Configurational forces are fundamental concepts in the description of the motion of dislocations, cracks and other defects, possibly introducing singularities within the solid state. They are defined by considering variations in energies associated with the movement of such defects, and are therefore different from the classical forces that enter the balance laws of Newtonian mechanics. We show how a configurational force can be viewed as the resultant of the (Newtonian) contact forces acting on the perturbed shape of an object of substance equivalent to the defect, and evaluated in the limit of the shape being restored to the primitive configuration. The object of substance is, for the case of dislocations, the inclusion that provokes the same stress field. For cohesive cracks, it is the bundle of cohesive ligaments forming the process zone, reducing to a material point coincident with the crack tip in the small-scalebridging limit. The expressions for the configurational forces obtained in the paradigmatic examples are in agreement with those determined using classical variational arguments. As a further step towards a physical interpretation of the contour integral of the energy momentum tensor, we propose to extend the classical J-integral approach for a propagating crack by prolonging the contour path inside the crack gap. This extension implicitly accounts for any source of dissipation associated with material separation such as cohesive forces, establishing an energetic balance à la Griffith in the limit of small scale bridging. The method finds a direct application to phase-field models of fracture mechanics where no neat material separation occurs, because it allows using closed contour paths that traverse the thin band where damage accumulates. A generalized energy momentum tensor permits to calculate the energy release rate associated with a propagating band, also when a residual elasticity is supposed to remain in the completely damaged material. These findings may open a new prospective in the use of configurational forces by permitting their physical and intuitive visualization as classical "real" forces, as well as by providing an enhanced tool for their calculation when the contours of the defect is not clearly identifiab.
|Titolo:||Are configurational forces real forces?|
ROYER CARFAGNI, Gianni (Corresponding)
|Data di pubblicazione:||2017|
|Appare nelle tipologie:||4.1b Atto convegno Volume|