Geodesic
Mathematical simulation of creep processes in metal patterns made of materials with different extension compression properties
Numerical methods and programming, Tome 9 (2008) no. 3, pp. 346-365.

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An algorithm for numerical solving the problems of creep in metal patterns made of materials with different extension and compression properties has been developed. The spatial discretization of nonlinear equations of solid mechanics is performed by the finite element method. To solve the three-dimensional problems, the 8-node isoparametric finite elements with trilinear approximation of geometrical parameters and displacements with respect to their values at the nodal element points have been used. The spatial discretization of equations is accompanied with the step-by-step procedure of time integration of quasi-static deformation equations with an iterative solution refinement at each discrete instant of time. The algorithm of determining the stress tensor components for defining creep constitutive relations has been presented with allowance for different properties of materials when extending and compressing. This algorithm has been implemented in a new material model of PIONER code and in the crplaw.f subroutine applied for the implementation of new creep models into MSC.Marc 2005 code. The problems of twisting during the creep of metal plates under constant concentrated forces applied at the corner points have been solved. Comparisons of the obtained numerical solutions with data of the full-scale experiments have been worked out. It is shown that the new model of material allows one to achieve a better correspondence of calculations and experimental data as compared to using the standard models of material (having the same properties when extending and compressing) being at hand in material libraries of PIONER and MSC.Marc 2005 codes.
Keywords: mathematical simulation, creep, finite element method. 
@article{VMP_2008_9_3_a14,
     author = {S. N. Korobeinikov and A. I. Oleinikov and B. V. Gorev and K. S. Bormotin},
     title = {Mathematical simulation of creep processes in metal patterns made of materials with different extension compression properties},
     journal = {Numerical methods and programming},
     pages = {346--365},
     publisher = {mathdoc},
     volume = {9},
     number = {3},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2008_9_3_a14/}
}
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S. N. Korobeinikov; A. I. Oleinikov; B. V. Gorev; K. S. Bormotin. Mathematical simulation of creep processes in metal patterns made of materials with different extension compression properties. Numerical methods and programming, Tome 9 (2008) no. 3, pp. 346-365. http://geodesic.mathdoc.fr/item/VMP_2008_9_3_a14/