New paradigms may help understanding unsolved scientific problems by looking on them from a different perspective. Or they may lead to a new unification theory of so far separate phenomena. The concept of “material” or “configurational” forces tracing back to a seminal publication of Eshelby in 1970 and significantly extended and promoted by Maugin twenty years later provides a generalised theory on the character of singularities of various kinds in continua, among which the “driving force” at a crack tip is a special case. Whereas Eshelby’s energy momentum tensor resulting in the J-integral is a firm constituent of fracture mechanics, the concept of configurational forces has only hesitantly been applied to fracture problems, e.g. by Kolednik, Predan, and Fischer in Engineering Fracture Mechanics, Vol. 77, 2010. Whether this new “look” upon J helped discovering anything new about it remains disputable.
Now there is a revival of this concept
K. Özenç, M. Kaliske, G. Lin, and G. Bhashyam: Evaluation of energy contributions in elasto-plastic fracture: A review of the configurational force approach. Engineering Fracture Mechanics, Vol. 115, 2014, pp. 137–153.
It is admittedly difficult to contribute some novel aspect to more than forty years of research on J in elastoplastic fracture mechanics. Though a clear perception of the nature of “path dependence” of J is often enough still missing in some publications to the point of the user’s manual of a major commercial FE code, there is no lack of theoretical knowledge. Background, applicability and limitations of J are quite clear. Those looking for deeper insight will be disappointed: The present publication just answers questions and solves problems which arose with the chosen approach of material forces.
“The path dependency of the material force approach in elasto-plastic continua is found to be considerably depending on the so-called material body forces.” This is well-known and trivial as the derivation of path independence of J is, among others, based on the absence of body forces. It does not need “numerical examples … to clarify the concept of path dependence nature of the crack tip domain (?) and effect of the material body forces”. Correction terms re-establishing path independence have been introduced years ago, see e.g. Siegele, Comput. Struct., 1989.As many continuum mechanics people, the authors start with a display of fireworks introducing the general nonlinear kinematics of large deformations which can be found in every respective textbook. In the end, this impressing framework is simmered down again to “small strain elasto-plasticity and hyperelasto-plasticity”, whatever “hyperelasto-plasticity” is supposed to mean. This does not become much clearer by the statement “the Helmholtz free energy function of finite elasto-plasticity is introduced in order to obtain geometrically nonlinear von Mises plasticity”. Finite, i.e. Hencky-type plasticity and incremental plasticity, i.e. the von Mises, Prandtl, Reuss theory are alternative approaches, where the latter is more appropriate for describing irreversible, dissipative processes. What a “geometrically nonlinear” material behaviour is remains the secret of the authors. They presumably applied the so-called “deformation theory of plasticity” which actually describes hyperelastic behaviour based on the existence of a strain-energy density as stress potential. Thus “path dependence” should not be an issue at all as the requirements for deriving path-independence are met. The rest is numerics!
So where are the problem and its solution after all? Can “material forces” be calculated by the finite element method – who doubts? Is the implementation of this concept in a commercial FE code a major scientific achievement – who knows?
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