Representing viscoelastic materials

SDT-visc Contents Functions

4.2 Representing viscoelastic materials

4.2.1 Introducing your own nomograms

You can introduce your own nomograms in the m_visco database. By simply defining an mvisco_*.m file (mvisco_3m.m serves as a prototype. The data structure defines a reference elastic material in mat.pl, complex modulus and shift factor tables, an finally additional properties stored in mat.nomo (which will be better documented later).

mat.pl=[1 fe_mat('m_elastic','SI',1) 1e6*2*1.49 .49 1500 1e6];
mat.name='ISD112 (1993)';
mat.type='m_visco';
mat.unit='SI';
mat.T0=[0];

mat.G=[ % Freq, Re(G) Im(G)
         1  1.72688e+004  3.51806e+003
        10  2.33865e+004  5.35067e+003
       100  3.49390e+004  8.25596e+003
      1000  5.76323e+004  1.67974e+004
     10000  1.03151e+005  5.72383e+004
    1e+005  2.10295e+005  1.79910e+005
    1e+006  6.59947e+005  6.57567e+005
    1e+007  2.06023e+006  1.95406e+006
    1e+008  5.83327e+006  3.57017e+006
    1e+009  1.48629e+007  5.60247e+006
    1e+010  3.25633e+007  7.33290e+006
    1e+011  6.16925e+007  5.40189e+006
    1e+012  1.01069e+008  2.48077e+006
];

mat.at=[ % T, at
       -10  1.32885e+007
         0  9.16273e+005
        10  1.14678e+005
        20  2.45660e+004
        30  9.00720e+003
        40  2.99114e+003
        50  1.27940e+003
        60  7.10070e+002
        70  2.88513e+002
        80  1.96644e+002
        90  1.37261e+002
       100  1.03674e+002
       110  6.84906e+001
       120  4.66815e+001
];
mat.nomo={'w',[-1 0 12],'Eeta',[4 9 2],'unit','SI', ...
          'www','www.3m.com', ...
          'file','ISD_112_93.png','Rect',[145    35   538   419], ...
          'type','G'};

4.2.2 Selecting a material for your application

cf=feplot; m_visco('database',cf); % select all materials
m_visco('info',cf);

m_visco('deffreq',cf) % set frequencies vector for all the material
m_visco('defT',cf)    % set temperature vector for all the material

cf.Stack{'info','Freq'}=logspace(3,log10(15e3),300); % range of interest
cf.Stack{'info','Range'}=20; % Temperature of interest
m_visco('nomo',cf) % list with all nomograms

Freq=stack_get(cf.mdl,'info','Freq','getdata'); 
T=stack_get(cf.mdl,'info','Range','getdata');
Mat=stack_get(cf.mdl,'mat');

m_visco('nomo',cf)

4.2.3 Selective components in constitutive law

General anisotropic elastic materials are described by a constitutive law of the form

(4.1)

where for orthotropic material the expression of [Λ] is given by:

(4.2)

with Δ= 1−ν_xyν_yx−ν_yzν_zy−ν_zxν_xz−2ν_yxν_zyν_xz/E_xE_yE_z. The expression of the flexibility allows easier identification of terms:

(4.3)

If one has no particular interest in the engineering constants, the orthotropic constitutive law (??) can also be written:

(4.4)

In the fevisco MatSplit command. ortho allows the decomposition in the 9 non-zero terms shown above, while EG groups C₄₄,C₅₅,C₆₆ as G and other terms as E.