Electrostriction
The Electrostriction multiphysics node () passes the electric polarization contribution to strain from Electrostatics interface to Solid Mechanics interface. In contrast to linear piezoelectricity, the electrostrictive strain is quadratic in polarization.
It also passes the mechanical stress contribution to polarization from Solid Mechanics interface to Electrostatics interface, which is called the inverse electrostrictive effect.
Settings
The Label is the multiphysics coupling feature name. The default Label (for the first multiphysics coupling feature in the model) is Electrostriction 1.
The Name is used primarily as a scope prefix for variables defined by the coupling node. Refer to such variables in expressions using the pattern <name>.<variable_name>. In order to distinguish between variables belonging to different coupling nodes or physics interfaces, the name string must be unique. Only letters, numbers, and underscores (_) are permitted in the Name field. The first character must be a letter.
The default Name (for the first multiphysics coupling feature in the model) is efe1.
Coupled Interfaces
This section defines the physics involved in the Electrostriction multiphysics coupling. The Solid mechanics and Electrostatics lists include all applicable physics interfaces.
The default values depend on how the Electrostriction node is created.
•
If it is added from the Physics ribbon (Windows users), Physics contextual toolbar (macOS and Linux users), or context menu (all users), then the first physics interface of each type in the component is selected as the default.
•
If it is added automatically when either Electrostriction or Ferroelectroelasticity multiphysics interface has been selected in the Model Wizard or Add Physics window, then the participating Solid Mechanics and Electrostatics interfaces are selected.
You can also select None from either list to uncouple the Electrostriction node from a physics interface. If the physics interface is removed from the Model Builder, for example Solid Mechanics is deleted, then the list defaults to None as there is nothing to couple to.
If a physics interface is deleted and then added to the model again, then in order to reestablish the coupling, you need to choose the physics interface again from the lists. This is applicable to all multiphysics coupling nodes that would normally default to the once present interface. See Multiphysics Modeling Workflow in the COMSOL Multiphysics Reference Manual.
Domain Selection
The domain selection is set by default to all domains, so that all applicable domains are selected automatically. Such domains represent an intersection of the applicable domains under the corresponding Electrostatics and Solid Mechanics interfaces selected in the coupling feature.
In Electrostatics interface, the following two domains are applicable:
•
 Charge Conservation, if its material type input is set to Solid. Use this domain feature for solid dielectric materials, for which a linear dependency can be assumed for the electric polarization with respect to the applied electric field.
•
 Charge Conservation, Ferroelectric. Use this domain feature for solid ferroelectric or nonlinear piezoelectric materials.
In the Solid Mechanics interface, the following domain material feature are applicable:
•
 Linear Elastic Material
•
 Nonlinear Elastic Material (with the Nonlinear Structural Materials Module)
•
 Hyperelastic Material (with the Nonlinear Structural Materials Module).
For nonsolid dielectric domains, remove them from the Solid Mechanics interface selection but keep them selected in the Electrostatics interface selection.
Coupling Type
From the list, choose one of these coupling types:
•
 Polarization contribution to strain (the default) also known as direct electrostrictive effect, include only the deformation of the material caused by its polarization in response to the applied electric field.
•
 Stress contribution to polarization, also known as inverse electrostrictive effect, to include only the change in the material polarization as a result of applied mechanical stress or strain.
•
 Fully coupled to include both the direct and inverse electrostrictive effects.
Electrostriction
From the list, choose one of these forms for the electrostrictive strain tensor:
•
 Quadratic (default)
•
 Quadratic, deviatoric. Use this form if the solid deformation due to the electrostrictive effect is volume-preserving.
•
 User defined. Any valid expression can be entered for the electrostrictive strain tensor components. It is recommended to use coupling feature scoped variables for the polarization components, for example: efe1.PX.
When the Electrostrictive strain tensor is set to Quadratic, one of the following options can be selected from the Material symmetry drop down menu:
•
 Isotropic (default)
•
 Cubic crystal
•
 Anisotropic
For Anisotropic choice, component of a 6x6 symmetric electrostrictive coupling matrix can be entered using either Voigt (default) or Standard option for the Material data ordering.
For Cubic crystal choice, only three independent components of the electrostrictive coupling matrix need to be entered.
For Isotropic choice, you can enter two independent components of the electrostrictive coupling matrix using either Q-matrix (default) or M-matrix notations. Alternatively, you can enter values for the Electrostrictive constant a1 and Electrostrictive constant a2 (SI units: F/m) using the definitions according to either Ref. 1 or Ref. 2.
You can neglect the terms quadratic in the reversible polarization components in the expression for the electrostrictive strain by checking the check box Small reversible polarization. This functionality is applicable only when this coupling node is used as a part of either Ferroelectroelasticity or Electrostriction multiphysics interface, and the corresponding Electrostatics interface is configured for hysteresis modeling.
When the Electrostrictive strain tensor is set to Quadratic, deviatoric, the material is assumed to be isotropic, and you can enter the saturation electrostriction and polarization.
If this coupling node is used as a part of Ferroelectroelasticity multiphysics interface, the Charge conservation, Ferroelectric feature under the corresponding Electrostatics interface also contains an input for the saturation polarization. That input will then become inaccessible (grayed out), and the value entered at this coupling node will be used in all computations.
References
1. J.A. Stratton, Electromagnetic Theory, Cambridge, MA, 1941.
2. L.D. Landau and E.M. Lifshitz, Electrodynamics of Continuous Media, Pergamon Press, pp. 69–73, 1960.