MINIMIZING STRAIN-RATE HISTORY AND RESULTING GREATEST LOWER BOUND ON WORK IN LINEAR VISCOELASITCITY

The paper considers isothermal deformations of a linear viscoelastic material in simple tension or compression. The relaxation modulus defining the material is assumed to be a sum of exponential functions, but need not necessarily be a monotonic function. The greatest lower bound on the work required to deform the material from its virgin state in a given time interval (0, T) is determined – independently of the strain‐rate history – in terms of T, the strain at the time T, and the constants entering the definition of the relaxation modulus. The optimum strain‐rate history, which actually produces the greatest lower bound on the work, is also determined. The results may be extended to the general deformations of a linear anisotropic viscoelastic solid. Copyright © 1969 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim