A new approach to a viscoelastic medium is presented and the constitutive equations of ageing viscoelastic materials are developed. The formulation is equivalent to ageing Kelvin or Maxwell chain models with age dependent elastic moduli and viscosities. It is shown that by using such models, the retaining of the complete past history of stress and strain in the memory of a digital computer is avoided. Finally, the formulation is generalized to deal with three-dimensional problems.

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International audienceThis paper deals with the development of a mathematical approach for the solution of linear, non-ageing viscoelastic materials undergoing mechanical deformation. The formulation is derived from integral approach based on a discrete spectrum representation for the creep tensor. Finite difference integration is used to discretize the integral operators. The resulting constitutive model contains an internal state variable which represents the influence of the whole past history of stress and strain. Thus the difficulty of retaining the strain history in computer solutions is avoided. A complete general formulation of linear viscoelastic stress-strain analysis is developed in terms of increments of stresses and strains. Numerical simulations are included in order to validate the incremental constitutive equations