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m_elastic

Purpose

Material function for elastic solids and fluids.

Syntax

 mat= m_elastic('default') 
 mat= m_elastic('database name') 
 mat= m_elastic('database -therm name') 
 pl = m_elastic('dbval MatId name');
 pl = m_elastic('dbval -unit TM MatId name');
 pl = m_elastic('dbval -punit TM MatId name');
 pl = m_elastic('dbval -therm MatId name');

Description

This help starts by describing the main commands of m_elastic : Database and Dbval. Materials formats supported by m_elastic are then described.

Database,Dbval] [-unit TY] [,MatiD]] Name

A material property function is expected to store a number of standard materials. See section 7.3 for material property interface.

m_elastic('database Steel') returns a the data structure describing steel.
m_elastic('dbval 100 Steel') only returns the property row.

  % List of materials in data base
  m_elastic info
  % examples of row building and conversion
  pl=m_elastic([100 fe_mat('m_elastic','SI',1) 210e9 .3 7800], ...
    'dbval 101 aluminum', ...
    'dbval 200 lamina .27 3e9 .4 1200 0  790e9 .3 1780 0');
  pl=fe_mat('convert SITM',pl);
  pl=m_elastic(pl,'dbval -unit TM 102 steel')

Command option -unit asks the output to be converted in the desired unit system. Command option -punit tells the function that the provided data is in a desired unit system (and generates the corresponding type). Command option -therm asks to keep thermal data (linear expansion coefficients and reference temperature) if existing.

You can generate orthotropic shell properties using the Dbval 100 lamina VolFrac Ef nu_f rho_f G_f E_m nu_m Rho_m G_m command which gives fiber and matrix characteristics as illustrated above (the volume fraction is that of fiber).

The default material is steel.

To orient fully anisotropic materials, you can use the following command

 % Behavior of a material grain assumed orthotropic
 C11=168.4e9; C12=121.4e9; C44=75.4e9; % GPa
 C=[C11 C12 C12 0 0 0;C12 C11 C12 0 0 0;C12 C12 C11 0 0 0;
   0 0 0 C44 0 0;    0 0 0 0 C44 0;    0 0 0 0 0 C44]; 

 pl=[m_elastic('formulaPlAniso 1',C,basis('bunge',[5.175 1.3071 4.2012]));
     m_elastic('formulaPlAniso 2',C,basis('bunge',[2.9208 1.7377 1.3921]))];

Subtypes

m_elastic supports the following material subtypes

1 : standard isotropic

Standard isotropic materials, see section 6.1.1 and  section 6.1.2, are described by a row of the form

 [MatID   typ   E nu rho G Eta Alpha T0]

with typ an identifier generated with the fe_mat('m_elastic','SI',1) command, E (Young's modulus), ν (Poisson's ratio), ρ (density), G (shear modulus, set to G=E/2(1+ν) if equal to zero). η loss factor for hysteretic damping modeling. α thermal expansion coefficient. T0 reference temperature. G=E/2(1+ν)

By default E and G are interdependent through G=E/2(1+ν). One can thus define either E and G to use this property. If E or G are set to zero they are replaced on the fly by their theoretical expression. Beware that modifying only E or G, either using feutilSetMat or by hand, will not apply modification to the other coefficient. In case where both coefficients are defined, in thus has to modify both values accordingly.

2 : acoustic fluid

Acoustic fluid , see section 6.1.3,are described by a row of the form

 [MatId typ rho C eta R]

with typ an identifier generated with the fe_mat('m_elastic','SI',2) command, ρ (density), C (velocity) and η (loss factor). The bulk modulus is then given by KC2.

For walls with an impedance (see p_solid 3 form 8), the real part of the impedance, which corresponds to a viscous damping on the wall is given by ZC R. If an imaginary part is to be present, one will use ZC R(1+i η). In an acoustic tube the absorbtion factor is given by α=4R/((R+1)2+(Rη)2).

3 : 3-D anisotropic solid

3-D Anisotropic solid, see section 6.1.1, are described by a row of the form

 [MatId typ Gij rho eta A1 A2 A3 A4 A5 A6 T0]

with typ an identifier generated with the fe_mat('m_elastic','SI',3) command, rho (density), eta (loss factor) and Gij a row containing

 [G11 G12 G22 G13 G23 G33 G14 G24 G34 G44 ...
  G15 G25 G35 G45 G55 G16 G26 G36 G46 G56 G66]

Note that shear is ordered gyz, gzx, gxy which may not be the convention of other software.

4 : 2-D anisotropic solid

2-D Anisotropic solid, see section 6.1.2, are described by a row of the form

 [MatId typ E11 E12 E22 E13 E23 E33 rho eta a1 a2 a3 T0]

with typ an identifier generated with the fe_mat('m_elastic','SI',4) command, rho (density), eta (loss factor) and Eij elastic constants and ai anisotropic thermal expansion coefficients.

5 : shell orthotropic material

shell orthotropic material, see section 6.1.4 corresponding to NASTRAN MAT8, are described by a row of the form

 [MatId typ E1 E2 nu12 G12 G1z G2z Rho A1 A2 T0 Xt Xc Yt Yc S Eta ...
   F12 STRN]

with typ an identifier generated with the fe_mat('m_elastic','SI',5) command, rho (density), ... See m_elastic Dbvallamina for building.

6 : Orthotropic material

3-D orthotropic material, see section 6.1.1, are described by a set of engineering constants, in a row of the form

 [MatId typ E1 E2 E3 Nu23 Nu31 Nu12 G23 G31 G12 rho a1 a2 a3 T0 eta]

with typ an identifier generated with the fe_mat('m_elastic','SI',6) command, Ei (Young modulus in each direction), ν ij (Poisson ratio), Gij (shear modulus), rho (density), ai (anisotropic thermal expansion coefficient), T0 (reference temperature), and eta (loss factor). Care must be taken when using these conventions, in particular, it must be noticed that

νji = 
Ej
Ei
 νij     (9.12)

See also

Section 4.5.1, section 7.3, fe_mat, p_shell


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