Obtaining a hyperelastic non-linear orthotropic material model via inverse bubble inflation analysis

Abstract

An inverse bubble inflation test is proposed utilizing full displacement field matching to obtain non-linear material models suitable for the Finite Element (FE) method. In this paper a known non-linear orthotropic material model is assumed as the solution for the inverse method to illustrate the process. A bubble inflation FE analysis is performed with the known material model to determine the load and displacement field from the assumed material. Polynomial surfaces are fit to the nodal displacement values of the FE model, such that the entire displacement field is stored as three unique polynomial surfaces. An error formulation was established to quantify the quality of fit between different bubble inflation displacement fields. Gradient based optimization is used to obtain the assumed material model by matching the full displacement field. The inverse bubble inflation test successful produces a non-linear orthotropic model that is analogous to the assumed non-linear orthotropic material, and thus demonstrates that the inverse bubble inflation analysis would be able to characterize other non-linear orthotropic materials.