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Finite strain plasticity, the stress condition and a complete shell model

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Abstract

The null stress (s 33 = 0) and incompressibility (J = 1) conditions in finite strain elasto-plastic shell analysis are studied in closed-form and implemented with a variant of the combined control by Ritto-Corrêa and Camotim. Coupling between constitutive laws and shell kinematics results from the satisfaction of either of the conditions; nonlocality results from the coupling. We prove that the conditions are, in general, incompatible. A new thickness-deformable is studied in terms of kinematics and strong-ellipticity. The affected continuum laws are derived and, in the discrete form, it is shown that thickness degrees-of-freedom and enhanced strains are avoided: a mixed displacement-shear strain shell element is used. Both hyperelastic and elasto-plastic constitutive laws are tested. Elasto-plasticity follows Lee’s decomposition and direct smoothing of the complementarity condition. A smooth root finder is employed to solve the resulting algebraic problem. Besides closed-form examples, numerical examples consisting of classical and newly proposed benchmarks are solved.

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Authors and Affiliations

  1. Departamento de Física, Universidade de Évora, Colégio Luís António Verney., Rua Romão Ramalho, 59, Edifício Fase III: 3° piso, 7002-554, Évora, Portugal

    Pedro M. A. Areias

  2. Departamento de Engenharia Civil, ICIST, Instituto Superior Técnico, Avenida Rovisco Pais s/n, 1049-001, Lisboa, Portugal

    Manuel C. Ritto-Corrêa

Authors
  1. Pedro M. A. Areias
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  2. Manuel C. Ritto-Corrêa
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  3. João A. C. Martins
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Correspondence to Pedro M. A. Areias.

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J. A. C. Martins: deceased.

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Areias, P.M.A., Ritto-Corrêa, M.C. & Martins, J.A.C. Finite strain plasticity, the stress condition and a complete shell model. Comput Mech 45, 189–209 (2010). https://doi.org/10.1007/s00466-009-0427-y

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