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Embedded regions

Embedded regions couple lower-dimensional guest entities to a continuum host without requiring matching meshes. The coupling geometry and all host interpolation data are constructed from the reference configuration during database completion and remain fixed throughout the analysis.

numgeo provides three distinct embedded-region methods:

Method Guest unknowns Mechanical contribution of guest Coupling concept Typical use
Absorbed eliminated or prescribed from host interpolation none perfect kinematic following passive tracking, measurement lines, geometry carried by the host
Interaction line retained full guest stiffness distributed springs along the beam centreline anchors, nails and very slender inclusions
Interaction surface retained; three translations and three rotations per beam node full guest stiffness distributed tractions on an implicit cylinder and optional base disk piles, pile groups, micropiles, anchors and other circular slender structures for which finite diameter or moment transfer matters

Shared host-search concept

All methods use an inverse isoparametric map to identify a containing host element and evaluate its shape functions. The search procedure is described in Determining host elements.

For interaction-surface regions, the search is performed for every generated shaft and base coupling point, not only for guest nodes. A point outside the declared host region is inactive and its tributary measure is not reassigned.

Reference-configuration coupling

The current implementation is geometrically linear with respect to the embedded coupling:

  • host-element identities and natural coordinates are not updated after database construction;
  • the interaction surface does not re-search the host after large relative motion;
  • material response of the guest and host may nevertheless be nonlinear;
  • explicit dynamic steps are not supported by the interaction methods.

State and convergence

Plastic interface slips and lagged pressure states are trial values during Newton iterations. They are copied to the committed state only after an increment has converged. A rejected increment or cutback therefore restarts from the last accepted embedded-region state.