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By Nicole Baumgarten a,*, Juliane House

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Material forces on the boundary appear as reaction forces to the constraint imposed by the fact that the boundary is fixed in the reference configuration. Question: does there exist a “better” internal arrangement of the nodes for which the material forces vanish? This is a finite dimensional optimization problem which may Figure 1. (a) Block loaded by displacement w; (b) network of material forces. Page 8 Figure 2. Specimen with a crack and a hole loaded by a dead displacement w. Figure 3. (a) Trajectory of crack tip: hole far enough from starting point; (b) Trajectory of crack tip: hole too close to starting point and the hole is missed.

This illustration having only pedagogical purpose no threshold value of crack initiation is here introduced although a value à la Griffith could be introduced (so-called energy criterion). Other examples can be found in Mueller and Maugin (2002). The question is naturally raised of the adaptivity of the FE method using the Eshelby-stress tensor notion. The magnitude of the discrete material forces which are computed in the post-processing of the solution of the material force balance–eqn. (23) written in a weak form -may be used as an indicator for mesh refinement (here a scalar indicator).

Material forces in thermoelastic ferromagnets. Continuum Mech. Thermodyn. 8:275–292. Grinfeld, M. 1991. Thermodynamic Methods in the Theory of Heterogeneous Systems. Harlow, Essex: Longman. E. 1999. Configurational Forces as Basic Concepts of Continuum Physics. New York: Springer-Verlag. Imatani, S. A. 2003. A Constitutive modeling for growing materials and its applications to finite-element analysis. ASME. Tran. J. Appl. Mech. (in the press). D. 2002. Configurational forces in magnetism with application to the dynamics of a small-scale ferromagnetic shape-memory cantilever.

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I think and I don’t know in English as lingua franca and native English discourse by Nicole Baumgarten a,*, Juliane House


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