Linearization of quasistatic fracture evolution in brittle materials
Friedrich M, Steinke P, Stinson K (2026)
Publication Type: Journal article
Publication year: 2026
Journal
Book Volume: 43
Pages Range: 1367-1417
Journal Issue: 6
DOI: 10.4171/AIHPC/161
Abstract
We prove a linearization result for quasistatic fracture evolution in nonlinear elasticity. As the stiffness of the material tends to infinity, we show that rescaled displacement fields and their associated crack sets converge to a solution of quasistatic crack growth in linear elasticity without any a priori assumptions on the geometry of the crack set. This result corresponds to the evolutionary counterpart of the static linearization result [Friedrich, Math. Eng. 2 (2020), 75–100], where a Griffith model for nonsimple brittle materials has been considered featuring an elastic energy which also depends suitably on the second gradient of the deformations. The proof relies on a careful study of unilateral global minimality, as determined by the nonlinear evolutionary problem, and its linearization together with a variant of the jump transfer lemma in GSBD [Friedrich and Solombrino, Ann. Inst. H. Poincaré C Anal. Non Linéaire 35 (2018), 27–64].
Authors with CRIS profile
Involved external institutions
Rheinische Friedrich-Wilhelms-Universität Bonn
Germany (DE)
University of Utah
United States (USA) (US)
Germany (DE)
University of Utah
United States (USA) (US)
How to cite
APA:
Friedrich, M., Steinke, P., & Stinson, K. (2026). Linearization of quasistatic fracture evolution in brittle materials. Annales de l'Institut Henri Poincaré - Analyse Non Linéaire, 43(6), 1367-1417. https://doi.org/10.4171/AIHPC/161
MLA:
Friedrich, Manuel, Pascal Steinke, and Kerrek Stinson. "Linearization of quasistatic fracture evolution in brittle materials." Annales de l'Institut Henri Poincaré - Analyse Non Linéaire 43.6 (2026): 1367-1417.
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