Group analysis of integro-differential equations describing stress relaxation behavior of one-dimensional viscoelastic materials

• Applying the group analysis method, mathematical modeling is given.
• Complete group classification of a system of integro-differential equations is presented.
• Invariant solutions of various models are obtained.

In this paper a recently developed approach of the group analysis method is applied to a system of integro-differential equations describing the stress relaxation behavior of one-dimensional viscoelastic materials. An admitted Lie group is defined by solving determining equations of the system. Using an optimal system of one-dimensional subalgebras, all invariant solutions are obtained.