A new exact integration method for the Drucker–Prager elastoplastic model with linear isotropic hardening

This paper presents the exact stress solution of the non-associative Drucker–Prager elastoplastic model governed by linear isotropic hardening rule. The stress integration is performed under constant strain-rate assumption and the derived formulas are valid in the setting of small strain elastoplast...

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Bibliographic Details
Published in:International journal of solids and structures 2012, Vol.49 (1), p.170-190
Main Authors: Szabó, László, Kossa, Attila
Format: Article
Language:English
Subjects:
Algorithms
Apexes
Consistent tangent tensor
Drucker–Prager elastoplasticity
Elastoplasticity
Exact sciences and technology
Exact time integration
Fundamental areas of phenomenology (including applications)
Hardening
Inelasticity (thermoplasticity, viscoplasticity...)
Linear isotropic hardening
Mathematical analysis
Mathematical models
Physics
Solid mechanics
Strain
Stresses
Structural and continuum mechanics
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Summary:This paper presents the exact stress solution of the non-associative Drucker–Prager elastoplastic model governed by linear isotropic hardening rule. The stress integration is performed under constant strain-rate assumption and the derived formulas are valid in the setting of small strain elastoplasticity theory. Based on the time-continuous stress solution, a complete discretized stress updating algorithm is also presented providing the solutions for the special cases when the initial stress state is located in the apex and when the increment produces a stress path through the apex. Explicit expression for the algorithmically consistent tangent tensor is also derived. In addition, a fully analytical strain solution is also derived for the stress-driven case using constant stress-rate assumption. In order to get a deeper understanding of the features of these solutions, two numerical test examples are also presented.
ISSN:0020-7683
1879-2146
DOI:10.1016/j.ijsolstr.2011.09.021