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

# Content:		This folder contains all data for the Plate-example using elasto-plastic material behaviour.
				
				The quarter of a homogeneous, rectangular thin plate is to be investigated. The plate is subjected
				to a uniformly distributed load p and has dimensions L=B=100 and thickness h=1. 
				A small strain elasto-plastic isotropic material (von Mises plasticity) is used with the following 
				parameters:
						E = 210 0000		nu = 0		fyk=240
						
				The macroscopic plate is discretised using 4x4 elements. The homogeneous RVE representing the mesoscopic
				scale has dimensions lx x ly x h = 1x1x1. 
				
				As a reference yield line theory is employed [2] (reference [179] in thesis) which results in an 
				ultimate load factor lambda = 14.4.
				Furthermore, a shell formulation is used as reference solution [3] (reference [61] in thesis). 
										
				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_7-19.pdf	- Figure 7.19 from [1], illustration of the quarter of the plate including dimensions 
								  and boundary conditions, (b) shows the analytically obtained yield line
				Fig_7-20.pdf 	- Figure 7.20 from [1], comparison of the load factor lambda vs. displacement uz for 
								  reference solutions proposed approach with different boundary conditions and 
								  RVE size 1x1x1
								  
				FE2_pbc.dat		- Data for load factor-displacement curve using proposed homogenisation approach with 
								  periodic boundary conditions (pbc) - RVE size is 1x1x1
				FE2_sbc.dat		- Data for load factor-displacement curve using proposed homogenisation approach with 
								  shell boundary conditions (sbc) - RVE size is 1x1x1
				FE2_tbc.dat		- Data for load factor-displacement curve using proposed homogenisation approach with 
								  traction boundary conditions (tbc) - RVE size is 1x1x1
				Shell_ref.dat	- Data for load factor -displacement curve obtained using the shell element from [3]
				YLT_ref.dat		- Data for analytically obtained load factor using yield line theory [2]
				
				
# 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]		J. Wst and W. Wagner. Systematic prediction of yield-line configurations for arbitrary 
						polygonal plates. Engineering Structures, 30(7):20812093, 2008. 
						DOI: 10.1016/j.engstruct.2008.01.005.
				[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.