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Abstract:
We provide an optimization framework that is capable of identifying the material parameters and contact traction field from two measured deformed geometries of a soft body in contact. The novelty of the framework is the idea of parametrizing the missing contact traction field and incorporating it into the inverse+forward hyper-elasticity formulation. We provide the continuum- and finite element formulation of the framework, as well as the direct differentiation method of sensitivity analysis to efficiently obtain necessary gradients for the BFGS optimizer. The correctness of the formulation and the excellent performance of the framework are confirmed by a series of benchmark numerical examples.

Keywords:
Hyper-elasticity, Inverse form, Large strains, Contact, Calibration, Soft bodies

Abstract:
Being able to reposition tumors from prone imaging to supine surgery stances is key for bypassing current invasive marking used for conservative breast surgery. This study aims to demonstrate the feasibility of using Digital Volume Correlation (DVC) to measure the deformation of a female quarter thorax between two different body positioning when subjected to gravity. A segmented multipart mesh (bones, cartilage and tissue) was constructed and a three-step FE-based DVC procedure with heterogeneous elastic regularization was implemented. With the proposed framework, the large displacement field of a hard/soft breast sample was recovered with low registration residuals and small error between the measured and manually determined deformations of phase interfaces. The present study showed the capacity of FE-based DVC to faithfully capture large deformations of hard/soft tissues.

Keywords:
Digital Volume Correlation, Elastic regularization, Hard/soft tissues, Large displacements, Kinematic fields, X-ray tomography