Piezomagnetic #

The piezomagnetic calculation can give you

1. effective stiffness of the system
2. effective permeability of the system
3. effective piezomagnetic of the system
4. strain distribution
5. stress distribution
6. magnetic field distribution
7. magnetization distribution
8. magnetic induction distribution

Equation solved #

The coupled equation of

$\nabla \cdot B = 0$, where $B = \mu_0 \mu_r H + q \sigma$

$\nabla \cdot \sigma = 0$, where $\sigma = C(\epsilon - q^T H)$

• B Magnetic induction
• $\mu_0$ vaccum permeability
• $\mu_r$ relative permeability
• H Magnetic field
• $\sigma$ The stress
• $\epsilon$ The strain
• $q$ Piezomagnetic coefficient
• $q^T$ The transpose of piezomagnetic coefficient, or converse piezomagnetic coefficient

Input options #

The following options are needed for the dielectric calculation.

• input->system The choice of calculation system must be piezomagnetic
• input->external->magneticField External applied electric field (V/m), if you want to calculate the electric field distribution within the composite
  • x Applied magnetic field along x
  • y Applied magnetic field along y
  • z Applied magnetic field along z
• input->external->elastic/type Either stress or strain, this will determine what external constraints are expected.
• input->external->elastic/stress External applied stress constraint, if you want to calculate the stress/strain distribution within the composite
  • tensor11$\sigma_{11}$
  • tensor12$\sigma_{12}$
  • tensor13$\sigma_{13}$
  • tensor22$\sigma_{22}$
  • tensor23$\sigma_{23}$
  • tensor33$\sigma_{33}$
• input->external->elastic/strain External applied strain constraint, if you want to calculate the stress/strain distribution within the composite
  • tensor11$\epsilon_{11}$
  • tensor12$\epsilon_{12}$
  • tensor13$\epsilon_{13}$
  • tensor22$\epsilon_{22}$
  • tensor23$\epsilon_{23}$
  • tensor33$\epsilon_{33}$
• input->solver->ref A property tensor for the reference phase called permeability and a tensor of stiffness are needed. Tensor definition is explained [here]

<system>
    <type>piezomagnetic</type>
    <external>
        <magneticField>
            <x>0</x>
            <y>0</y>
            <z>0.1</z>
        </magneticField>
        <elastic>
            <type>strain</type>
            <strain>
                <tensor11>0.0</tensor11>
                <tensor22>0.0</tensor22>
                <tensor33>0.0</tensor33>
                <tensor23>0.0</tensor23>
                <tensor13>0.001</tensor13>
                <tensor12>0.0</tensor12>
            </strain>
        </elastic>
    </external>
    <solver>
        <ref>
            <tensor>
                <name>permeability</name>
                <rank>2</rank>
                <pointGroup>custom</pointGroup>
                <component>
                    <value>100</value>
                    <index>11</index>
                    <index>22</index>
                    <index>33</index>
                </component>
            </tensor>
            <tensor>
                <pointGroup>Oh</pointGroup>
                <name>stiffness</name>
                <rank>4</rank>
                <component>
                    <value>1000</value>
                    <index>1111</index>
                </component>
                <component>
                    <value>1200</value>
                    <index>1122</index>
                </component>
                <component>
                    <value>1100</value>
                    <index>1212</index>
                </component>
                <component>
                    <value>1100</value>
                    <index>1221</index>
                </component>
            </tensor>
        </ref>
    </solver>
</system>

Output files #

There are a total of 10 possible output files for the piezomagnetic calculation

1. effMagneticPermeability.dat
2. effElasticStiffness.dat
3. effPiezomagnetic.dat
4. avMagneticVariables.dat
5. avElasticVariables.dat
6. magnField.00000000.dat
7. magnetiz.00000000.dat
8. magIndc.00000000.dat
9. stress.00000000.dat
10. strain.00000000.dat