Mathematical analysis on Fracture phenomena and Aging problems in (visco)elasticity

2018 Fiscal Year Final Research Report

• Project/Area Number: 26400178
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: Tokyo University of Science
• Principal Investigator: Itou Hiromichi 東京理科大学, 理学部第二部数学科, 准教授 (30400790)
• Research Collaborator: IKEHATA masaru ; KHLUDNEV A. M. ; KOVTUNENKO V. A. ; NAKAMURA gen ; RAJAGOPAL K. R.
• Project Period (FY): 2014-04-01 – 2019-03-31
• Keywords: 非線形弾性体 / き裂 / 非貫通条件 / 非線形粘弾性体 / 逆問題

Outline of Final Research Achievements

We studied elasticity models describing fracture phenomena and obtained the following results. First, in nonlinear elastic model called strain-limiting model, well-posedness of the generalized solution of a boundary value problem with a crack is shown. Second, we extended to the case of nonlinear viscoelastic model and similar results are obtained. Further, as an application of this study, we considered a reconstruction problem for cracks in two dimensional electrical conductive body by using electrical impedance tomography, and then we established a theoretical algorithm to extract cracks from measured data on the boundary.

Free Research Field

偏微分方程式

Academic Significance and Societal Importance of the Research Achievements

本研究で扱った非線形（粘）弾性体モデルは線形弾性体モデルよりも広汎な破壊現象を捉えられるモデルである。そのき裂問題に対して得られた定性的理論は、き裂を含むような滑らかでない領域における非線形偏微分方程式論の発展に寄与し、新しい近似解の構成法の示唆を与えた。また、非破壊検査に関わるき裂（もしくは溶接部）の逆問題について、１回の観測データを用いた再構成アルゴリズムを開発した。これによりスポット溶接部の精度評価手法への貢献が見込まれる。