12 Citations (SciVal)


Recent research investigations have reported the benefit of enhancing conventional AFM-based nanoscale machining operations by the introduction of high frequency vibrations between the AFM tip and the processed material. The technique relies on piezoelectric actuation and is relatively straight forward to implement in practice. However, the non-linearity of piezoelectric actuators when operated under high electric field and frequency conditions can affect the dimensional accuracy of the fabricated nanostructures. To address these issues, the paper reports a method based on coupled mechanical-electrical Finite Element (FE) modelling to predict the relative motion between an AFM tip and a workpiece for vibration-assisted AFM-based nanomachining applications. In particular, the novelty of the proposed method is that it combines two classical approaches for modelling the nonlinear behaviour of piezoelectric materials. More specifically, two sources of non-linearity are considered simultaneously by combining the field-dependant model from Muller and Zhang with the frequency-dependant model from Damjanovic. The resulting combined model is employed to establish the piezoelectric constitutive equations implemented in the developed coupled field FE model. A further distinguishing characteristic of the work is that the proposed approach was subsequently validated by comparing the predicted widths of nanoscale grooves against those machined with a custom AFM-based vibration-assisted nanomachining configuration.

Original languageEnglish
Article number108048
JournalInternational Journal of Mechanical Sciences
Early online date20 Dec 2022
Publication statusPublished - 1 Apr 2023

Bibliographical note

Funding Information:
The reported research was funded by the Engineering and Physical Sciences Research Council (EPSRC) under the grant EP/M020703/1. The first author also gratefully acknowledges complementary support from the National Natural Science Foundation of China ( 52105434 ). All data created during this research are openly available from Cardiff University data archive at http://doi.org/10.17035/d.2022.0220305153


  • AFM-based vibration-assisted nanomachining
  • Coupled field FE modelling

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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