Local unloading element process in finite element continuum

A. Yu. Burtsev   ; V. V. Glagolev   ; A. A. Markin

Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 69 (2021), pp. 86-96

Résumé

The subcritical elastoplastic deformation and the fracturing of an element of a finite element continuum in the Ansys Workbench complex are considered. When solving the elastoplastic problem of the subcritical deformation, a finite element with the failure criterion reached is selected. In a pre-fracture state of the element, the nodal forces provided by the interaction with an adjacent element are determined using the Ansys Workbench internal procedure. The following step is the consideration of the varying stress-strain state of the body during the element destruction. The elastoplastic problem is solved in the conditions of simple unloading of the body surface adjacent to the destructible element while maintaining the external load corresponding to the destruction initiation. When implementing the local unloading, a possibility of the new plastic region formation and the partial unloading are studied. As a result, the stress-strain state of the body at the beginning of local unloading is not the same as that at the end of the process. The proposed approach differs from the “element killing” procedure when the element stiffness after the failure criterion reached is assumed to be close to zero. The paper provides solutions to the problems of deformation of elastic and elastoplastic plates with a side cut taking into account their element destruction.

Détail

Keywords: finite element method, finite element removal, Ansys Workbench.

Bibliographie

[1] Zenkevich O., Morgan K., Konechnye elementy i approksimatsii, Mir, M., 1986, 318 pp. | MR

[2] Kuzmichev S. V., Kukushkin S. A., Osipov A. V., “Uprugoe vzaimodeistvie tochechnykh defektov v kristallakh s kubicheskoi simmetriei”, Izv. RAN. MTT, 2013, no. 4, 88–97

[3] Stepanova L. V., “Kompyuternoe modelirovanie protsessov nakopleniya povrezhdenii v tverdykh telakh s treschinami s pomoschyu polzovatelskoi protsedury UMAT vychislitelnogo kompleksa Simulia Abaqus”, Vestnik Permskogo natsionalnogo issledovatelskogo politekhnicheskogo universiteta. Mekhanika, 2018, no. 3, 71–86 | DOI

[4] Afanasev A. A., Gornostaev K. K., Kovalev A. V., Chebotarev A. S., “O mekhanicheskom povedenii uprochnyayuschegosya uprugoplasticheskogo diska pod deistviem istochnika tepla”, Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, 2017, no. 50, 57–66 | DOI

[5] ANSYS. User's Guide, Release 11.0, ANSYS Inc, Pennsylvania, USA, 2006

[6] Abaqus 6.11, User's Manual, Dassault Systemes Simulia Corp., 2011

[7] Park M., Frey K., Simon L., “Modeling and analysis of composite bonded joints”, American Journal of Mechanical and Industrial Engineering, 2:1 (2017), 1–7 | DOI | Zbl

[8] Jain S., Na S. R., Liechti K. M., Bonnecaze R. T., “A cohesive zone model and scaling analysis for mixed-mode interfacial fracture”, International Journal of Solids and Structures, 129 (2017), 167–176 | DOI

[9] de Morais A. B., “Cohesive zone beam modelling of mixed-mode I-II delamination”, Composites Part A: Applied Science and Manufacturing, 64 (2014), 124–131 | DOI

[10] Lee M. J., Cho T. M., Kim W. S., Lee B. C., Lee J. J., “Determination of cohesive parameters for a mixed-mode cohesive zone model”, International Journal of Adhesion and Adhesives, 30:5 (2010), 322–328 | DOI

[11] de Morais A. B., “Simplified cohesive zone analysis of mixed-mode I-II delamination in composite beams”, Polymer Composites, 34:11 (2013), 1901–1911 | DOI

[12] Panettieri E., Fanteria D., Danzi F., “Delaminations growth in compression after impact test simulations: Influence of cohesive elements parameters on numerical results”, Composite Structures, 137 (2016), 140–147 | DOI

[13] Ryzhak E. I., “K voprosu ob osuschestvimosti odnorodnogo zakriticheskogo deformirovaniya pri ispytaniyakh v zhestkoi trekhosnoi mashine”, Izvestiya AN SSSR. Mekhanika tverdogo tela, 1991, no. 1, 111–127

[14] Struzhanov V. V., “Ob odnom podkhode k izucheniyu mekhanizma zarozhdeniya treschin”, Prikladnaya mekhanika i tekhnicheskaya fizika, 1986, no. 6, 118–123

[15] Vasin R. A., Enikeev F. U., Mazurskii M. I., “O materialakh s padayuschei diagrammoi”, Izvestiya Akademii nauk. Mekhanika tverdogo tela, 1995, no. 2, 181–182

[16] Struzhanov V. V., “Opredelenie diagrammy deformirovaniya materiala s padayuschei vetvyu po diagramme krucheniya tsilindricheskogo obraztsa”, Sibirskii zhurnal industrialnoi matematiki, 15:1 (2012), 138–144 | Zbl

[17] Glagolev V. V., Markin A. A., “Ob odnom sposobe opredeleniya svyazei mezhdu kriticheskimi znacheniyami kharakteristik protsessa ustanovivshegosya razdeleniya materiala”, Problemy prochnosti, 2006, no. 2, 47–58

[18] Glagolev V. V., Markin A. A., Fursaev A. A., “Modelirovanie obrazovaniya novykh materialnykh poverkhnostei v protsessakh kogezionnogo razrusheniya kompozita s adgezionnym sloem”, Vestnik Permskogo natsionalnogo issledovatelskogo politekhnicheskogo universiteta. Mekhanika, 2017, no. 2, 45–59 | DOI

[19] Glagolev V. V., Markin A. A., “Model of the discrete destruction process of a solid body”, Journal of Physics, Conference Series, 973 (2018) | DOI