3.7 Energy balance

Energy output is often an important part of an ABAQUS/Explicit analysis. Comparisons between various energy components can be used to help evaluate whether an analysis is yielding an appropriate response.

3.7.1 Statement of energy balance

An energy balance for the entire model can be written as

where

is the internal energy,

is the viscous energy dissipated,

is the frictional energy dissipated,

is the kinetic energy, and

is the work done by the externally applied loads. The sum of these energy components is

, which should be constant. In the numerical model

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, ; the energy dissipated through inelastic processes such as plasticity, ; the energy dissipated through viscoelasticity or creep, ; and the artificial strain energy, :

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.

3.7.2 Output of the energy balance

Each of the energy quantities can be requested as output and can be plotted as time histories summed over the entire model, particular element sets, individual elements, or as energy density within each element. The variable names associated with the energy quantities summed over the entire model or element sets are as listed in Table 3–2.

Table 3–2 Whole model energy output variables.

Variable Name	Energy Quantity
ALLIE	Internal energy, :ALLIE = ALLSE + ALLPD + ALLCD + ALLAE.
ALLKE	Kinetic energy, .
ALLVD	Viscous dissipated energy, .
ALLFD	Frictional dissipated energy, .
ALLCD	Energy dissipated by viscoelasticity, .
ALLWK	Work of the external forces, .
ALLSE	Stored strain energy, .
ALLPD	Inelastic dissipated energy, .
ALLAE	Artificial strain energy, .
ETOTAL	Energy balance: .

In addition, ABAQUS/Explicit can produce element-level energy output and energy density output, as listed in Table 3–3.

Table 3–3 Whole element energy output variables.

Variable Name	Whole Element Energy Quantity
ELSE	Elastic strain energy.
ELPD	Plastic dissipated energy.
ELCD	Creep dissipated energy.
ELVD	Viscous dissipated energy.
ELASE	Artificial energy = drill energy + hourglass energy.
EKEDEN	Kinetic energy density in the element.
ESEDEN	Elastic strain energy density in the element.
EPDDEN	Plastic energy density dissipated in the element.
EASEDEN	Artificial strain energy density in the element.
ECDDEN	Creep strain energy density dissipated in the element.
EVDDEN	Viscous energy density dissipated in the element.