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Complex‐Step Derivative Approximation Schemes for the Robust Calculation of Numerical Constitutive Tangent Moduli
Author(s) -
Tanaka Masato,
Fujikawa Masaki,
Balzani Daniel,
Schröder Jörg
Publication year - 2013
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201310079
Subject(s) - tangent , moduli , tangent modulus , scheme (mathematics) , tensor (intrinsic definition) , tangent vector , mathematics , tangent stiffness matrix , derivative (finance) , mathematical analysis , modulus , geometry , physics , finite element method , engineering , structural engineering , stiffness matrix , quantum mechanics , financial economics , economics
Many material models lead to complicated formulations of the exact consistent tangent modulus tensor and therefore its derivation and implementation might be elaborate. In this case numerical approximations of the moduli can provide an alternative in particular for scientific development purposes. Here, a robust numerical approximation of the tangent modulus tensor that can be implemented within FE‐software is proposed using an innovative numerical derivative scheme. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)