Analytical CPP in Rotated Energy-Mapped Stress Space: A Finite-Element Implementation in Mathematica Software

AbstractThis 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 implementati...

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Bibliographic Details
Published in:Journal of engineering mechanics 2020-04, Vol.146 (4)
Main Author: Cecílio, Diogo L
Format: Article
Language:English
Subjects:
Constitutive relationships
Euclidean geometry
Exact solutions
Mapping
Mathematical analysis
Technical Papers
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Summary:AbstractThis 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.
ISSN:0733-9399
1943-7889
DOI:10.1061/(ASCE)EM.1943-7889.0001737