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Incremental kinematics for finite element applications
Author(s) -
Rashid M. M.
Publication year - 1993
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.1620362302
Subject(s) - objectivity (philosophy) , kinematics , finite element method , algorithm , rotation (mathematics) , computer science , tensor (intrinsic definition) , compatibility (geochemistry) , mathematics , geometry , artificial intelligence , classical mechanics , engineering , physics , structural engineering , philosophy , epistemology , chemical engineering
A kinematical algorithm is proposed in which the input is the incremental deformation gradient corresponding to an increment in motion for a time step, and the output is a constant rate‐of‐stretching tensor and a rotation tensor. The concept of algorithmic objectivity is discussed, with a stronger statement of objectivity than those advanced in previous works being set forth. The importance of strong objectivity is illustrated for applications in which moderately large rotation increments are to be expected. Accuracy of the proposed algorithm is discussed and illustrated with example calculations, and it is shown that the accuracy of the algorithm may be extended to arbitrary order. Also, the computational effort associated with the proposed algorithm is seen to compare favourably to that of other algorithms.