Interaction

*Embedded region, interaction
<guest element set>, <host element set>, k_t, k_n

or, with a limited skin traction:

*Embedded region, interaction
<guest element set>, <host element set>, k_t, k_n, t_ult

or, with a stress-dependent (Mohr-Coulomb) skin traction:

*Embedded region, interaction, type=Mohr-Coulomb
<guest element set>, <host element set>, k_t, k_n, c, phi, A_s

Upcoming release

The *Embedded region, interaction feature will be available with the upcoming release

This keyword embeds line (guest) elements - truss or beam elements - into a region of continuum (host) elements using the embedded beam approach: in contrast to the absorbed method, the guest elements retain their independent degrees of freedom and interact with the host region through distributed interface springs which are numerically integrated over the embedded length. Typical applications are grouted anchors, soil nails and micro piles.

The keyword can be followed by an arbitrary number of data lines, each defining one interaction between a guest element set and a host element set:

• guest element set: Name of the element set containing the line elements to be embedded. Only elements of shape beam (trusses, beams) are permitted.
• host element set: Name of the element set defining the host region. Only continuum elements (triangular, rectangular, tetrahedral, hexahedral) are considered as potential host elements; other element types contained in the set (e.g. the guest elements themselves in case of an all-inclusive set) are ignored.
• k_t: Axial (tangential) interface stiffness per unit length in F/L², e.g. kN/m/m. Required, k_t > 0.
• k_n: Lateral (normal) interface stiffness per unit length in F/L², e.g. kN/m/m. Required, k_n ≥ 0.
• t_ult: Ultimate axial skin traction per unit length in F/L, e.g. kN/m (optional). If provided and positive, the axial interface traction is limited to \(|t_s| \le t_{ult}\) (elastic - perfectly plastic slider); the plastic slip is stored at the integration points of the guest elements and updated upon convergence of each increment. If omitted (or ≤ 0), the axial interface behaviour is linear elastic.

For type=Mohr-Coulomb, the constant t_ult is replaced by three parameters defining a stress-dependent capacity \(t_{cap}(x) = A_s \cdot \max(c - \sigma_n(x)\tan\varphi,\ 0)\), where \(\sigma_n = \tfrac{1}{2}(\operatorname{tr}\boldsymbol{\sigma} - \boldsymbol{a}\cdot\boldsymbol{\sigma}\cdot\boldsymbol{a})\) is the mean lateral (effective) stress of the host material, mapped from the converged host element stresses onto the anchor (tension-positive; compression increases the capacity, the max-term is the tension cutoff):

• c: Interface cohesion (adhesion) in F/L², e.g. kPa. Required, c ≥ 0 (c and phi must not both be zero).
• phi: Interface friction angle in degrees. Required, 0 ≤ phi < 90.
• A_s: Shear surface per unit anchor length in L, converting the interface stress to a force per unit length. In 3D, \(A_s = \pi D\) with the effective grout body diameter \(D\); in 2D plane strain, the anchor represents a row with out-of-plane spacing \(s\), hence \(A_s = \pi D / s\). Required, A_s > 0.

For the underlying formulation refer to the Theory Manual. Verification examples are provided as benchmarks, in 2D and in 3D, and for the Mohr-Coulomb capacity in a geostatic stress field.

Host element search

A guest element is embedded only if all of its nodes are located inside (or on the boundary of) a host element. Guest elements with at least one node outside the host region are skipped (no interaction forces are generated for them) and reported to the log file. This allows e.g. the free length of an anchor to extend beyond the host region without further measures. If none of the guest elements can be embedded, an error is issued.

Wished-in-place installation

The interface transmits only relative displacements between the guest elements and the surrounding host material. Guest elements activated "wished-in-place" therefore follow the deformation of the host region free of interface forces until relative movement occurs. A typical modelling sequence for a grouted anchor is: assign a very soft (dummy) material to the anchor elements during the initial (geostatic) steps and switch to the real material using *Model change, material in the installation step. No additional measures (reference configurations, stress resets) are required.

Large relative slip does not disengage the interface

The host element and coupling weights are determined once, from the reference configuration, and never re-searched: there is no concept of the guest "leaving" the host in a geometric sense. Large relative displacement (e.g. pulling an anchor most of the way out) is handled entirely by the interface law: the axial traction saturates at t_ult and stays engaged, rather than the coupling being lost. See Behaviour under large relative slip for details.

Mohr-Coulomb capacity update

The capacity is evaluated from the converged host stresses of the previous increment: it is constant within each increment, which preserves the consistent linearisation of the slider (robust Newton convergence), and lags the host stress state by one increment. Since the host element stresses are effective stresses, coupled (u-p) analyses automatically yield an effective-stress friction criterion. The host stress assigned to a guest node is the mean over the integration points of its host element; guest elements should not be larger than the host elements.

Limitations

• The interface geometry (embedded length, axial direction) and the coupling to the host elements are evaluated in the reference configuration. For analyses with large deformations of the host region (nlgeom) the interface does not follow the deformed configuration.

• The lateral stiffness k_n has no capacity limit (no analogue of t_ult): arbitrarily large lateral relative displacement produces an unbounded elastic lateral force. This also holds for type=Mohr-Coulomb, whose capacity applies to the axial direction only.

• *Embedded region, interaction is not available in explicit dynamic steps.

• The plastic slip of the interface (if t_ult is used) is not written to restart files.

• Do not combine *Embedded region, absorbed and *Embedded region, interaction for the same guest elements.