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A new path‐following constraint for strain‐softening finite element simulations
Author(s) -
Lorentz E.,
Badel P.
Publication year - 2004
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.971
Subject(s) - softening , constraint (computer aided design) , dissipative system , finite element method , path (computing) , robustness (evolution) , structural engineering , constitutive equation , convergence (economics) , plasticity , mathematics , computer science , materials science , engineering , physics , geometry , composite material , quantum mechanics , economics , gene , programming language , economic growth , biochemistry , statistics , chemistry
The application of strain‐softening constitutive relations to model the failure modes of real‐life structures is faced to numerical difficulties related to instabilities that appear as sharp snap‐backs of the structural response. A path‐following method has to complement the solution algorithm to achieve convergence despite these critical points. Because of the sharpness of the snap‐backs, it is believed essential that the path‐following constraint distinguish between a purely elastic unloading and a dissipative path. For that purpose, a new constraint based on the maximal value of the elastic predictor for the yield function is proposed. As it is highly non linear, a specific solution algorithm is required. The robustness of this constraint is illustrated by three applications: the study of crack propagations by means of a cohesive zone model, the failure of a structure submitted to nonlocal damage and the simulation of a nonlocal strain‐softening plastic specimen. Copyright © 2004 John Wiley & Sons, Ltd.