TABLE OF CONTENTS In order to define the LATIN algorithm, we introduce here a convenient manner to describe the finite element model. The considered thermo-mechanical problem involves small strains, small displacements, elasticity, and contact producing thermo-mechanical coupling. Equations are given for each sub-domain ?. Boundary conditions are given for interfaces between a sub-domain ? and a sub-domain ?', and for interfaces between a sub-domain ? and the boundary ?? of the system. A mesh is used to describe the displacement field 
and the temperature field T by introducing matrix of shape functions N U and N T, and Finite Element degrees of freedom 
and 
respectively. The shape functions N U and N T define two subspaces 
and T respectively. We assume that these subspaces are large enough to represent accurately the evolution of the gradients of 
and T. The time interval ]0, t f] is divided into time steps ] t j, t j+ 1]. The forward Euler scheme is used to solve the time differential equations.
Inside each sub-domain ? the following conditions must be satisfied. There are initial conditions for temperatures and stresses ?. Stresses, normal stresses 
over ??, temperatures, heat transfer 
, internal energy e normal heat transfer ? over ?? and heat dissipation r, must satisfy equilibrium conditions at...
