This paper describes a proposal on how to model formal requirements in Modelica for simulation-based verification. The approach is implemented in the open source Modelica_Requirements library. It requires extensions to the Modelica language, that have been prototypically implemented in the Dymola and Open-Modelica software. The design of the library is based on the FOrmal Requirement Modeling Language (FORM-L) defined by EDF, and on industrial use cases from EDF and Dassault Aviation. It uses 2-and 3valued temporal logic to describe requirements.

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In order to improve the engineering processes and especially the corresponding verification and validation phases, this article deals with the modeling of system properties in a Modelica framework. The term "property" is intended here to be generic and refers to a system requirement or limitation as well as a validity domain of a model. The choice of the Modelica language is justified by a desire to use its equation-based feature to model system properties in an unambiguous and explicit way. Besides, choosing only one formalism to describe the system properties and the physical equations of the model should ease the expression of the model validity domains.After having introduced several theoretical concepts to formally describe a system property, the development of a dedicated library is explained and illustrated on an industrial example taken from the aeronautics domain. Some checks of system properties are thus performed by co-simulating behavioral and properties models. Finally, some extensions of the Modelica language are advocated in order to improve the applicability range and efficiency of properties modeling for complex systems, and especially to increase the rigor of their validations by enabling formal proofs.

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Deviations from Miner's linear law of cumulative damage have been observed and modeled many times for the fatigue of metals, but almost no analogous studies have been performed for elastomers. The first aim of this paper is to present a simple phenomenological model, applicable to any type of material and able to quantitatively reproduce such deviations. This model is based on continuum damage mechanics and relates the fatigue damage of the material to the number of cycles through some suitable evolution law, in which the derivative of damage is expressed as a non-factorizable function of the instantaneous cyclic load and the damage itself. The second aim is to report fatigue experiments performed on "diabolo" specimens made of two different elastomeric materials, and subjected to two different successive cyclic loadings. These experiments clearly evidence deviations from Miner's rule: Miner's "total cumulated damage" may be lower or larger than unity by a small or large amount, depending on the sequence of loadings and the type of material. As a rule, the deviation from Miner's rule systematically changes sign upon reversal of the sequence of loadings. The model allows for an acceptable reproduction of the experimental results, and especially of this systematic change of sign.