Extension of the node-to-segment contact element for surface-expansion-dependent contact laws

A class of friction laws depending on the measure of contact surface expansion is defined in the paper within the continuum contact mechanics framework. The nominal and spatial forms of constitutive relations are discussed, including incremental penalty relations. Further, an extended node-to-segment element is derived which is capable of treating surface-expansion-dependent contact laws in a consistent way. The approach is suitable for any kind of node-to-segment contact elements. Finally, the computational efficiency of the extended element as well as other possible approaches are illustrated by numerical examples relevant to metal forming applications.