Simulation of inextensible elasto-plastic beams based on an implicit rate type model

Zhujiang Wang, Arun R. Srinivasa*, K. R. Rajagopal, J. N. Reddy

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


The aim of this paper is to show that it is possible to model the elasto-plastic behavior of an inextensible beam undergoing finite bending by using a novel implicit rate type response relation directly between the bending moment, curvature, and their rates. This is in contrast to conventional approaches that require the integration of elasto-plastic stress–strain relations across the thickness of the beam at each time step. The model proposed here (a) is rate independent and exhibits hysteresis, (b) requires no notion of plastic strain and no integration across the thickness, and (c) does not have a sharp yield point and instead transits smoothly between nominally elastic and inelastic response. The governing equations are solved numerically as a set of first order differential equations with very low order interpolation functions for quasi-static response and are capable of modeling both hardening and softening behavior as well as the formation of plastic hinges, etc. Since there is no yield function, there is no necessity to use a return mapping algorithm that was developed specifically for use in elasto-plasticity with sharp yield functions. This simplifies the numerical algorithm also. The simulations for an elastic perfectly plastic beam are compared with elasto-plastic models in ABAQUSTM, and they show good agreement at a fraction of the computational time. Moreover we have compared simulations of large deformations of an aluminum alloy bar subject to three point bending experiments. The simulations also match the experimental results very well. We demonstrate that it is possible to incorporate frictionless sliding contact (which is needed for the three point bending comparison) in a relatively straightforward manner without the complexity that arises when it is handled in a full three-dimensional (3D) model.

Original languageEnglish
Pages (from-to)165-172
Number of pages8
JournalInternational Journal of Non-Linear Mechanics
StatePublished - Mar 2018
Externally publishedYes


  • Aluminum alloy beam
  • Elastic perfectly plastic
  • Elasto plastic deformation
  • Implicit constitutive relation
  • Isotropic hardening
  • Linear hardening
  • Three point bending


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