Energy Balance in Composite Explicit Analysis

What Is It?

Energy balance in explicit dynamic analysis is the accounting of the various energy components that make up the total energy of the system during a transient simulation. In a composite damage analysis using explicit time integration (e.g. for impact, crash or high-rate loading), the energy is distributed among kinetic energy, internal energy (elastic strain plus damage dissipation), contact energy, artificial energy (hourglass control) and other components. Monitoring the energy balance is a key diagnostic — it confirms that the analysis is behaving physically and that no energy is being created or lost non-physically.

Why It Matters

The energy balance is the primary check on the physical validity of an explicit analysis. If energy is not conserved — if the total energy increases without external work, or if a component dominates unexpectedly — the analysis has a numerical problem that may invalidate the results. For composite damage analysis, the energy balance also provides insight into the damage process: the damage energy component shows how much energy is dissipated by damage, and the ratio of damage energy to total energy indicates how much of the impact energy goes into damaging the structure versus kinetic or elastic response.

The energy balance is the primary physical validity check for explicit analysis. If energy is not conserved, the analysis has a numerical problem. Monitor all components and interpret them physically — not against arbitrary universal thresholds.

Energy Components

The total energy in an explicit analysis is the sum of several components. Each component has a physical meaning, and their relative magnitudes depend on the loading, the structure and the analysis parameters. Understanding each component is essential for interpreting the energy balance correctly.

Kinetic Energy

Kinetic energy is the energy of mass in motion. In an impact analysis, the kinetic energy starts high (the impactor has velocity) and decreases as the energy transfers to the structure — into internal energy (deformation and damage) and back into kinetic energy (rebound). The kinetic energy history shows how quickly the impact energy is absorbed. In a quasi-static analysis performed with explicit dynamics (mass scaling), the kinetic energy should be small relative to the internal energy — if it is not, the analysis is not quasi-static and the results may be dynamic, not static.

• Kinetic energy = ½ × m × v² for each element, summed over the model
• In impact: starts high (impactor velocity), decreases as energy transfers to structure
• In quasi-static explicit: should be small relative to internal energy — otherwise not quasi-static
• KE history shows the rate of energy absorption — useful for interpreting the impact event
• Excessive KE in a quasi-static analysis indicates the mass scaling or loading rate is too aggressive

Internal Energy

Internal energy is the energy stored and dissipated in the material. It has two parts: the elastic strain energy (recoverable) and the dissipated energy from damage or plasticity (non-recoverable). In a composite damage analysis, the internal energy increases as the structure deforms elastically, then increases further as damage dissipates energy. The damage energy component — the part of internal energy dissipated by the damage evolution — is a key indicator of how much damage has occurred and how much energy the damage process has absorbed.

Internal energy decomposition:

IE = IE_elastic + IE_dissipated

IE_elastic  = recoverable elastic strain energy
IE_dissipated = energy dissipated by damage

For damage evolution:
  IE_dissipated = ∫ σ dε_damage  (over the damage process)

For fracture-energy-based evolution:
  IE_dissipated → G_c × A_crack  (as damage completes)

where A_crack = crack area created.

The damage energy is the portion of
IE that has been dissipated — it is
physically the fracture energy times
the crack area.

Contact Energy

Contact energy is the energy dissipated at contact interfaces. In an impact analysis, contact occurs between the impactor and the target, and potentially between delaminated plies (self-contact). The contact energy should be physical — it represents the energy absorbed by the contact process. If the contact energy is excessively large or negative, it may indicate a contact formulation problem (penetration, over-closure, unstable contact). The contact energy should be monitored and interpreted physically — it should be consistent with the contact behaviour expected for the impact scenario.

Contact energy should be physical — consistent with the expected contact behaviour. Excessively large or negative contact energy may indicate a contact formulation problem. Monitor and interpret physically, not just numerically.

Artificial Energy

Artificial energy is the energy introduced by hourglass control or artificial viscosity in reduced-integration elements. It is a numerical artefact — not a physical energy. The purpose is to prevent zero-energy modes (hourglassing) that can destabilise the analysis. Ideally, the artificial energy should be small relative to the total energy. If the artificial energy is large, it indicates that hourglassing is significant — the mesh, the element formulation or the loading may need to be adjusted. Large artificial energy means the analysis is being controlled by numerical artefacts, not by the physics.

• Artificial energy = energy from hourglass control / artificial viscosity — a numerical artefact
• Should be small relative to total energy — large values indicate hourglassing
• If large: check element formulation (switch to enhanced strain or non-reduced integration)
• Check mesh quality — distorted elements are more prone to hourglassing
• Check loading rate — too-fast loading can excite hourglass modes
• Artificial energy is not physical — it should not be a major part of the energy balance

Damage Energy

Damage energy is the portion of the internal energy that has been dissipated by the damage evolution process. It represents the energy that has gone into creating fracture surfaces — intralaminar cracks and delaminations. For a fracture-energy-based damage model, the damage energy should equal the fracture energy times the crack area created. Monitoring the damage energy shows how the damage progresses over time — when it initiates, how fast it grows and how much energy is absorbed by damage versus elastic deformation. The damage energy is a key output for interpreting the physical damage process.

Damage energy = energy dissipated by damage evolution = fracture energy × crack area (for G_c-based models). It shows how much energy goes into creating damage. Monitor it to understand the damage progression and the energy absorption mechanism.

Interpreting the Energy Balance

The energy balance is interpreted by examining the components and their evolution over time, in the context of the specific analysis. The key checks are: (1) total energy should equal external work (energy conservation), (2) no component should dominate unexpectedly, (3) artificial energy should be small, (4) the damage energy should be consistent with the observed damage, and (5) for quasi-static analyses, kinetic energy should be small. The interpretation must be specific to the analysis — the expected energy distribution depends on the loading, the structure and the material.

Do NOT set universal numerical acceptance percentages for energy balance components. The acceptable ratio of artificial energy, kinetic energy or contact energy to total energy depends on the specific analysis — the loading, structure, material and analysis parameters. Interpret the energy balance in the context of the specific problem, not against arbitrary universal thresholds.

Energy Balance Checks

Rather than universal thresholds, the energy balance should be checked against problem-specific criteria. The checks should confirm physical behaviour and identify numerical problems, using the specific context of the analysis to determine what is acceptable.

Key Takeaways

• Energy balance is the primary physical validity check for explicit dynamic composite damage analysis
• Components: kinetic, internal (elastic + damage), contact, artificial, frictional — each has a physical meaning
• Kinetic energy: high in impact, should be small in quasi-static explicit
• Internal energy: elastic strain + damage dissipation — damage energy = fracture energy × crack area
• Contact energy: should be physical — large or negative values indicate contact problems
• Artificial energy: numerical artefact — should be small; large values indicate hourglassing
• Do NOT set universal numerical acceptance percentages — interpret in the context of the specific analysis
• Check: conservation, artificial ratio, quasi-static KE, contact sign/magnitude, damage consistency, spikes