@article{DriesWallmerspergerKessler2023, author = {Dries, Fabian W. and Wallmersperger, Thomas and Kessler, J{\"o}rg}, title = {Homogenization of plane ring mesh under static loading}, volume = {23}, pages = {e202300021}, journal = {Proceedings in applied mathematics and mechanics: PAMM}, number = {2}, publisher = {Wiley}, address = {Weinheim}, issn = {1617-7061}, doi = {https://doi.org/10.1002/pamm.202300021}, year = {2023}, abstract = {Plane ring meshes can be produced in large dimensions for various applications, for example, in architecture or protective systems. The numerical simulation of all individual rings of ring meshes is very costly, which is why methods to abstract the structure have been sought in the past. In this paper, a method for determining the strain parameters of a representative ring mesh section under in-plane tensile loads is presented. Methods of rigid body analysis and representative volume elements with periodic boundary conditions are used. Green Lagrangian strain tensors are determined for both an exemplary representative ring mesh section under different tensile load cases and an experimental ring mesh under one load case. The comparison of the Green Lagrangian strain tensors of the ring meshes between numerical simulations and experiments shows a very good agreement.}, language = {en} } @article{DriesWallmerspergerKessler2022, author = {Dries, Fabian W. and Wallmersperger, Thomas and Kessler, J{\"o}rg}, title = {Deformation of planar ring mesh under static in-plane tensile loads}, volume = {234}, journal = {Acta Mechanica}, number = {3}, publisher = {Springer-Verlag GmbH Austria}, address = {Wien}, issn = {1619-6937}, doi = {https://doi.org/10.1007/s00707-022-03393-2}, pages = {959 -- 973}, year = {2022}, abstract = {A ring mesh is a large-scale manufacturable structure with versatile applications in architecture and for protective systems. However, the static and dynamic numerical simulation of a large-scale ring mesh is a resource-intensive task due to the many nonlinear contact points between the individual rings. To characterize the rigid body behavior of the ring mesh, in this paper, a representative volume element is loaded under different in-plane directions. The Green-Lagrangian strain tensor components are obtained as a result. An implicit one-step algorithm is used for this dynamic relaxation issue, modified by the use of stiff springs. Static convergence positions of a representative volume element are determined in several multiaxial tensile directions. The obtained deformation parameters can be used to simulate large deformations of large-scaled ring meshes.}, language = {en} }