Dashpot constant

The dashpot constant, t i, for the Maxwell element is obtained from the slope of the creep curve in the steady state region (see equation (2.32)). 

The dashpot constant, rj2, for the Kelvin-Voigt element may be determined by selecting a time and corresponding strain from the creep curve in a region where the retarded elasticity dominates (i.e. the knee of the curve in Fig. 2.40) and substituting into equation (2.42). If this is done then r)2 = 3.7 X 10 MN.s/m ... 

Example 2.13 A plastic which can have its creep behaviour described by a Maxwell model is to be subjected to the stress history shown in Fig. 2.43(a). If the spring and dashpot constants for this model are 20 GN/m and 1000 GNs/m respectively then predict the strains in the material after 150 seconds, 250 seconds, 350 seconds and 450 seconds. 

A plastic which behaves like a Kelvin-Voigt model is subjected to the stress history shown in Fig. 2.87. Use the Boltzmanns Superposition Principle to calculate the strain in the material after (a) 90 seconds (b) 150 seconds. The spring constant is 12 GN/m and the dashpot constant is 360 GNs/m. ... 

Note 4 The Maxwell model may be represented by a spring and a dashpot filled with a Newtonian liquid in series, in which case Ha is the spring constant (force = 1/a) extension) and 1// is the dashpot constant (force = (l/y9) rate of extension). 

Note 2 The retardation time of a Voigt-Kelvin element is r = 1/g o = pia = (dashpot constant)/(spring constant). 

Note 2 For a Voigt-Kelvin solid, with P(D)=1 and Q y)=a+pD, where a is the spring constant and P the dashpot constant, the equation describing the deformation becomes... 

The differential equations for the forces, in terms of the spring constant k, the dashpot constant c and the time derivatives x and x of the displacement, are... 

K2 = second Kelvin model S = Spring D = Dashpot. for parameters Tii, TI2, Hd = Dashpot constants (Viscosity) ... 

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