Introduction
============

Two distinct solids are said to be in contact when they share a common surface that is part of their border. Treating one-sided contact is to prevent one of the solids from "crossing" the other. Friction characterizes the tangential sliding of one solid with respect to the other. In *Code_Aster*, only Coulomb dry rub is available.

The contact in discrete formulation in*Code_Aster* has the following characteristics:


* The laws of contact and friction are established from quantities that are already discretized: displacements and nodal forces on mesh structures;


* The touch/friction problem is solved by decoupling it from the structural balance problem.



In this document we will present the various ingredients of the problem:


* Description of the laws of contact and friction;


*Geometric pairing: this is the phase where we link a node to another node or a node to a mesh to create a*potential* contact couple, i.e. we identify the degrees of freedom for which we will write discrete relationships of non-penetration;


* Establishing the touch/friction problem;


* Description of the algorithms available to solve the touch/friction problem.

This document is therefore limited to the methods known as GCP, CONTRAINTE and PENALISATION.

The so-called "continuous" formulation (FORMULATION =' CONTINUE 'in DEFI_CONTACT) is the subject of document [:external:ref:`R5.03.52 <R5.03.52>`].

The wording associated with elements XFEM (FORMULATION =' XFEM 'in DEFI_CONTACT) is discussed in [:external:ref:`R5.03.53 <R5.03.53>`].

This document also contains theoretical elements to describe the resolution of general unilateral problems (without pairing such as oozing for example) usable by the keyword FORMULATION =' LIAISON_UNIL '.

.. _RefNumPara__16391_333953971: