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Numerical calculation of the tangent stiffness matrix in materials modeling
Author(s) -
Meier Felix,
Schwarz Cornelia,
Werner Ewald
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410200
Subject(s) - tangent stiffness matrix , jacobian matrix and determinant , tangent , stiffness , stiffness matrix , matrix (chemical analysis) , direct stiffness method , logarithm , finite element method , mathematics , mathematical analysis , structural engineering , geometry , materials science , engineering , composite material
Abstract The Finite Element Method in the field of materials modeling is closely connected to the tangent stiffness matrix of the constitutive law. This so called Jacobian matrix is required at each time increment and describes the local material behavior. It assigns a stress increment to a strain increment and is of fundamental importance for the numerical determination of the equilibrium state. For increasingly sophisticated material models the tangent stiffness matrix can be derived analytically only with great effort, if at all. Numerical methods are therefore widely used for its calculation. We present our method to calculate the tangent stiffness matrix for the logarithmic strain measure. The approach is compared with other commonly used procedures. A significant increase in accuracy can be achieved with the proposed method. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)