Statement of energy balance

An energy balance for the entire model can be written as

EI+EV+EF⁢D+EK⁢E+EI⁢H⁢E-EW-EP⁢W-EC⁢W-EM⁢W-EH⁢F=Et⁢o⁢t⁢a⁢l=constant,
where EI is the internal energy, EV is the viscous energy dissipated, EF⁢D is the frictional energy dissipated, EK⁢E is the kinetic energy, EI⁢H⁢E is the internal heat energy, EW is the work done by the externally applied loads, and EP⁢W, EC⁢W, and EM⁢W are the work done by contact penalties, by constraint penalties, and by propelling added mass, respectively. EH⁢F is the external heat energy through external fluxes. The sum of these energy components is Et⁢o⁢t⁢a⁢l, which should be constant. In the numerical model Et⁢o⁢t⁢a⁢l is only approximately constant, generally with an error of less than 1%.

Internal energy

The internal energy is the sum of the recoverable elastic strain energy, EE; the energy dissipated through inelastic processes such as plasticity, EP; the energy dissipated through viscoelasticity or creep, EC⁢D; the artificial strain energy, EA; the energy dissipated through damage, ED⁢M⁢D; the energy dissipated through distortion control, ED⁢C; and the fluid cavity energy, EF⁢C:

EI=EE+EP+EC⁢D+EA+ED⁢M⁢D+ED⁢C+EF⁢C.

The artificial strain energy includes energy stored in hourglass resistances and transverse shear in shell and beam elements. Large values of artificial strain energy indicate that mesh refinement or other changes to the mesh are necessary.

Viscous energy

The viscous energy is the energy dissipated by damping mechanisms, including bulk viscosity damping and material damping. A fundamental variable in the global energy balance, viscous energy is not part of the energy dissipated through viscoelasticity or inelastic processes.

External work of applied forces

The external work is integrated forward continuously, defined entirely by nodal forces (moments) and displacements (rotations). Prescribed boundary conditions also contribute to the external work.