Weeger, Oliver ; Schillinger, Dominik ; Müller, Ralf (2022)
Mixed isogeometric collocation for geometrically exact 3D beams with elasto-visco-plastic material behavior and softening effects.
doi: 10.26083/tuprints-00021123
Artikel, Zweitveröffentlichung, Preprint
Kurzbeschreibung (Abstract)
A geometrically nonlinear, shear-deformable 3D beam formulation with inelastic material behavior and its numerical discretization by a mixed isogeometric collocation method are presented. In particular, the constitutive model captures elasto-visco-plasticity with damage/softening from Mullin's effect, which applies to the modeling of metallic and polymeric materials, e.g., in additive manufacturing applications and meta-materials. The inelastic material behavior is formulated in terms of thermodynamically consistent internal variables for viscoelastic and plastic strains and isotropic and kinematic hardening variables, as well as accompanying evolution equations. A mixed isogeometric collocation method is applied for the discretization of the strong form of the quasi-static nonlinear differential equations. Thus, the displacements of the centerline curve, the cross-section orientations, and the stress resultants (forces and moments) are discretized as B-spline or NURBS curves. The internal variables are defined only locally at the collocation points, and an implicit return-mapping algorithm is employed for their time discretization. The method is verified in comparison to 1D examples as well as reference results for 3D beams. Furthermore, its applicability to the simulation of beam lattice structures subject to large deformations and instabilities is demonstrated.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2022 |
| Autor(en): | Weeger, Oliver ; Schillinger, Dominik ; Müller, Ralf |
| Art des Eintrags: | Zweitveröffentlichung |
| Titel: | Mixed isogeometric collocation for geometrically exact 3D beams with elasto-visco-plastic material behavior and softening effects |
| Sprache: | Englisch |
| Publikationsjahr: | 2022 |
| Kollation: | 25 Seiten |
| DOI: | 10.26083/tuprints-00021123 |
| URL / URN: | https://tuprints.ulb.tu-darmstadt.de/21123 |
| Zugehörige Links: | |
| Herkunft: | Zweitveröffentlichungsservice |
| Kurzbeschreibung (Abstract): | A geometrically nonlinear, shear-deformable 3D beam formulation with inelastic material behavior and its numerical discretization by a mixed isogeometric collocation method are presented. In particular, the constitutive model captures elasto-visco-plasticity with damage/softening from Mullin's effect, which applies to the modeling of metallic and polymeric materials, e.g., in additive manufacturing applications and meta-materials. The inelastic material behavior is formulated in terms of thermodynamically consistent internal variables for viscoelastic and plastic strains and isotropic and kinematic hardening variables, as well as accompanying evolution equations. A mixed isogeometric collocation method is applied for the discretization of the strong form of the quasi-static nonlinear differential equations. Thus, the displacements of the centerline curve, the cross-section orientations, and the stress resultants (forces and moments) are discretized as B-spline or NURBS curves. The internal variables are defined only locally at the collocation points, and an implicit return-mapping algorithm is employed for their time discretization. The method is verified in comparison to 1D examples as well as reference results for 3D beams. Furthermore, its applicability to the simulation of beam lattice structures subject to large deformations and instabilities is demonstrated. |
| Status: | Preprint |
| URN: | urn:nbn:de:tuda-tuprints-211233 |
| Zusätzliche Informationen: | Keywords: Geometrically exact 3D beams, Isogeometric collocation, Mixed methods, Inelastic materials, Elasto-visco-plasticity, Mullin’s effect Graphical Abstract included |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften und Maschinenbau |
| Fachbereich(e)/-gebiet(e): | Studienbereiche 13 Fachbereich Bau- und Umweltingenieurwissenschaften 13 Fachbereich Bau- und Umweltingenieurwissenschaften > Fachgebiete der Mechanik 13 Fachbereich Bau- und Umweltingenieurwissenschaften > Fachgebiete der Mechanik > Fachgebiet Festkörpermechanik 13 Fachbereich Bau- und Umweltingenieurwissenschaften > Fachgebiete der Mechanik > Fachgebiet Kontinuumsmechanik 16 Fachbereich Maschinenbau 16 Fachbereich Maschinenbau > Fachgebiet Cyber-Physische Simulation (CPS) Studienbereiche > Studienbereich Mechanik Studienbereiche > Studienbereich Computational Engineering |
| Hinterlegungsdatum: | 19 Apr 2022 13:20 |
| Letzte Änderung: | 20 Apr 2022 05:21 |
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