Application of material forces to hyperelastostatic fracture mechanics. I. Continuum mechanical setting

By Paul Steinmann. 2000

197 citations recorded by the source corpus.

Subfields: Mechanics of Materials, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/d66d75c0c30f06c27ead9ace00021e8b919035ed

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mechanics of Materials

1. Paul Steinmann
2. C. Miehé
3. John Dolbow
4. H. Ji
5. Ellen Kuhl
6. Timon Rabczuk
7. Ralf Müller
8. Eliot Fried

In Ocean Engineering

1. John Dolbow
2. H. Ji
3. Eliot Fried
4. Ralf Müller
5. G. Maugin
6. C. Miehé
7. Ercan Gürses

Citations in the corpus

• A robust algorithm for configurational‐force‐driven brittle crack propagation with R‐adaptive mesh alignment (2007, background): “[34] appear in a natural format in the expression of the global dissipation postulate.”
• Adaptive strategies and error control for computing material forces in fracture mechanics (2004, background): “We denote the exact quantity by Q(u) and introduce E(u, uh) that measures the difference between the exact and the approximated quantity E(u, uh) = Q(u) − Q(uh) (2) The directional derivative for E(u, uh) in the direction w is defined as E′(u, uh; w) = E(u + w, uh)| =0 (3) and the secant form of E(u”
• On material forces and finite element discretizations (2002, background): “A nice feature of discrete material forces is the fact that they can directly be interpreted in terms of the J-integrals in linear elastic fracture mechanics, see Steinmann (2000) and Steinmann, Ackermann and Barth (2001), and driving forces on interfaces, see also Mueller, Kolling and Gross (2002).”
• A numerical strategy for investigating the kinetic response of stimulus-responsive hydrogels (2005, methodology): “The techniques used by Steinmann et al. (2001) and Mueller et al. (2002) do, however, have much in common with the widely-used domain-integral methods introduced by Li et al. (1985) and those methods have been implemented with the X-FEM to extract energy release rates along crack fronts.”
• On deformational and configurational mechanics of micromorphic hyperelasticity – Theory and computation (2007, background): “…concept of deformational vs. configurational mechanics in general and the material force method in particular, see for instance the contributions of Maugin and coworkers [5] [19] [20] [23] [21], Gurtin [10] or the group of Steinmann [27] [28] [30] [17] [18] as well as the references cite therein.”