Treatment of Experimental Data: The Problem of the Initial Strain (or Stress) Ramps

The problem of how to treat the initial strain and stress rampsStrain and stress ramps in experiments in the case of stress relaxation is considered, with the objective of correcting the initial measured values of the stress relaxation modulus and the measured times, which is important in model evaluation. A similar problem exists in the case of creep, but it is not dealt with in this chapter, being left as a final Study Question for the interested reader. Using the respective rConstitutive equation, we derive the complete stress relaxation modulus curve of a standard and a generalized standard linear solid, including the initial strain rampInitial strain ramp, for three cases: ideal linearIdeal linearinitial strain ramp, delayed linearDelayed linearinitial strain ramp, and delayed realDelayed realinitial strain ramp ramps. Then, by comparison with the ideal stress relaxation modulus response to an ideal step strain at \(t = 0\) , we obtain the best correctionBest correctioninitial strain ramp to the whole experimental curve as a negative shift of \(2t_{r} /3\) to the entire set of measured times, where \(t_{r}\) is the total ramp timeRamp timeinitial strain ramp.