Overview of Forces in Continuum Mechanics
The deformation of linear elastic materials subject to external loads is described by Cauchy’s equation:
where ρ is the density, r denotes the position of a point fixed in the material at time t=0, T is the stress tensor, and fext is an external volume force, such as gravity (fext = ρg). If a linear elastic material is added to the Electromechanics interface, this equation is solved in the absence of an electric field.
In the stationary case there is no acceleration, and the equation representing the force balance is
The stress tensor must be continuous across a stationary boundary between two materials. This corresponds to the equation
(5-1)
where T1 and T2 represent the stress tensor in Materials 1 and 2, respectively, and n1 is the normal vector pointing out from the domain containing Material 1.