In this paper a state variable approach for the description of an hysteretic restoring force model is presented. In particular the approach is able to describe the nonlinear behaviour in the force-displacement plane by substantial modifications at the basic set of differential equation governing the dynamics of the oscillator and the state equation formulated on the basis of an endochronic relation. The attention is focussed on the loading-reloading paths of short amplitude where the effective reproduction of the behaviour is usually more difficult, as reported in experimental tests. It is observed that the phenomenological nature of the basic model can be responsible of certain violations to fundamental physical postulates for stable materials especially during short amplitude load cycles. The smooth solution to the problem that is here proposed is presented as an implementation of the existing hysteretic model. In fact a new hysteretic term is introduced in the state differential equation acting in phase opposition with respect to the fundamental term. The amplitude of the added term is ruled by a suitable nonlinear relation. The mechanical effect is the creation of an increment to the stiffness of the system along the reloading path obtaining stable conditions of energy dissipation also during short amplitude load cycles. In the numerical example a comparison is set up imposing a critical displacement path. Moreover the dynamic response of an oscillator under evolutionary excitations of environmental nature is examined. It is supposed to degradate in both stiffness and strength under the given load history. The basic and the improved model are compared showing significant differences both in the local and in the global behaviour.

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