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A Finite Element Formulation for Highly Deformable Elastoplastic Beams Accounting for Ductile Damage and Plane Stress State

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Abstract

In this work, a finite element formulation is proposed to the analysis of flexible beams under plastic strains, ductile damage and plane-stress conditions. The novel feature of the study is the combination involving an any-order beam element transversely enriched and a Gurson’s porous plasticity theory together with nonlinear isotropic hardening, as well as void growth, nucleation and coalescence. The result is a high-order cross-sectional kinematics and a constitutive elastoplastic model with a competition between strain hardening and porosity-induced softening. The elastic prediction and plastic correction phases are employed together with the Newton-Raphson iterative scheme and the backward Euler time integration of the evolution equations.

To validate the proposed formulation, a cantilever beam and a column under buckling are numerically analyzed. The influence of the mesh refinement, the set of elastoplastic parameters and the material model on the mechanical behavior is investigated in detail. High-order elements are preferable in terms of accuracy of results, despite their high computational effort regarding processing time and memory usage. Results show that the present model can reproduce finite deformations and through-the-thickness variation of 2D strains and stresses, as well as evolution of ductile damage. The importance of accounting for all the model features is also highlighted.

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Funding

The authors are thankful for all the support provided by the Lorena School of Engineering, of the University of São Paulo, including both Materials Engineering Department and Chemical Engineering Department.

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Authors and Affiliations

  1. Lorena School of Engineering, University of São Paulo, Lorena, São Paulo, Brazil

    J. P. Pascon & V. M. Daniel

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  1. J. P. Pascon
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  2. V. M. Daniel
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Correspondence to J. P. Pascon or V. M. Daniel.

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Pascon, J., Daniel, V. A Finite Element Formulation for Highly Deformable Elastoplastic Beams Accounting for Ductile Damage and Plane Stress State. Mech. Solids 57, 1194–1213 (2022). https://doi.org/10.3103/S0025654422050119

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