A finite strain gradient theory for viscoplasticity by means of micromorphic regularization. Issue 1 (24th March 2023)

• Record Type: Journal Article
• Authors: Hamdoun, Ayoub; Mahnken, Rolf
• Other Names: Böhm Ch. guestEditor.; Mang K. guestEditor.; Markert B. guestEditor.; Reese S. guestEditor.; Schmidtchen M. guestEditor.; Waimann J. guestEditor.; Kaliske M. editorInChief.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 22:Issue 1(2023)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2023-03-24
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.202200074
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: Stretching of polycarbonate films leads to the formation of shear bands in the necking zone [1]. Standard viscoplastic material models render mesh size dependent results, which requires a mathematical regularization. To this end, we present a finite strain gradient theory for a viscoplastic, isotropic material model where we extend the model presented in [2] to a micromorphic model by introducing a new micromorphic variable as an additional degree of freedom with its first gradient [3, 4]. The variable here has the meaning of a micro plastic strain, and is coupled with the macro plastic by a micro penalty term, forcing the macro‐plastic strain to be close to the micro‐plastic strain for the targeted shear band regularization effect. We have implemented the model equations as a three dimensional initial boundary value problem in an in house FE‐tool, to simulate different geometries with different thickness and to compare it the experimental tests. The analysis is performed for a uniaxial tensile geometry as well as for a biaxial tensile geometry. The numerical examples show the ability of the model to regularize the shear bands and solve the problem of localization.