TY - JOUR
T1 - The Boussinesq flat-punch indentation problem within the context of linearized viscoelasticity
AU - Itou, Hiromichi
AU - Kovtunenko, Victor A.
AU - Rajagopal, Kumbakonam R.
PY - 2020/6
Y1 - 2020/6
N2 - The Boussinesq problem, namely the indentation of a flat-ended cylindrical punch into a viscoelastic half-space is studied. We assume a linear viscoelastic model wherein the linearized strain is expressed as a function of the stress. However, this expression is not invertible, which makes the problem very interesting. Based on the Papkovich–Neuber representation in potential theory and using the Fourier–Bessel transform for axisymmetric bodies, an analytical solution of the resulting time-dependent integral equation is constructed. Consequently, distribution of the displacement and the stress fields in the half space with respect to time is obtained in the closed form.
AB - The Boussinesq problem, namely the indentation of a flat-ended cylindrical punch into a viscoelastic half-space is studied. We assume a linear viscoelastic model wherein the linearized strain is expressed as a function of the stress. However, this expression is not invertible, which makes the problem very interesting. Based on the Papkovich–Neuber representation in potential theory and using the Fourier–Bessel transform for axisymmetric bodies, an analytical solution of the resulting time-dependent integral equation is constructed. Consequently, distribution of the displacement and the stress fields in the half space with respect to time is obtained in the closed form.
KW - Axisymmetric body
KW - Boussinesq problem
KW - Closed form solution
KW - Fourier–Bessel transform
KW - Implicit material response
KW - Linear viscoelasticity
KW - Papkovich–Neuber representation
KW - Potential theory
KW - Punch indentation
UR - http://www.scopus.com/inward/record.url?scp=85082664900&partnerID=8YFLogxK
U2 - 10.1016/j.ijengsci.2020.103272
DO - 10.1016/j.ijengsci.2020.103272
M3 - Article
AN - SCOPUS:85082664900
SN - 0020-7225
VL - 151
JO - International journal of engineering science
JF - International journal of engineering science
M1 - 103272
ER -