An implicit finite element method for elastic solids in contact

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Abstract
Focuses on the simulation of mechanical contact between nonlinearly elastic objects such as the components of the human body. The computation of the reaction forces that act on the contact surfaces (contact forces) is the key for designing a reliable contact handling algorithm. In traditional methods, contact forces are often defined as discontinuous functions of deformation, which leads to poor convergence characteristics. This problem becomes especially serious in areas with complicated self contact such as skin folds. We introduce a novel penalty finite element formulation based on the concept of material depth, the distance between a particle inside an object and the object's boundary. By linearly interpolating pre-computed material depths at node points, contact forces can be analytically integrated over contact surfaces without increasing the computational cost. The continuity achieved by this formulation supports an efficient and reliable solution of the nonlinear system. This algorithm is implemented as part of our implicit finite element program for static, quasistatic and dynamic analysis of nonlinear viscoelastic solids. We demonstrate its effectiveness on an animation showing realistic effects such as folding skin and sliding contacts of the tissues involved in knee flexion. The finite element model of the leg and its internal structures was derived from the Visible Human data set.

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