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− | ==1 Title, abstract and keywords<!-- 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.
| + | Published in ''Journal of the Mechanics and Physics of Solids'' Vol. 82, pp. 137-163, 2015<br /> |
| + | doi: 10.1016/j.jmps.2015.05.016 |
| + | == Abstract == |
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− | 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.
| + | This work investigates systematically traction- and stress-based approaches for the modeling of strong and regularized discontinuities induced by localized failure in solids. Two complementary methodologies, i.e., ''discontinuities localized in an elastic solid'' and ''strain localization'' of an inelastic softening solid, are addressed. In the former it is assumed ''a priori'' that the discontinuity forms with a continuous stress field and along the known orientation. A traction-based failure criterion is introduced to characterize the discontinuity and the orientation is determined from Mohr's maximization postulate. If the displacement jumps are retained as independent variables, the strong/regularized discontinuity approaches follow, requiring constitutive models for both the bulk and discontinuity. 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 and continuity upon strain localization is established for general inelastic softening solids. Application to a unified stress-based 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 and smeared discontinuity approaches, whereas in the later the discontinuity orientation and associated failure criterion are determined consistently from the kinematic constraint rather than given ''a priori''. The ''bi-directional'' connections and equivalence conditions between the traction- and stress-based approaches are classified. Closed-form results under plane stress condition are also given. A generic failure criterion of either elliptic, parabolic or hyperbolic type is analyzed in a unified manner, with the classical von Mises (<math>J_2</math>), Drucker–Prager, Mohr–Coulomb and many other frequently employed criteria recovered as its particular cases. |
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− | 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. -->==
| + | <pdf>Media:Draft_Samper_497988132_1744_2015-JMPS-equivalence-no.pdf</pdf> |
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− | ==2 The main text<!-- You can enter and format the text of this document by selecting the ‘Edit’ option in the menu at the top of this frame or next to the title of every section of the document. This will give access to the visual editor. Alternatively, you can edit the source of this document (Wiki markup format) by selecting the ‘Edit source’ option.
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− | ==4 Acknowledgments<!-- Acknowledgments should be inserted at the end of the document, before the references section. -->==
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− | ==5 References<!--[1] Author, A. and Author, B. (Year) Title of the article. Title of the Publication. Article code. Available: http://www.scipedia.com/ucode.
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− | [2] Author, A. and Author, B. (Year) Title of the article. Title of the Publication. Volume number, first page-last page.
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This work investigates systematically traction- and stress-based approaches for the modeling of strong and regularized discontinuities induced by localized failure in solids. Two complementary methodologies, i.e., discontinuities localized in an elastic solid and strain localization of an inelastic softening solid, are addressed. In the former it is assumed a priori that the discontinuity forms with a continuous stress field and along the known orientation. A traction-based failure criterion is introduced to characterize the discontinuity and the orientation is determined from Mohr's maximization postulate. If the displacement jumps are retained as independent variables, the strong/regularized discontinuity approaches follow, requiring constitutive models for both the bulk and discontinuity. 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 and continuity upon strain localization is established for general inelastic softening solids. Application to a unified stress-based 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 and smeared discontinuity approaches, whereas in the later the discontinuity orientation and associated failure criterion are determined consistently from the kinematic constraint rather than given a priori. The bi-directional connections and equivalence conditions between the traction- and stress-based approaches are classified. Closed-form results under plane stress condition are also given. A generic failure criterion of either elliptic, parabolic or hyperbolic type is analyzed in a unified manner, with the classical von Mises (), Drucker–Prager, Mohr–Coulomb and many other frequently employed criteria recovered as its particular cases.