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 NameEnergy Quantity
ALLIE Internal energy, :ALLIE = ALLSE + ALLPD + ALLCD + ALLAE.
ALLKE Kinetic energy, .
ALLVDViscous dissipated energy, .
ALLFD Frictional dissipated energy, .
ALLCDEnergy dissipated by viscoelasticity, .
ALLWK Work of the external forces, .
ALLSE Stored strain energy, .
ALLPD Inelastic dissipated energy, .
ALLAE Artificial strain energy, .
ETOTALEnergy 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 NameWhole Element Energy Quantity
ELSE Elastic strain energy.
ELPD Plastic dissipated energy.
ELCDCreep dissipated energy.
ELVD Viscous dissipated energy.
ELASEArtificial energy = drill energy + hourglass energy.
EKEDENKinetic energy density in the element.
ESEDENElastic strain energy density in the element.
EPDDENPlastic energy density dissipated in the element.
EASEDENArtificial strain energy density in the element.
ECDDENCreep strain energy density dissipated in the element.
EVDDENViscous energy density dissipated in the element.