalent approaches, i.e., the traction-based elastoplastic damage model and the stress-based projected discontinuity model, are identified. The former is equivalent to the embedded/smeared discontinuity approaches, whereas in the later the discontinuity orientation and associated failure criterion, not given a priori, are determined consistently from the kinematic constraint. The bi-directional connections and equivalence conditions between the traction- and stress-based approaches are classified. Closed-form 2D results under plane stress condition are also given, with the classical Rankine, Mohr-Coulomb, von Mises and Drucker-Prager criteria analyzed as the illustrative examples. A generic failure criterion of either elliptic, parabolic or hyperbolic type, is then considered in a unified manner, resulting in many failure criteria frequently employed in practice.
-−
-Provide a maximum of 6 keywords, and avoiding general and plural terms and multiple concepts (avoid, for example, 'and', 'of'). Be sparing with abbreviations: only abbreviations firmly established in the field should be used. These keywords will be used for indexing purposes.
-−
-An abstract is required for every document; it should succinctly summarize the reason for the work, the main findings, and the conclusions of the study. Abstract is often presented separately from the article, so it must be able to stand alone. For this reason, references and hyperlinks should be avoided. If references are essential, then cite the author(s) and year(s). Also, non-standard or uncommon abbreviations should be avoided, but if essential they must be defined at their first mention in the abstract itself.
 ==2 The main text==