Identification of mechanical properties of heterogeneous soft bodies using gravity loading

This study investigates the use of multiple gravity‐loaded configurations of a soft heterogeneous body for the identification of its mechanical properties. It is largely motivated by the need for in vivo , non‐invasive determination of the mechanical properties of biological tissue, such as the breast, for the purposes of tracking and predicting tumor locations. In order to validate this approach, experiments were performed on a heterogeneous two‐layered silicone gel cantilever beam, laser scanned in eight different orientations under gravity loading. A finite element model of the beam was constructed and analyzed using non‐linear finite elasticity and a neo‐Hookean stress–strain relationship. The constitutive parameters representing the stiffness of each layer were estimated, using non‐linear optimization techniques, to best fit the laser‐scanned data. Different subsets of the experiments were used for training (parameter fitting), with the remaining experiments being used for validation. In both experimental sets, a cross‐validation study was performed in order to compare and assess the predictive power of the identified parameters. Several determinability criteria were used to assess the objective function in the neighborhood of the identified minimum. We found that individual experiments were not sufficient for reliable parameter identification of heterogeneous soft bodies under gravity loading, but that a small number of gravity‐loaded configurations were sufficient to reliably estimate the parameters within the scale of experimental errors. We also discuss the practical and numerical issues related to both single and multi‐experiment parameter estimation. Copyright © 2011 John Wiley & Sons, Ltd.