Adaptive strategies and error control for computing material forces in fracture mechanics

Heintz, Per,1975Chalmers University of Technology,Chalmers tekniska högskola (author)

The concept of material forces pertains to a variation of the inverse motion map while the placement field is kept fixed. From the weak formulation of the self-equilibrating Eshelby (material) stress tensor it turns out that the classical J-integral formulations in fracture mechanics are just special cases due to the choice of particular weight functions. In this contribution, we discuss a posteriori error control of the material forces as part of an adaptive strategy to reduce the discretization error to an acceptable level. The data of the dual problem involves the quite non-conventional tangent stiffness of the (material) Eshelby stress tensor with respect to a variation of the (physical) strain field. The suggested strategy is applied to the common fracture mechanics problem of a single-edged crack, whereby different strategies for computing the J-integral are compared. We also consider the case in which the crack edges are not parallel, i.e. a notch.

Larsson, Fredrik,1975Chalmers University of Technology,Chalmers tekniska högskola(Swepub:cth)lafr (author)
Hansbo, PeterJönköping University,JTH. Forskningsmiljö Produktutveckling - Simulering och optimering,Chalmers tekniska högskola,Chalmers University of Technology(Swepub:cth)hansbo (author)
Runesson, Kenneth,1948Chalmers University of Technology,Chalmers tekniska högskola(Swepub:cth)keru (author)
Chalmers University of TechnologyChalmers tekniska högskola (creator_code:org_t)

In:International Journal for Numerical Methods in Engineering: Wiley60:7, s. 1287-12990029-59811097-0207

By the author/editor: Heintz, Per, 197 ...; Larsson, Fredrik ...; Hansbo, Peter; Runesson, Kennet ...

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