An unphysical force that appears near coupling interfaces or coarse–fine model boundaries in multiscale, atomistic–continuum, or heterogeneous discretizations, produced by inconsistent inter-model force transfer or incompatible energy representations.

Principle

Occur when the coupling scheme does not preserve mechanical equilibrium across the interface at the discrete level, so imbalance terms act as spurious body or interface forces that perturb atoms or nodes adjacent to the coupling zone.

Demonstration

In a concurrent atomistic-to-continuum simulation, naive blending of atomistic and continuum forces can produce a residual force on atoms near the hand-shake region that drives nonphysical displacements and alters stress fields.

Misapplication

Attributing observed microstructural changes exclusively to material physics without checking for ghost forces can lead to false material response conclusions and incorrect parameter identification.

Consequence

Ghost forces distort local deformation, stress, and energy distributions near interfaces, can nucleate spurious defects or waves, and degrade the accuracy and predictive power of multiscale simulations if untreated.

Reversal

A correct, physically motivated coupling yields vanishing artificial forces in the continuum limit and preserves equilibrium across scales; the absence of residual interfacial forces under refinement distinguishes faithful coupling from ghost-force-afflicted schemes.

Boundary

Refers specifically to numerical or modeling interfaces (multiscale hand-shake regions, mesh transition zones, domain decomposition interfaces); does not describe genuine interfacial physics such as surface forces arising from chemistry or external fields.

Semantic Tension

Related to interface consistency and patch-test concepts; can be conflated with discretization error or projection error, but ghost forces specifically denote persistent spurious interfacial forces arising from coupling inconsistencies rather than benign truncation error.

Synthesis

A ghost force is a numerically induced, nonphysical interface force produced by inconsistent coupling between models or discretizations; eliminating it requires designing coupling operators that exactly balance forces and energies at the discrete interface.