Direct material property determination: One‐dimensional formulation utilising full‐field deformation measurements

Abstract

A direct approach is described to determine the elastic modulus distribution in a nominally heterogeneous material subject to tensile/compression loading and primarily experiencing deformations in the axial direction. The formulation is developed for uniaxial applications using basic theoretical constructs, resulting in a computational framework that has a matrix form [A] {E} = {R}, where the [A] matrix components are known functions of measured axial strains and axial positions, {R} components are known functions of axial body forces, applied loads and reactions and {E} components are the unknown elastic moduli at discrete locations along the length of the specimen. For a series of one‐dimensional (1D) material property identification procedure with known axial strains at discrete locations and various levels of random noise, results are presented to demonstrate the accuracy and noise sensitivity of the methodology. Finally, experimental measurements for a heterogeneous bone specimen are compared to our 1D model predictions, demonstrating that the predictions are in very good agreement with independent estimates at each load level of interest along the length of the bone specimen.