An inverse problem for adhesive contact and non-direct evaluation of material properties for nanomechanics applications

F.M. Borodich; B.A. Galanov; S.N. Gorb; M.Y. Prostov; Y.I. Prostov; M.M. Suarez-Alvarez

Nanoscale Systems: Mathematical Modeling, Theory and Applications (2012)

  • Volume: 1, page 80-92
  • ISSN: 2299-3290

Abstract

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We show how the values of the effective elastic modulus of contacting solids and the work of adhesion, that are the crucial material parameters for application of theories of adhesive contact to nanomechanics, may be quantified from a single test using a non-direct approach (the Borodich-Galanov (BG) method). Usually these characteristics are not determined from the same test, e.g. often sharp pyramidal indenters are used to determine the elastic modulus from a nanoindentation test, while the work of adhesion is determined from a different test by the direct measurements of pull-off force of a sphere. The latter measurements can be greatly affected by roughness of contacting solids and they are unstable due to instability of the load-displacement diagrams at tension. The BG method is based on an inverse analysis of a stable region of the force-displacements curve obtained from the depth-sensing indentation of a sphere into an elastic sample. Various aspects related to solving the inverse problem for adhesive contact and experimental evaluation of material properties for nanomechanics applications are discussed. It is shown that the BG method is simple and robust. Some theoretical aspects of the method are discussed and the BG method is developed by application of statistical approaches to experimental data. The advantages of the BG method are demonstrated by its application to soft polymer (polyvinylsiloxane) samples.

How to cite

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F.M. Borodich, et al. "An inverse problem for adhesive contact and non-direct evaluation of material properties for nanomechanics applications." Nanoscale Systems: Mathematical Modeling, Theory and Applications 1 (2012): 80-92. <http://eudml.org/doc/267285>.

@article{F2012,
abstract = {We show how the values of the effective elastic modulus of contacting solids and the work of adhesion, that are the crucial material parameters for application of theories of adhesive contact to nanomechanics, may be quantified from a single test using a non-direct approach (the Borodich-Galanov (BG) method). Usually these characteristics are not determined from the same test, e.g. often sharp pyramidal indenters are used to determine the elastic modulus from a nanoindentation test, while the work of adhesion is determined from a different test by the direct measurements of pull-off force of a sphere. The latter measurements can be greatly affected by roughness of contacting solids and they are unstable due to instability of the load-displacement diagrams at tension. The BG method is based on an inverse analysis of a stable region of the force-displacements curve obtained from the depth-sensing indentation of a sphere into an elastic sample. Various aspects related to solving the inverse problem for adhesive contact and experimental evaluation of material properties for nanomechanics applications are discussed. It is shown that the BG method is simple and robust. Some theoretical aspects of the method are discussed and the BG method is developed by application of statistical approaches to experimental data. The advantages of the BG method are demonstrated by its application to soft polymer (polyvinylsiloxane) samples.},
author = {F.M. Borodich, B.A. Galanov, S.N. Gorb, M.Y. Prostov, Y.I. Prostov, M.M. Suarez-Alvarez},
journal = {Nanoscale Systems: Mathematical Modeling, Theory and Applications},
keywords = {Molecular adhesion; nano-mechanics; nanoindentation; soft polymers and biological materials; inverse problems; BG method},
language = {eng},
pages = {80-92},
title = {An inverse problem for adhesive contact and non-direct evaluation of material properties for nanomechanics applications},
url = {http://eudml.org/doc/267285},
volume = {1},
year = {2012},
}

TY - JOUR
AU - F.M. Borodich
AU - B.A. Galanov
AU - S.N. Gorb
AU - M.Y. Prostov
AU - Y.I. Prostov
AU - M.M. Suarez-Alvarez
TI - An inverse problem for adhesive contact and non-direct evaluation of material properties for nanomechanics applications
JO - Nanoscale Systems: Mathematical Modeling, Theory and Applications
PY - 2012
VL - 1
SP - 80
EP - 92
AB - We show how the values of the effective elastic modulus of contacting solids and the work of adhesion, that are the crucial material parameters for application of theories of adhesive contact to nanomechanics, may be quantified from a single test using a non-direct approach (the Borodich-Galanov (BG) method). Usually these characteristics are not determined from the same test, e.g. often sharp pyramidal indenters are used to determine the elastic modulus from a nanoindentation test, while the work of adhesion is determined from a different test by the direct measurements of pull-off force of a sphere. The latter measurements can be greatly affected by roughness of contacting solids and they are unstable due to instability of the load-displacement diagrams at tension. The BG method is based on an inverse analysis of a stable region of the force-displacements curve obtained from the depth-sensing indentation of a sphere into an elastic sample. Various aspects related to solving the inverse problem for adhesive contact and experimental evaluation of material properties for nanomechanics applications are discussed. It is shown that the BG method is simple and robust. Some theoretical aspects of the method are discussed and the BG method is developed by application of statistical approaches to experimental data. The advantages of the BG method are demonstrated by its application to soft polymer (polyvinylsiloxane) samples.
LA - eng
KW - Molecular adhesion; nano-mechanics; nanoindentation; soft polymers and biological materials; inverse problems; BG method
UR - http://eudml.org/doc/267285
ER -

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