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, u denotes the structural displacement vector, σ is the stress tensor, and fv is an external volume force (such as gravity).
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 σ1 and σ2 represent the stress tensor in Materials 1 and 2, respectively, and n1 is the normal vector pointing out from the domain containing Material 1.