Material Forces: Concepts and Applications

The unifying notion of material force which gathers under one vision all types of driving “forces” on defects and smooth or abrupt inhomogeneities in fracture, defect mechanics, elastodynamics (localized solutions) and allied theories such as in electroelasticity, magnetoelasticity, and the propagation of phase transition fronts, is reviewed together with its many faceted applications. The presentation clearly distinguishes between the role played by local physical balance laws in the solution of boundary-value problems and that played by global material balance laws in obtaining the expression of relevant material forces and devising criteria of progress for defects, in a general way. The advances made along this line, which may be referred to as Eshelbian mechanics, are assessed and perpectives are drawn.