ProductsAbaqus/StandardAbaqus/CAE Piezoelectric responseThe electrical response of a piezoelectric material is assumed to be made up of piezoelectric and dielectric effects: where
Defining piezoelectric and dielectric properties is discussed in Piezoelectric behavior. The theoretical basis of the piezoelectric analysis capability in Abaqus is defined in Piezoelectric analysis. Procedures available for piezoelectric analysisPiezoelectric analysis can be carried out with the following procedures: Initial conditionsInitial conditions of piezoelectric quantities cannot be specified. See Initial conditions in Abaqus/Standard and Abaqus/Explicit for a description of the initial conditions that can be applied in static or dynamic procedures. Boundary conditionsThe electric potential at a node (degree of freedom 9) can be prescribed using a boundary condition (see Boundary conditions in Abaqus/Standard and Abaqus/Explicit). Displacement and rotation degrees of freedom can also be prescribed by using boundary conditions as described in the relevant static and dynamic analysis procedure sections. See Boundary conditions in Abaqus/Standard and Abaqus/Explicit. Boundary conditions can be prescribed as functions of time by referring to amplitude curves (Amplitude Curves). In an eigenfrequency extraction step (Natural frequency extraction ) involving piezoelectric elements, the electric potential degree of freedom must be constrained at least at one node to remove singularities from the dielectric part of the element operator. LoadsBoth mechanical and electrical loads can be applied in a piezoelectric analysis. Applying mechanical loadsThe following types of mechanical loads can be prescribed in a piezoelectric analysis:
Applying electrical loadsThe following types of electrical loads can be prescribed, as described in Electromagnetic loads:
Loading in mode-based and subspace-based proceduresElectrical charge loads should be used only in conjunction with residual modes in the eigenvalue extraction step, due to the “massless” mode effect. Since the electrical potential degrees of freedom do not have any associated mass, these degrees of freedom are essentially eliminated (similar to Guyan reduction or mass condensation) during the eigenvalue extraction. The residual modes represent the static response corresponding to the electrical charge loads, which will adequately represent the potential degree of freedom in the eigenspace. Predefined fieldsThe following predefined fields can be specified in a piezoelectric analysis, as described in Predefined Fields:
Material optionsThe piezoelectric coupling matrix and the dielectric matrix are specified as part of the material definition for piezoelectric materials, as described in Piezoelectric behavior. They are relevant only when the material definition is used with coupled piezoelectric elements. The mechanical behavior of the material can include linear elasticity only (Linear elastic behavior). ElementsPiezoelectric elements must be used in a piezoelectric analysis (see Choosing the appropriate element for an analysis type). The electric potential, , is degree of freedom 9 at each node of these elements. In addition, regular stress/displacement elements can be used in parts of the model where piezoelectric effects do not need to be considered. OutputThe following output variables are applicable to the electrical solution in a piezoelectric analysis: Element integration point variables:
Whole element variables:
Nodal variables:
LimitationsAbaqus does not account for piezoelectric effects in the total energy balance equation, which can lead to an apparent imbalance of the total energy of the model in some situations. For example, if a piezoelectric truss is fixed at one end point and subjected to a potential difference between its two end points, it deforms due to the piezoelectric effect. Subsequently if the truss is held fixed in this deformed configuration and the potential difference removed, strain energy will be generated due to the constraints. This results in an equivalent increase in the total energy of the model. Input file templateHEADING … MATERIAL, NAME=matl ELASTIC Data lines to define linear elasticity PIEZOELECTRIC Data lines to define piezoelectric behavior DIELECTRIC Data lines to define dielectric behavior … AMPLITUDE, NAME=name Data lines to define amplitude curve for defining concentrated electric charge ** STEP, (optionally NLGEOM) STATIC ** or DYNAMIC, FREQUENCY, MODAL DYNAMIC, ** STEADY STATE DYNAMICS (, DIRECT or , SUBSPACE PROJECTION) BOUNDARY Data lines to define boundary conditions on electrical potential and displacement (rotation) degrees of freedom CECHARGE, AMPLITUDE=name Data lines to define time-dependent concentrated electric charges DECHARGE and/or DSECHARGE Data lines to define distributed electric charges CLOAD and/or DLOAD and/or DSLOAD Data lines to define mechanical loading END STEP |