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 \u201cmaterial\u201d or \u201cconfigurational\u201d 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 \u201cdriving force\u201d at a crack tip is a special case. Whereas Eshelby\u2019s 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 \u201clook\u201d upon J helped discovering anything new about it remains disputable.<\/p>\n\n\n\n
Now there is a revival of this concept<\/p>\n\n\n\n
K. \u00d6zen\u00e7, 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\u2013153.<\/p>\n\n\n\n
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 \u201cpath dependence\u201d of J is often enough still missing in some publications to the point of the user\u2019s 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.<\/p>\n\n\n\n
\u201cThe path dependency of the material force approach in elasto-plastic continua is found to be considerably depending on the so-called material body forces.\u201d 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 \u201cnumerical examples \u2026 to clarify the concept of path dependence nature of the crack tip domain (?) and effect of the material body forces\u201d. 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 \u201csmall strain elasto-plasticity and hyperelasto-plasticity\u201d, whatever \u201chyperelasto-plasticity\u201d is supposed to mean. This does not become much clearer by the statement \u201cthe Helmholtz free energy function of finite elasto-plasticity is introduced in order to obtain geometrically nonlinear von Mises plasticity\u201d. 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 \u201cgeometrically nonlinear\u201d material behaviour is remains the secret of the authors. They presumably applied the so-called \u201cdeformation theory of plasticity\u201d which actually describes hyperelastic behaviour based on the existence of a strain-energy density as stress potential. Thus \u201cpath dependence\u201d should not be an issue at all as the requirements for deriving path-independence are met. The rest is numerics!<\/p>\n\n\n\n
So where are the problem and its solution after all? Can \u201cmaterial forces\u201d 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?<\/p>\n\n\n\n
\u00bbW. Brocks’s blog<\/p>\n\n\n\n