Data for the Assessment of Stress Integration Schemes for Large-Deformation Finite Element Analysis

Files "results_comp_ext_repository.xlsx", "results_ext_rot_repository.xlsx", "results_simple_shear_repository.xlsx", "results_uniaxial_extension_repository.xlsx" gather the results (stress predictions) of four tests, aimed to check stress integration algorithms in four corresponding deformation paths: “extension-compression”, “extension-rotation”, “simple shear”, "uniaxial extension". They are chosen in order to include the most common motions of the structure particles, i.e. relative motions that yield extension, compression and shear combined with possible rigid rotations of the body. Particularly, the rotation motion is simulated in order to test the incremental objectivity or, better, the priority on rigid motion or weak objectivity of the algorithms. The exact analytical solutions of the three tests are known from literature.
In all of the tests, a unit square (1 x 1 m2) with unit thickness undergoes a deformation path under plane stress conditions. It is made of linear elastic material with Young’s modulus E = 1 Pa and Poisson ratio nu = 0. A fixed number of time steps N equal to 50 (the highest employed in the reference papers) is chosen.
The simulated “time” parameter t ranges between 0 and 1 in “extension-compression” as well as “extension-rotation” tests, whereas it raises from 0 to 0.9 in “simple shear” test. Therefore, the corresponding time steps t are equal to 1/50 and 9/500, respectively.
The various simulation models include different stress integration methods labelled as described in the reference research paper [1]. In addition, data for plane elements (PLANE42, PLANE182) of Ansys code are added. The files include a data sheet and a corresponding plot for each category of algorithms (classical update-Lagrange algorithms, CC methods, and commercial software). The data are organized in columns, where stress components are given for each stress update method.
The file "test_Rodriguez.ans" collects the APDL commands required to generate the data for the Ansys plane elements considered.
In the file "cc methods_validation_repository.xlsx" the simple shear test is used in order to validate the methods based on a corotated configuration (CC methods) that use Green-Naghdi and Zaremba-Jaumann objective stress rates. Such validation is cited in the reference article.

[1] F. Stefani, M. Frascio, C. A. Niccolini Marmont Du Haut Champ, Choice of the stress integration scheme for accurate large-deformation finite element analysis, Proc IMechE Part C: J Mechanical Engineering Science, 2023, Vol. 237(17) 3977–3986