document: Energy conservation is critical to ensure stability of a numerical method, especially for contact and collision problems [28,43]. A number of conserving schemes have been developed to ensure energy conservation. These schemes make use of the penalty regulation of normal contact constraint and inherit the conservation property from continuum problems. These conservation schemes can conveniently be combined with the finite element method to simulate frictionless [44] and frictional [43] contact and collision. Hesch and Betsch [45] formulated the node-to-segment contact method and solved large deformation contact problems with the conserving scheme. More recently, an energy and momentum-conserving temporal discretization scheme [46] was developed for adhesive contact problems without considering friction and dissipation. Even though the conserving scheme improves numerical stability, it also inherits from the penalty method the difficulty of having to determine penalty parameters. In order to remove penalty sensitivity, Chawla and Laursen [47] proposed an energy and momentum conserving algorithm, which makes use of Lagrange multipliers instead of penalty parameters.
extractive_keyphrases: adhesive contact problems conservation schemes conserving scheme contact and collision problems continuum problems dissipation energy and momentum conserving algorithm energy conservation finite element method friction large deformation contact problems penalty regulation
abstractive_keyphrases: energy and momentum-conserving temporal discretization scheme node-to-segment contact method simulate frictionless [44] and frictional [43] contact and collision