# Name: 		_README.txt fr Ordner "\03_Multiscale\02"

# Content:		This folder contains all data for the "Layered cylindrical shell" multiscale example.
				
				A layered cylindrical composite shell is investigated, following the example in [2]. Three layers with
				transversal isotropic material are investigated, where the layers have equal thicknesses and take the
				angles [90/0/90]. 
				The material properties used are: 
						E1 = 125000		E2 = 7400		G12 = 4800		G23 = 2700		nu12 = 0.34
						
				A quarter of the cylinder is modeled and geometric nonlinearity is considered.
				
				Two reference solutions are used for comparison:
					1) The homogenised solution using a first order homogenisation approach following [2] (reference [62] in thesis)
					2) Using a shell element which accounts for the layers [3] (reference [61] in thesis)
					
				For the shell and periodic boundary conditions (sbc and pbc) the RVE size is chosen to be 
				lx x ly x h = 1x1x1. Because the traction boundary conditions using these RVE dimensions do not yield 
				sufficient results, the in-plane size of the RVE is further increased for this case. 
								
				Abbreviation of the boundary conditions:
				pbc - periodic boundary conditions
				sbc - shell boundary conditions
				tbc - traction boundary conditions
				
				Detailed description may be found in [1].

# Datum:		29.08.2024

# Author:		Leonie Mester

# Files:		Fig_7-17.pdf	- Figure 7.17 from [1], illustration of the cylindrical shell including dimensions 
								  and boundary conditions
				Fig_7-18.pdf 	- Figure 7.18 from [1], comparison of the load-deflection curves for the reference solutions
								  and the solution using the proposed boundary conditions
				FE2_pbc_p-w.dat	- Data for load-displacement curve using proposed homogenisation approach with periodic
								  boundary conditions (pbc) - RVE size is 1x1x1
				FE2_sbc_p-w.dat	- Data for load-displacement curve using proposed homogenisation approach with shell
								  boundary conditions (sbc) - RVE size is 1x1x1
				FE2_tbc_RVE1x1x1_p-w.dat	- Data for load-displacement curve using proposed homogenisation approach with
											  traction boundary conditions (tbc) - RVE size is 1x1x1
				FE2_tbc_RVE2x2x1_p-w.dat	- Data for load-displacement curve using proposed homogenisation approach with
											  traction boundary conditions (tbc) - RVE size is 2x2x1
				FE2_tbc_RVE4x4x1_p-w.dat	- Data for load-displacement curve using proposed homogenisation approach with
											  traction boundary conditions (tbc) - RVE size is 4x4x1
				Gruttmann2013_F-w_ref.dat	- Data for load-displacement curve from reference [2]
				Shell_F-w_ref.dat			- Data for load-displacement curve obtained using the shell element from [3]
				
				
# References:	[1]  	Leonie Mester, Computational Homogenisation and Multiscale Modelling Employing an Image-based
						Approach for the Structural Analysis of Shells, RWTH Aachen, PhD Thesis (2024)
				[2]		F. Gruttmann and W. Wagner. A coupled two-scale shell model with applications to layered structures. 
						International Journal for Numerical Methods in Engineering, 94(13):12331254, 2013. 
						DOI: 10.1002/nme.4496.
				[3]		F. Gruttmann and W. Wagner. Structural analysis of composite laminates using a mixed hybrid 
						shell element. Computational Mechanics, 37(6):479497, 2006. DOI: 10.1007/s00466-005-0730-1.