• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.813-823
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• 2021

In this work, we present the classical formulation for the antiplane problem of a eletro-viscoelastic materialswith total sliprate dependent friction and write the corresponding variational formulation. In the second step, we prove that the solution converges to the solution of the corresponding electro-elastic problem as the viscosity converges to zero.

• Journal of applied mathematics & informatics
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• 제41권3호
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• pp.487-510
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• 2023

We propose a mathematical model which describes the frictional contact between a piezoelectric body and an electrically conductive foundation. The behavior of the material is described with a linearly electro-viscoelastic constitutive law with long term memory. The mechanical process is dynamic and the electrical conductivity coefficient depends on the total slip rate, the friction is modeled with Tresca's law which the friction bound depends on the total slip rate with taking into account the electrical conductivity of the foundation both. The main results of this paper concern the existence and uniqueness of the weak solution of the model; the proof is based on results for second order evolution variational inequalities with a time-dependent hemivariational inequality in Banach spaces.