2020 Fiscal Year Final Research Report
Geometric modeling and Monte Carlo simulations for anisotropic and non-linear deformation of polymeric materials
| Project/Area Number |
17K05149
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Computational science
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| Research Institution | Sendai National College of Technology (2019-2020)
Ibaraki National College of Technology (2017-2018) |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2021-03-31
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| Keywords | ポリマー / 数学的モデル化 / 統計力学的モデル / Monte Carloシミュレーション / 離散Finsler幾何 |
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| Outline of Final Research Achievements |
We successfully explain highly nonlinear behaviors in stress-strain curves of liquid crystal elastomer and animal skins from Finsler geometry (FG) viewpoint within the conventional model of polymers. The FG model has been developed and studied by the authors using a mathematical framework, which is applicable to direction-dependent phenomena. The key idea in the FG model is the assumption that material strength locally varies depending on directional degrees of freedom, such as the direction of liquid crystal molecules. This assumption implies that interaction strength between two neighboring molecules depends on external forces. This principle, which is realized in the FG model indicating that molecular interactions are controlled by external forces, allows us to explain many reported experimental data.
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| Free Research Field |
計算物理学，応用数学
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| Academic Significance and Societal Importance of the Research Achievements |
これまで，材料の分子間に働く力の強さは一定と考えられてきた。一方，測定される力学的物性値はミクロには変動する物性値の平均値になると考えれば，ミクロなレベルでは一定でなくともよい。数学的には，分子間の相互作用は微分と関係し微分は距離と関係する。一方，Finsler幾何の仮定から，その距離は液晶分子の向きに応じて動的に変わる。その結果，外力によって液晶分子がある方向にそろえば，その向きの分子間力はそれと垂直方向とは大きく変わることになる。このような原理，即ち，分子間に働く力は制御できるものである，ことが様々な現象で成り立っていると確認できたことが学術的および社会的意義である。
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