A bi-potential contact formulation of orthotropic adhesion between soft bodies

An orthotropic adhesion model is proposed based on the bi-potential method to solve adhesive contact problems with orthotropic interface properties between hyperelastic bodies. The model proposes a straightforward description of interface adhesion with orthotropic adhesion stiffness, whose components are conveniently expressed according to the local coordinate system. Based on this description, a set of extended unilateral and tangential contact laws has been formulated. Furthermore, we use an elementwise scalar parameter β to characterize the strength of interface adhesive bonds, and the effects of damage. Therefore, complete cycles of bonding and de-bonding of adhesive links with the account for orthotropic interface effects can be modelled. The proposed model has been tested on cases involving both tangential and unilateral contact kinematics. The test cases allowed emergence of orthotropic interface effects between elastomer bodies involving hyperelasticity. Meanwhile, the model can be implemented with minimum effort, and provides inspiration for the modelling of adhesive interface effects in areas of applications such as biomechanics.