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Optimised determination of viscoelastic properties using compliant measurement systems

An analysis of a novel indentation model has been implemented to obtain master curves describing the optimal experimental parameters necessary to achieve the highest possible accuracy in the determination of viscoelastic properties of soft materials. The indentation model is a rigid indenter driven by a compliant measurement system, such as an atomic force microscope or optical tweezers, into a viscoelastic half space. The viscoelastic material is described as a multiple relaxation Prony series. The results have been extended via an application of a viscoelastic equivalence principle to other physical models such as poroelasticity. Optimisation of the indentation parameters has been conducted over many orders of magnitude of the velocity, viscoelastic moduli, spring stiffness, relaxation times and the duration of indentation resulting in a characteristic master curve. It is shown that using sub-optimal conditions gives the appearance of a more elastic material than is actually the case. For a two term Prony series the ideal ramp duration was found to be approximately one eighth of the relaxation. Also the ideal ramp duration for a three term Prony series was determined and shown to guarantee distinct relaxation times under specific conditions.

 The paper may be found at the following address: 


The above paper is now open access.

this time the numerical codes associated with this paper appear to not
currently be downloadable from the page for the paper. If the codes are not
available when you want please do contact me (comment here or my e-mail address
is on the paper, as I am the corresponding author). I can offer the following
options depending on your access to the NAG library,

1) No NAG library access: A matlab scripts and associated


  • Allows multiple relaxation times.
  • This code performs very well for soft springs and agrees with the NAG library
    solution to within the numerical error when the stability condition in the
    supporting information of the paper is met. 
  • The code is always stable at ideal
    indentation values.
  • Typically takes minutes to tens of minutes per simulation.




2) NAG library access: Assuming this is for matlab and you can
connect to the NAG library, a matlab script and associated functions: 


  • Allows multiple relaxation times.
  • Code is stable regardless of stiffness of spring.
  • Typically takes fraction of minutes to minutes per simulation.

Note typical simulation times assume that the accepted relative errors are at most 10^(-6).


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