title: Ramp-hold relaxation solutions for the KVFD model applied to soft viscoelastic media.
abstract: The standard step-hold load-relaxation profile can yield variable estimates of mechanical properties due to the difficulty in achieving a step strain experimentally. A ramp-hold profile overcomes this limitation if appropriate model functions can be derived. Utilizing Boltzmann hereditary integral operators for two indentation geometries, analytical ramp solutions for load-relaxation were developed based on the Kelvin-Voigt fractional derivative (KVFD) model. The results identify three model parameters for characterizing viscoelastic behavior from a single model curve fit to the data: the elastic modulusE0, fractional-order parameterα, and relaxation time constantτ. The quantitative nature of the analysis was validated through measurements on gelatin emulsion samples exhibiting viscoelastic behavior. KVFD-model-based solutions provide mathematically simple and experimentally flexible descriptions of load-relaxation behavior for a range of viscoelastic properties and experimental conditions; e.g. one closed-form solution can fit the ramp and the hold phases of the relaxation time series. Experiments show that the solution for a spherical indenter and plate compressor each fit well to the corresponding experimental relaxation curves with a coefficient of determinationR2> 0.98. Parameters obtained from the spherical-tip indentation and plate-compression geometries agree within one standard deviation, confirming that the ramp solution based KVFD model yields consistent measurements for characterizing viscoelastic materials.
authors.affiliation: Key Laboratory of Biomedical Information Engineering, Ministry of Education, School of Life Science and Technology, Xi'an Jiaotong University, Xianning West Road No.28, Xi'an, Shaanxi, 710049, People's Republic China; Department of Bioengineering and Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA.
authors.forename: HongMei
authors.initials: H
authors.lastname: Zhang
authors.affiliation: Department of Bioengineering and Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA.
authors.forename: Yue
authors.initials: Y
authors.lastname: Wang
authors.affiliation: Department of Bioengineering and Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA.
authors.forename: Michael F
authors.initials: MF
authors.lastname: Insana
keywords: mechanical properties; plate compression; ramp-hold relaxation; soft polymer emulsion; spherical indentation