MATPZO

Bulk Data Entry Defines the coupling terms between structural and dielectric materials for defining a piezoelectric coupling.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MATPZO MID PIEZO11 PIEZO12 PIEZO13 PIEZO14 PIEZO15 PIEZO16 FLAG
PIEZO21 PIEZO22 PIEZO23 PIEZO24 PIEZO25 PIEZO26
PIEZO31 PIEZO32 PIEZO33 PIEZO34 PIEZO35 PIEZO36
DAMP DPZO11 DPZO12 DPZO13 DPZO15 DPZO15 DPZO16
DPZO21 DPZO22 DPZO23 DPZO25 DPZO25 DPZO26
DPZO31 DPZO32 DPZO33 DPZO35 DPZO35 DPZO36

Example

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MATPZO 1 0.1 1.5 0.01 STRS
0.01
0.02

Definitions

Field Contents SI Unit Example
MID Unique material identification number.

No default (Integer > 0)
PIEZOij Coupling terms for the piezoelectric material where i and j denote coordinate axes. 1

Default = 0.0 (Real)
FLAG Flag to indicate the form of the coupling terms (PIEZOij).
STRSCHG (Default)
Stress-charge form
STRNCHG
Strain-charge form
DAMP Flag to indicate the damping coefficients for piezoelectric coupling terms.
DPZOij Coupling terms for the piezoelectric damping where i and j denote coordinate axes.

Default = 0.0 (Real)

Comments

  1. Values in PIEZOij and DPZOij can be blank, but at least one non-zero value of PIEZOij and DPZOij must be defined for a MATPZO Bulk Data Entry.
  2. The material identification number can be the shared with structural materials (MAT1, MAT2, MAT8, MAT9 or MGASK), thermal materials (MAT4, MAT5), or electrical materials (MAT1EC, MAT2EC) but must be unique with respect to other dielectric materials (MAT1PT, MAT2PT).
  3. MATPZO is supported for solid elements only.
  4. The formulation is as follows:
    • When FLAG=STRSCHG, the piezoelectric material matrix has the following form:
      c E e T e − ε S MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaafa qabeGacaaabaGaam4yamaaBaaaleaacaWGfbaabeaaaOqaaiaadwga daahaaWcbeqaaiaadsfaaaaakeaacaWGLbaabaGaeyOeI0IaeqyTdu 2aaSbaaSqaaiaadofaaeqaaaaaaOGaay5waiaaw2faaaaa@4063@
      e = e 11 e 12 e 13 e 14 e 15 e 16 e 21 e 22 e 23 e 24 e 25 e 26 e 31 e 32 e 33 e 34 e 35 e 36 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaaca WGLbaacaGLBbGaayzxaaGaeyypa0ZaamWaaeaafaqabeWagaaaaeaa caWGLbWaaSbaaSqaaiaaigdacaaIXaaabeaaaOqaaiaadwgadaWgaa WcbaGaaGymaiaaikdaaeqaaaGcbaGaamyzamaaBaaaleaacaaIXaGa aG4maaqabaaakeaacaWGLbWaaSbaaSqaaiaaigdacaaI0aaabeaaaO qaaiaadwgadaWgaaWcbaGaaGymaiaaiwdaaeqaaaGcbaGaamyzamaa BaaaleaacaaIXaGaaGOnaaqabaaakeaacaWGLbWaaSbaaSqaaiaaik dacaaIXaaabeaaaOqaaiaadwgadaWgaaWcbaGaaGOmaiaaikdaaeqa aaGcbaGaamyzamaaBaaaleaacaaIYaGaaG4maaqabaaakeaacaWGLb WaaSbaaSqaaiaaikdacaaI0aaabeaaaOqaaiaadwgadaWgaaWcbaGa aGOmaiaaiwdaaeqaaaGcbaGaamyzamaaBaaaleaacaaIYaGaaGOnaa qabaaakeaacaWGLbWaaSbaaSqaaiaaiodacaaIXaaabeaaaOqaaiaa dwgadaWgaaWcbaGaaG4maiaaikdaaeqaaaGcbaGaamyzamaaBaaale aacaaIZaGaaG4maaqabaaakeaacaWGLbWaaSbaaSqaaiaaiodacaaI 0aaabeaaaOqaaiaadwgadaWgaaWcbaGaaG4maiaaiwdaaeqaaaGcba GaamyzamaaBaaaleaacaaIZaGaaGOnaaqabaaaaaGccaGLBbGaayzx aaaaaa@6AB5@
    • When FLAG=STRNCHG, the coefficients form the coupling matrix d MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaaca WGKbaacaGLBbGaayzxaaaaaa@38CE@ as:
      d = d 11 d 12 d 13 d 14 d 15 d 16 d 21 d 22 d 23 d 24 d 25 d 26 d 31 d 32 d 33 d 34 d 35 d 36 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaaca WGKbaacaGLBbGaayzxaaGaeyypa0ZaamWaaeaafaqabeWagaaaaeaa caWGKbWaaSbaaSqaaiaaigdacaaIXaaabeaaaOqaaiaadsgadaWgaa WcbaGaaGymaiaaikdaaeqaaaGcbaGaamizamaaBaaaleaacaaIXaGa aG4maaqabaaakeaacaWGKbWaaSbaaSqaaiaaigdacaaI0aaabeaaaO qaaiaadsgadaWgaaWcbaGaaGymaiaaiwdaaeqaaaGcbaGaamizamaa BaaaleaacaaIXaGaaGOnaaqabaaakeaacaWGKbWaaSbaaSqaaiaaik dacaaIXaaabeaaaOqaaiaadsgadaWgaaWcbaGaaGOmaiaaikdaaeqa aaGcbaGaamizamaaBaaaleaacaaIYaGaaG4maaqabaaakeaacaWGKb WaaSbaaSqaaiaaikdacaaI0aaabeaaaOqaaiaadsgadaWgaaWcbaGa aGOmaiaaiwdaaeqaaaGcbaGaamizamaaBaaaleaacaaIYaGaaGOnaa qabaaakeaacaWGKbWaaSbaaSqaaiaaiodacaaIXaaabeaaaOqaaiaa dsgadaWgaaWcbaGaaG4maiaaikdaaeqaaaGcbaGaamizamaaBaaale aacaaIZaGaaG4maaqabaaakeaacaWGKbWaaSbaaSqaaiaaiodacaaI 0aaabeaaaOqaaiaadsgadaWgaaWcbaGaaG4maiaaiwdaaeqaaaGcba GaamizamaaBaaaleaacaaIZaGaaGOnaaqabaaaaaGccaGLBbGaayzx aaaaaa@6AA2@
      The d MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaaca WGKbaacaGLBbGaayzxaaaaaa@38CE@ matrix is converted to the e MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaaca WGLbaacaGLBbGaayzxaaaaaa@38CF@ matrix by:
      e = d c E MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyzaiabg2 da9iaadsgacaWGJbWaaSbaaSqaaiaadweaaeqaaaaa@3AAA@
    Where,
    c E MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4yamaaBa aaleaacaWGfbaabeaaaaa@37D1@
    Elastic material matrix
    ε S MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aaS baaSqaaiaadofaaeqaaaaa@389E@
    Permittivity matrix defined by MAT1PT or MAT2PT
    e i j MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyzamaaBa aaleaacaWGPbGaamOAaaqabaaaaa@38E6@
    Refers to the coupling terms ( P I E Z O i j MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuaiaadM eacaWGfbGaamOwaiaad+eadaWgaaWcbaGaamyAaiaadQgaaeqaaaaa @3C1C@ ) when FLAG=STRSCHG
    d i j MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaWGPbGaamOAaaqabaaaaa@38E5@
    Refers to the coupling terms ( P I E Z O i j MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuaiaadM eacaWGfbGaamOwaiaad+eadaWgaaWcbaGaamyAaiaadQgaaeqaaaaa @3C1C@ ) when FLAG=STRNCHG
  5. For more information, refer to Piezoelectric Analysis in the User Guide.