Identifying hyperelastic material parameters using force balance and partial displacement data

Abstract

This article presents an inverse method for extracting constitutive parameters in hyperelastic materials from partial field displacement data. The work is motivated by applications in which some displacement data are unavailable or too noisy to use. The method is developed on the basis of finite element force balance, and can be readily interfaced with finite element program. The method is evaluated using simulated displacement data with added noise. Two-dimensional and three-dimensional test problems are introduced to collectively assess the sensitivity to noise level, tolerance to missing data, the feasibility identifying heterogeneous properties using surface data only, and the influence of using local force distribution versus using the force resultant. In addition, a cross-model analysis is conducted in some test problems to evaluate influence of material model. A novel scheme involving deep learning network is introduced to smooth the noised displacement and generate the input displacements for different meshes. The forward displacement computation is carried out only at the finest mesh level. The simulated displacements with added white noised is smoothed, and the ensuing displacement field is evaluated at coarse meshes to generate the input data for the coarse models. The tests showed that, up to 10% noise, method performed satisfactorily and robustly in all cases.