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Internal energy dissipation in many materials, per stress cycle and per unit volume, is frequency-independent and proportional to some power of an equivalent stress amplitude, σ eq m. For triaxial stress states, the definition of σ eq has so far been ad hoc. In this paper a micromechanically motivated constitutive model for such internal dissipation is developed by assuming a multitude of dispersed microscopic ellipsoidal elasto-plastic flaws. Both detailed ABAQUS simulations and a semi-analytical approach based on formulas given by Eshelby are used. Two limiting special cases are identified where the dissipation in a single flaw is analytically tractable: spherical flaws, and flaws that are flat and thin. For these, Weibull-distributed flaw strengths and spatially homogeneously distributed flaws are assumed. Formulas for the macroscopic dissipation are obtained, analytically for spherical flaws and semi-analytically for …