Embedded Reinforcement
Add an Embedded Reinforcement multiphysics node () to create a coupling where elements from the Truss, Beam, or Membrane interface are embedded in solid elements. The meshes used in the coupled interfaces do not have to coincide; the displacements inside the solid elements at the locations where the nodes of the lower-dimension element are located are automatically identified.
See Embedded Elements in the Structural Mechanics Theory Chapter.
The Embedded Reinforcement node is only available with some COMSOL products (see https://www.comsol.com/products/specifications/)
Coupled Interfaces
Select the Solid interface to couple.
Select the Embedded structure to couple — Truss, Beam, or Membrane.
When coupling the Beam interface to a Solid Mechanics interface, only the displacement degrees of freedom of the beam are constrained.
Connection Settings
Select the Connection type — Rigid, Spring constant per unit length, or Spring constant per unit surface area. The available types of spring connections depend on the selected Embedded Structure interface.
When the Embedded structure is a Beam interface, select whether to Suppress rotation around beam axis or not. The default is to suppress axial rotation, to avoid rigid body rotation around the beam axis.
Rigid Connection
The Rigid connection type couples the selected interfaces using pointwise constraints applied to the selection of the embedded structure. The constraints are only active for the parts of the selection that lies within the solid.
Spring connection
All spring connection types couple the selected interfaces by inserting springs between the Embedded structure and the Solid. The properties of the spring connection are determined by user defined spring constants.
When the Embedded structure is a Truss interface, enter the Axial spring constant ka, and the Transverse spring constant kt. The default unit and expression for the spring constants depend on the Connection type:
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For Spring constant per unit length, the default expression for both ka and kt is 1e3*<tag>.Eequ*<tag>.area/h^2.
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For Spring constant per unit surface area, the default expression for both ka and kt is 1e3*<tag>.Eequ*<tag>.perimeter/h^2.
The variable <tag>.Eequ is a placeholder for the equivalent stiffness of the Truss interface, and <tag>.area and <tag>.perimeter for the cross-sectional area and perimeter, respectively. The multiplier 1e3 can be modified to tune the stiffness of the connection. Both connection types internally use the same formulation, and the spring constant per unit area is converted to a spring constant per unit length.
When the Embedded structure is a Beam interface and Spring constant per unit length is selected, enter the Axial spring constant ka, and two Transverse spring constants in the local coordinate system of the beam, kyl and kzl. The default expression for the spring constants is 1e3*<tag>.Eequ*<tag>.area/h^2.
The variable <tag>.Eequ is a placeholder for the equivalent stiffness of the Beam interface, and <tag>.area for the cross-sectional area. The multiplier 1e3 can be modified to tune the stiffness of the connection.
When the Embedded structure is a Membrane interface and Spring constant per unit surface area is selected, enter the three components of the stiffness vector in the boundary system coordinates, kt1, kt2, and kn. The default expression for each component is 1e5*<tag>.Eequ*<tag>.d/h^2.
The variable <tag>.Eequ is a placeholder for the equivalent stiffness of the Membrane interface, and <tag>.d for the thickness. The multiplier 1e5 can be modified to tune the stiffness of the connection.
Bond Slip Model
When a spring connection type is selected, it is also possible to also include a Bond slip model. By default, a No bond slip model is added. If Friction is selected, it is also possible to model sliding between the Solid and the Embedded Structure.
By selecting Friction, the bond slip behavior of the interface is defined by using a plasticity model. Enter a value for the Cohesion c0 to define the initial resistance to sliding. You can also specify a Hardening model — None, Linear, or User defined.
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For Linear, enter the Hardening coefficient kp. This option defines a linear hardening function kpupe, where upe is the accumulated slip. The current sliding resistance is then c = c0 + kpupe.
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For User defined, enter an expression for the Hardening function ch. The default expression is 0[unit]*<tag>.upe. The unit depends on the Embedded structure interface, and the variable <tag>.upe is the accumulated slip. The current sliding resistance is then c = c0 + ch
The bond slip friction model formally describes the so-called Tresca friction, that is, the sliding resistance does not depend on the normal force acting on the interface between the Solid and the Embedded Structure. However, a Coulomb type friction model can by implemented by adding a dependence with respect to a ‘normal force’ in the expression for the Cohesion c0. The difficulty lies in estimating the normal force
Advanced
To display this section, click the Show More Options button () and select Advanced Physics Option in the Show More Options dialog box.
Enter a scalar positive value in the Extrapolation tolerance; the default is 0.3. This tolerance is used by an internal general extrusion operator that maps expressions from the Solid (source) to the Embedded Structure (destination). If a point of the embedded structure is within a distance of the extrapolation tolerance times the mesh element size, the point is considered to be within the solid. Otherwise, the mapping fails.
Select the Calculate dissipated energy check box as needed to compute the energy dissipated when including a Bond slip model in the connection.
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For more information about coupling different element types, see Coupling Techniques.
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For details about how work with embedded structures, see Modeling Embedded Structures and Reinforcements.
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For details about the formulation of this coupling, see Embedded Elements.