The bi-potential method has been successfully applied to the modeling of frictional contact problems in static cases. This paper presents an extension of this method for dynamic analysis of impact problems with deformable bodies. A first order algorithm is applied to the numerical integration of the time-discretized equation of motion. Using the Object-Oriented Programming (OOP) techniques in Cþþ and OpenGL graphical support, a finite element code including pre/postprocessor FER/Impact is developed. The numerical results show that, at the present stage of development, this approach is robust and efficient in terms of numerical stability and precision compared with the penalty method.

The present paper is devoted to the modeling of finite deformations of hyperelastic bodies described by the Yeoh model under contact/impact conditions. A total Lagrangian formulation is adopted to describe the geometrically nonlinear behavior. A first order algorithm is applied to integrate the equations of motion. For the finite element implementation, an explicit expression of the tangent operator is derived. Two numerical examples are presented to show the applicability of the developed approach.

have proposed a study of contact problems between Blatz-Ko hyperelastic bodies in static cases using the bi-potential method. The extension of this method for dynamic analysis of impact problems is realized in the present work. The total Lagrangian formulation is adopted to describe large strains and large displacements non-linear behavior. A first order algorithm is applied for the numerical integration of the time-discretized equation of motion. Numerical examples are carried out in two cases: rigid-deformable and deformable-deformable-rigid impacts in 2D. Numerical results show that the proposed approach is robust and efficient and the physical energy dissipation phenomena are apparently illustrated.

International audienceThe bipotential method has been successfully applied for the modelling of frictional contact problems in static cases. This paper presents the application of this method for dynamic analysis of impact problems with friction. Instead of second order algorithms, a first order algorithm is applied for the numerical integration of the time-discretized equation of motion. The numerical results prove that the algorithm preserves quasi perfectly the principle of energy conservation without any regularization. In addition, it is possible to quantify the physical energy dissipation introduced by frictional effects between the solids in contact

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