Single integral creep models

CREEP AND STRESS RELAXATION AS THERMALLY ACTIVATED PROCESSES 231 10.2.4 Comparison of single-integral models... 

The models discussed here, which are phenomenological and have no direct relation with chemical composition or molecular structure, in principle enable the response to a complicated loading pattern to be deduced from a single creep (or stress-relaxation) plot extending over a long time interval. Interpretation depends on the assumption in linear viscoelasticity that the total deformation can be considered as the sum of independent elastic (Hookean) and viscous (Newtonian) components. In essence, the simple behaviour is modelled by a set of either integral or differential equations, which are then applicable in other situations. 

Single hereditary formulation has proven to reproduce all the crucial aspects of rubber behavior (hysteresis, relaxation and creep). In the simplest situatirm, the current value of the stress is the sum of two different contributions a purely elastic term depending oti the current value of the strain and a hereditary integral depending oti the whole strain history. In the linear model of viscoelasticity, introduced by Bernstein et al. [166], the stress dependence on the strain histoiy is assumed to be linear, i.e.. 

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