This example solves for the stress and strain of a 2D membrane in 3D space, under incremental Xi(1) displacement, using the exponential strain energy equation detailed in Tong & Fung 1976. See: "The Stress-Strain Relationship for the Skin" J. Biomechanics, Vol 9, 1976. pp 649-657

#Example 513: Membrane deformation using the Tong & Fung skin strain energy function #Deformation of a membrane, using the strain energy equation #for skin detailed in Tong & Fung. #See: # "The Stress-Strain Relationship for the Skin" # P. Tong and Y-C. Fung. # J. Biomechanics, Vol 9, 1976. # pp 649-657 #Define a coordinate system. The problem details a two-dimensional #membrane in 3d space. fem de coor 3,1 #Define four nodes describing the initial #membrane geometry (a square). fem de node;r;skin;example #Define a bilinear basis function. fem de base;r;;example #Define the membrane as one element and assign fibre #information to that element. The fibres are aligned #parallel to Xi(1). fem de elem;r;;example #1 element fem de fibr;r;;example fem de elem;r;;example fibre #Define the problem equations. # Finite elasticity. # Membrane theory. # Incompressible. fem de equa;r;;example #Define the material. #This is default for the first three questions. #The strain enegry question W is an exponential equation. #The Tong & Fung skin function is chosen. #This function has 13 constitutive law parameters which are #taken from the paper by Tong and Fung. #Membrane thickness is taken to be 1. #Gravity is not used and so is set to 0. fem de mate;r;;example #Define the initial and boundary conditions. #No pressure is applied on the Xi(3) faces of the membrane. #Initial displacements are all zero. #In the Xi(1) direction: # Nodes 1 and 3 are tethered with zero displacement. # Nodes 2 and 4 are displaced by 0.1 (giving an extension # ratio of 1.1. #In the Xi(2) direction: # Nodes 1 and 2 are tethered with zero displacement. # Nodes 3 and 4 are allowed to move freely. #There are no constraints on displacement in Xi(3). #There are no force boundary conditions. fem de init;r;;example #Define the solution method. fem de solv;r;;example fem solve #List the solution values fem list node sol fem list strain fem list stress #Loop over the commands below 20 times. The solves the problem #with an incremental increase of 50% of the initial displacement #finishing with an overall extension ration of 2.15. for $M (0..20) { fem solve increment 0.5 error 1.0E-10 fem list node sol fem list strain fem list stress } quit

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example_513.com 05-Dec-2002 2.3k skin.ipbase 05-Dec-2002 1.1k skin.ipelem 05-Dec-2002 393 skin.ipelfb 05-Dec-2002 225 skin.ipequa 02-May-2004 2.4k skin.ipfibr 05-Dec-2002 734 skin.ipinit 05-Dec-2002 1.3k skin.ipmate 13-Oct-2003 5.5k skin.ipnode 05-Dec-2002 1.1k skin.ipsolv 16-Aug-2010 2.3k skin.ipsolv.old 13-Apr-2007 2.2k

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