524 Mechanics of Materials 2 §12.5 (b)Maxwell model An alternative model for viscoelastic behaviour proposed by Maxwell again uses a combi- nation of a spring and dashpot but this time in series as shown in Fig.12.11. Whereas in the Voigt-Kelvin (parallel)model the stress is shared between the components, in the Maxwell (series)model the stress is common to both elements. Stress a Stress input LLEEEE66EE6E501656616660166 Stress suddenly 00 releosed here Hookean' Constant stress. spring input element Time t Stroin e Newtonion doshpot element Time t Stroin response Fig.12.11.Maxwell model with elements in series. The strain,however,will be the sum of the strains of the two parts,i.e.,the strain of the spring ss plus the strain of the dashpot ep e=eS十eD Differentiating: E=Es +ED (1) Now os EEs . 5二 s and op=nep.∴. OD ED= Now,for the series model, 0S=0D=0 .'substituting in (1)we obtain the basic response equation for the Maxwell model. 0 =E+n (12.26) The response of this model to a stress oo held constant over a time t and released,is shown in Fig.12.11. Let us now consider the response of the Maxwell model to the "standard"relaxation and recovery stages as was carried out previously for the Voigt-Kelvin model.524 Mechanics of Materials 2 $12.5 (b) Maxwell model nation of a spring and dashpot but this time in series as shown in Fig. 12.11. in the Maxwell (series) model the stress is common to both elements. An alternative model for viscoelastic behaviour proposed by Maxwell again uses a combi￾Whereas in the Voigt-Kelvin (parallel) model the stress is shared between the components, 'Hookeon' spring element 'Newtonian' doshpot element Stress Stress input Stress suddenly /released here input Strain c I t I E Time t Strain response Fig. 12.11. Maxwell model with elements in series. The strain, however, will be the sum of the strains of the two parts, Le., the strain of the spring ES plus the strain of the dashpot ED .. Differentiating: . 3s ES = - E NOW OS = EES ... Now, for the series model, 0s = OD = 0 :. substituting in (1) we obtain the basic response equation for the Maxwell model. uu i=-+- Erl (12.26) The response of this model to a stress 00 held constant over a time t and released, is shown in Fig. 12.11. Let us now consider the response of the Maxwell model to the "standard" relaxation and recovery stages as was carried out previously for the Voigt-Kelvin model