Constraint-Based Contact Analysis between Deformable Objects

The key to the successful simulation of deformable objects is to model the realistic behavior of deformation when they are influenced by intricate contact conditions and geometric constraints. This paper describes constraint-based contact modeling between deformable objects using a nonlinear finite element method. In contrast to the penalty force based approaches, constraint-based enforcement of contact provide accuracy and freedom from finding proper penalty coefficients. This paper is focused on determining contact regions and calculating reaction forces at appropriate nodes and elements within the contact regions. The displacement and deformation of all nodes are dynamically updated based on the contact reaction forces. Our constraint based contact force computation method guarantees tight error bound at the contact regions and maintains hard constraints without overshoot or oscillation at the boundaries. In addition, the proposed method doesn't require us to choose proper penalty coefficients, thus greater numerical stability can be achieved and generally large integration steps can be utilized for the ODE solver. Contact conditions are formulated as nonlinear equality and inequality constraints and the force computation is cast into a nonlinear optimization problem. Our rigidto-deformable and deformable-to-deformable contact simulation demonstrates that the non-penetration constraints are well maintained.