Analytical CPP in Rotated Energy-Mapped Stress Space: A Finite-Element Implementation in Mathematica Software
Publication: Journal of Engineering Mechanics
Volume 146, Issue 4
Abstract
This study describes step-by-step analytical closest-point projection (CPP) implicit return mapping solutions for von Mises, Drucker-Prager, and Hyperbolic Drucker-Prager yield surfaces in rotated energy-mapped stress space (REMSS) along with discussion, nonlinear finite-element implementation and examples within the Wolfram Mathematica environment. The CPP in conventional stress space does not give the closest point in the Euclidean norm, but in the energy norm. In REMSS, the correct return trajectory is a closest-point return, allowing the constitutive relations to be simplified and turning the determination of a CPP solution in a systematic task. The obtained finite-element results are in excellent agreement with the analytical solutions.
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Published In
Journal of Engineering Mechanics
Volume 146 • Issue 4 • April 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Feb 21, 2019
Accepted: Sep 11, 2019
Published online: Feb 11, 2020
Published in print: Apr 1, 2020
Discussion open until: Jul 11, 2020
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