A generalised algorithm for anelastic processes in elastoplasticity and biomechanics

Alfio Grillo*, Raphael Prohl, Gabriel Wittum

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


A computational algorithm for solving anelastic problems in finite deformations is introduced. The presented procedure, termed the Generalised Plasticity Algorithm (GPA) hereafter, takes inspiration from the Return Mapping Algorithm (RMA), which is typically employed to solve the Karush-Kuhn-Tucker (KKT) system arising in finite elastoplasticity, but aims to modify and extend the RMA to the case of more general flow rules and strain energy density functions as well as to non-classical formulations of elastoplasticity, in which the plastic variables are not treated as internal variables. To assess its reliability, the GPA is tested in two different contexts. First, it is used for solving two classical problems (a shear-compression test and the necking of a circular bar). In both cases, the GPA is compared with the RMA in terms of structural set-up, computational effort and flexibility, and its convergence is evaluated by solving several benchmarks. Some restrictions of the classical form of the RMA are pointed out, and it is shown how these can be overcome by adopting the proposed algorithm. Second, the GPA is applied to characterise the mechanical response of a biological tissue that undergoes large deformations and remodelling of its internal structure.

Original languageEnglish (US)
Pages (from-to)502-527
Number of pages26
JournalMathematics and Mechanics of Solids
Issue number3
StatePublished - Mar 1 2017
Externally publishedYes

Bibliographical note

Publisher Copyright:
© SAGE Publications.


  • Finite strain elastoplasticity
  • Generalised Plasticity Algorithm
  • Return Mapping Algorithm

ASJC Scopus subject areas

  • Mathematics(all)
  • Materials Science(all)
  • Mechanics of Materials


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