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Determination of the effective 2D material stiffness matrix using ABAQUS
Author(s) -
Horn Tobias Daniel,
Bartelt Matthias,
Wulf Hans,
Ihlemann Jörn
Publication year - 2021
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.202000299
Subject(s) - stiffness , direct stiffness method , stiffness matrix , homogenization (climate) , matrix (chemical analysis) , structural engineering , scale (ratio) , materials science , composite material , engineering , physics , biodiversity , ecology , quantum mechanics , biology
A cross‐scale homogenization approach for multi‐phase materials is to calculate an effective material stiffness in the smaller scale for the multiple states. These detailed results are used to identify a calculation rule for the effective material stiffness in the larger scale. The calculation of the stiffness matrix using ABAQUS for 3D finite elements was already described by [1]. This can be transferred to the calculation of the 2D stiffness matrix in ℝ 3×3 without much effort. However, some 2D elements in ABAQUS require the specification of a matrix in ℝ 4×4 . In this article, the methods for calculating this type of stiffness matrix in 2D are presented.