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The nature of configurational forces. (English) Zbl 0836.73002
The author presents a variational definition of so-called “configurational forces”. Then the basic idea of configurational forces is introduced in a single-phase material. The next step is the introduction of configurational forces for an evolving surface, neglecting bulk behavior. Finally, the case of the two-phase theory of deformation is considered, and the process of solidification with the Stefan and Gibbs-Thompson conditions obtained as consequences of a configurational-force balance is given as an application. This is complemented by an appendix on evolving surface.
This very well written paper highlights the role of the “Eshelby” stress tensor. Parallel developments concerning configurational forces (but referred to as “material forces” because of their obvious role in the completely material formulation of continuum mechanics) are given in a long paper by the reviewer [Appl. Mech. Rev. 48, 213-245 (1995)], where, in addition the topic is treated in dynamics using the notion of pseudomomentum.
Reviewer: G.A.Maugin (Paris)

MSC:
74A99 Generalities, axiomatics, foundations of continuum mechanics of solids
74A15 Thermodynamics in solid mechanics
74B20 Nonlinear elasticity
80A22 Stefan problems, phase changes, etc.
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