Advanced Finite Elements The College of （学院先进的有限元素）.pdf

Advanced Finite Elements ME EN 7540 Hyperelastic Circular Plate Spring 2006 This handout shows an example of hyperelastic problem using Neo-Hookean Hyperelastic material constants. The strain energy potential is given by µ 1 2 W (I 1 −3) + (J −1) 2 d where µ is the initial shear modulus, d is material incompressibility, I 1 is the first deviatoric strain invariant, J is the determinant of the elastic deformation gradient. The Neo-Hookean option (TB,HYPER,,,,NEO) represents the simplest form of strain energy potential, and has an applicable strain range of 20-30%. An example input listing showing a typical use of the Neo-Hookean option is presented below. TB,HYPER, 1,,,NEO !Activate Neo-Hookean data table TBDATA,1,0.577148 !Define µ shear modulus TBDATA,2,7.0e-5 !Define incompressibility parameter !(as 2/K, K is the bulk modulus) Example: Hyperelastic Circular Plate A flat circular membrane made of a rubber material is subjected to uniform water pressure. The edges of the membrane are fixed. Determine the response as pressure is increased to 50 psi. Figure 1. Hyperelastic Circular Plate Project Sketch Table 1 Material, geometric and loading properties Material Properties Geometric Properties Loading m = 200 psi R = 7.5 in Pres = 25 psi T = 0.5 in The full circular plate is reduced to a 7.5 degree sector for analysis. The mid-plane of the outer edge of the circle is considered to be fixed. A pressure of 25 psi is applied