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Discrete mechanics proposes an alternative formulation of the equations ofmechanics where the Navier-Stokes and Navier-Lam\'e equations becomeapproximations of the equation of discrete motion. It unifies the fields offluid and solid mechanics by extending the fields of application of theseequations to all space and time scales. This article presents the essentialdifferences induced by the abandonment of the notion of continuous medium andglobal frame of reference. The results of the mechanics of continuous mediumvalidated by fluid and solid observations are not questioned. The concept ofcontinuous medium is not invalidated, the discrete formulation proposed simplywidens the spectrum of the applications of the classical equations.  The discrete equation of motion introduces several important modifications,in particular the fundamental law of the dynamics on an element of volumebecomes a law of conservation of the accelerations on an edge. The accelerationconsidered as an absolute quantity is written as a sum of two components, onesoledoidal the other irrotational according to a local orthogonalHelmholtz-Hodge decomposition. The mass is abandoned and replaced by thecompression and rotation energies represented by the scalar and vectorialpotentials of the acceleration. The equation of motion and all the physicalparameters are expressed only with two fundamental units, those of length andtime. The essential differences between the two approaches are listed and someof them are discussed in depth. This is particularly the case with the knownparadoxes of the Navier-Stokes equation or the importance of inertia for theNavier-Lam\'e equation.

An alternative to the concept of continuous medium