Eulerian constitutive equations for the coupled influences of anisotropic yielding, the Bauschinger effect and the strength-differential effect for plane stress

Recently, an Eulerian formulation based on evolving microstructural vectors was used (Lee and Rubin, 2020) to model anisotropic inelastic deformation rate in sheet metals. In contrast to Lagrangian formulations, the Eulerian formulation is insensitive to arbitrariness of reference and intermediate c...

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Bibliographic Details
Published inInternational journal of solids and structures Vol. 241; p. 111475
Main Authors Lee, Eun-Ho, Rubin, M.B.
Format Journal Article
LanguageEnglish
Published New York Elsevier Ltd 01.04.2022
Elsevier BV
Subjects
Anisotropic yielding
Bauschinger effect
Constitutive equations
Constitutive relationships
Datasets
Deformation
Eulerian formulation
Mathematical models
Microstructural vectors
Permanent softening
Plane stress
Strength-differential effect
Microstructural vectors
Eulerian formulation
Bauschinger effect
Anisotropic yielding
Permanent softening
Strength-differential effect
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Summary:Recently, an Eulerian formulation based on evolving microstructural vectors was used (Lee and Rubin, 2020) to model anisotropic inelastic deformation rate in sheet metals. In contrast to Lagrangian formulations, the Eulerian formulation is insensitive to arbitrariness of reference and intermediate configurations. Here, additional constitutive equations are introduced to model asymmetric inelastic behaviors, such as the Bauchinger effect, permanent softening and the strength-differential effect within the context of the Eulerian formulation. The resulting model is calibrated to produce good agreement with several material data sets. In addition, example data sets are used to demonstrate advantages of the new model, especially for severe anisotropic response and large deformations. •An Eulerian formulation based on microstructural vectors is used for sheet metal.•Microstructural vectors determine elastic deformations and orthotropic axes.•Strength-differential Effect modeled using the Lode angle and a hardening parameter.•Baushinger effect and permanent softening in cyclic loading modeled using a directional hardening tensor.•The constitutive equations are validated using five material data sets.
ISSN:0020-7683
1879-2146
DOI:10.1016/j.ijsolstr.2022.111475