On the integration schemes for Drucker-Prager's elastoplastic models based on exponential maps

• Published in: International journal for numerical methods in engineering 2008-04, Vol.74 (5), p.799-826
• Main Authors: Rezaiee-Pajand, M., Nasirai, Cyrus
• Format: Article
• Language: English
• Subjects: augmented stress vector; Computational techniques; Drucker-Prager; Exact sciences and technology; exponential maps; Fundamental areas of phenomenology (including applications); Inelasticity (thermoplasticity, viscoplasticity...); integrating factor; Mathematical methods in physics; numerical integration; Physics; Solid mechanics; Structural and continuum mechanics
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.2178

Rate plasticity equations for the case of Drucker–Prager's model in small strain regime are considered. By defining an augmented stress vector, the formulations convert the original problem into a quasi‐linear differential equation system. Two new exponential mapping schemes for integrating model equations are proposed. In addition, two traditional schemes for solving the dynamical system in an explicit manner are discussed. The two semi‐implicit schemes developed pose higher accuracy and better convergency. Error contours are provided for all four methods to display the accuracy of each scheme. In order to compare the results, these contours for the classical one‐step backward Euler integration method are also displayed. Accuracy and efficiency along with the rate of convergency of the existing and the proposed methods are examined by numerical examples. Copyright © 2007 John Wiley & Sons, Ltd.