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Embedded regions

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

numgeo provides three embedded-region methods:

Method Guest unknowns Mechanical contribution Coupling concept Typical use
Absorbed prescribed from host interpolation none perfect kinematic following passive tracking and measurement lines
Interaction line retained full guest stiffness distributed springs along the guest 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 and other circular inclusions for which diameter, moment transfer or circumferential contact matter

Shared host-search concept

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

For an interaction surface, the search is performed for every generated shaft and base coupling point. A point outside the declared host region is inactive and its tributary measure is not reassigned. Guest beam nodes must remain topologically distinct from host continuum nodes, even when they occupy the same coordinates.

Reference-configuration coupling

  • Host-element identities and natural coordinates are not updated after database construction.
  • Material response of the guest and host may be nonlinear, but the embedded geometry is fixed.
  • Interaction-surface points may open and reclose at their fixed associations; finite sliding with repeated contact search is not represented.
  • Explicit dynamic steps are not supported by the interaction methods.

State and convergence

Plastic interface slips, lagged pressure states and base history variables are trial quantities during Newton iterations. They are committed only after convergence. A rejected increment or cutback therefore restarts from the last accepted embedded-region state.