Energy Release Rate Approximation for Small Surface Cracks in Three-Dimensional Domains Using the Topological Derivative

Alidoost, Kazem; Feng, Meng; Geubelle, Philippe H.; Tortorelli, Daniel A.

doi:10.1115/1.4045793

Title: Energy Release Rate Approximation for Small Surface Cracks in Three-Dimensional Domains Using the Topological Derivative

Journal Article · 16 January 2020 · Journal of Applied Mechanics

DOI: https://doi.org/10.1115/1.4045793 · OSTI ID:1669244

Alidoost, Kazem ^[1]; Feng, Meng ^[1]; Geubelle, Philippe H. ^[1]; Tortorelli, Daniel A. ^[2]

Univ. of Illinois at Urbana-Champaign, IL (United States)
Univ. of Illinois at Urbana-Champaign, IL (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Design and Optimization

The topological derivative describes the variation of a response functional with respect to infinitesimal changes in topology, such as the introduction of an infinitesimal crack or hole. In this three-dimensional fracture mechanics work, we propose an approximation of the energy release rate field associated with a small surface crack of any boundary location, direction, and orientation combination using the topological derivative. Furthermore, this work builds on the work of Silva et al. (“Energy Release Rate Approximation for Small Surface-Breaking Cracks Using the Topological Derivative,” J. Mech. Phys. Solids 59(5), pp. 925–939), in which the authors proposed an approximation of the energy release rate field which was limited to two-dimensional domains. The proposed method is computationally advantageous because it only requires a single analysis. By contrast, current boundary element and finite element-based methods require an analysis for each crack length-location-direction-orientation combination. Furthermore, the proposed method is evaluated on the non-cracked domain, obviating the need for refined meshes in the crack tip region.

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Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1669244

Report Number(s):: LLNL-JRNL--801520; 1004898

Journal Information:: Journal of Applied Mechanics, Journal Name: Journal of Applied Mechanics Journal Issue: 4 Vol. 87; ISSN 0021-8936

Publisher:: ASMECopyright Statement

Country of Publication:: United States

Language:: English

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