Modern Problems of Frictional Contacts of Elastomers

Abstract

A specific feature of formulating the boundary value problems of the linear viscoelasticity [1, 2, 3] is the need to take into account the hereditary-temporal properties on the components of the stress–strain state. As a result, the stresses, strains, and displacements, arising in the linear viscoelastic body under the boundary loading, can be found by solving the integral–differential system of equations which describe the quasi-static equilibrium of structure. At the end, the actual dimension of the solving problem increases by one unit in comparison with the elastic calculations. Generally, we will have a three-dimensional boundary value problem of the hereditary elasticity with respect to the spatial variables and the dependence of solution on the history of varying loads for the time interval \( \left[ {0, t} \right] \). While solving numerically the problems of the linear viscoelasticity, it heavily relies on the usage of computer technologies.