Relaxation indentation experiments using atomic force microscopy (AFM) are used to obtain viscoelastic material properties of soft samples. The quasilinear viscoelastic (QLV) model formulated by Fung (1972, “Stress Strain History Relations of Soft Tissues in Simple Elongation,” in Biomechanics, Its Foundation and Objectives, Prentice-Hall, Englewood Cliffs, NJ, pp. 181–207) for uniaxial compression data was modified for the indentation test data in this study. Hertz contact mechanics was used for the instantaneous deformation, and a reduced relaxation function based on continuous spectrum is used for the time-dependent part in the model. The modified QLV indentation model presents a novel method to obtain viscoelastic properties from indentation data independent of relaxation times of the test. The major objective of the present study is to develop the QLV indentation model and implement the model on AFM indentation data for 1% agarose gel and a viscoelastic polymer using spherical indenter.
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