IMPACT OF PRESSURE ON THE DEFORMATION OF BLATZ-KO CYLINDRICAL MATERIAL

Abstract

This paper examines the finite deformation of hollow cylinders made from compressible Blatz-Ko hyperelastic material under internal, external, and combined pressure loading. It derives parametric closedform solutions for radial displacement and stress using the Cauchy stress tensor and equilibrium equations. Materials that can be modeled under Blatz-Ko are polymeric foams, biological materials, industrial or engineering foams. These materials are known for their high porosity, low Poisson's ratio from 0 to 0.3, large volume change, very soft in tension and stiff in compression once cells collapse. The deformation of a hollow cylinder made of Blatz-Ko materials by the use of pressure is considered. The analysis of the deformation resulted in a non-linear second order ordinary differential equation, which sought for parametric method of solutions for the determination of displacement and stresses associated with the deformation at every component of the cylinder and with the help of appropriate boundary conditions, we obtained the constants involved in the solution. From the table of values generated from the solution, we plotted the graphs of the different variables and interpreted the results. For internally pressurized Blatz-Ko material, it was observed that displacement occurs mostly internally at the initial stage of the deformation and slightly small towards the outer surface of the material. For externally pressurized Blatz-Ko material, it was observed that displacement occurs mostly at the outer part of the material, then towards the inner part of the cylinder. This implies that displacement is greater in the direction of stresses, be it internally or externally. The investigations show that external pressure causes more radial displacement on larger volumes than smaller volumes of the same thicknesses and material and thereby having more effect on larger volumes than smaller volumes. This is because the magnitude of the radial displacement is higher in larger volume than in smaller volume.