Shape derivative of potential energy and energy release rate in fracture mechanics

2008/06/20 by Masato Kimura, Kimura, Masato, Isao Wakano +1
Engineering · Mathematics · #35J20 (Primary) 74G65 #74R10 (Secondary) #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Numerical methods in engineering #Rock Mechanics and Modeling #math.AP #msc:35J20 #msc:74G65 #msc:74R10

paper · pdf · doi:10.48550/arxiv.0806.3449

17 pages

arxiv created 2008/06/20 · openalex publication_date 2008/06/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We study general mathematical framework for variation of potential energy with respect to domain deformation. It enables rigorous derivation of the integral formulas for the energy release rate in crack problems. Applying a technique of the shape sensitivity analysis, we formulate the shape derivative of potential energy as a variational problem with a parameter. Key tools of our abstract theory are a new parameter variational principle and the classical implicit function theorem in Banach spaces.

Citations

• A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks

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