関連する実験動画

Updated: Sep 9, 2025

Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics

Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics

Published on: December 1, 2023

熱性/孔性粘性モデルの統一された不連続ガールキン分析

Stefano Bonetti¹, Mattia Corti¹

¹MOX-Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy.

Journal of scientific computing

|September 5, 2025

まとめ

複雑なKelvin-Voigtの熱弾性/多孔弾性材料をモデル化するための堅牢な数学的方法を開発しましたこの断続的なガレルキンの方法は,地質学的アプリケーションの様々な物理的パラメータとグリッドタイプの安定性と精度を保証します.

科学分野:

コンピュータ用地物理学
数値分析
固体力学

背景:

ケルビン・ヴォイグトの熱/孔粘弾性モデルは,複雑な材料の振る舞いをシミュレートするために不可欠です.
これらのモデルを解決するには,特に強い異質性などの困難な条件下で,正確な数学的方法が必要です.
現存する方法は,地質学的シナリオに強度や広範な適用性が欠けている可能性があります.

研究の目的:

ケルビン-ヴォイグトの熱/孔粘弾性問題に対する新しい不連続ガールキン (DG) 方法の提示と分析.
慣性のケースと準静的なケースの両方で,提案されたDGスキームの安定性と正確性を確立する.
物理的パラメータと複雑なグリッド構造に関して,方法の堅実性を実証する.

主な方法:

ケルビン・ヴォイグトの熱・ポロ・ビスコ弾性モデルの導出
物理的なパラメータに強固な継続的な安定性分析
任意の順序で加重された対称な内部ペナルティGDスキームの開発
半離散的な問題に対する先入観の誤差推定.

主要な成果:

提案されたDG方法は,慣性問題と準静的問題の両方に安定性を示しています.
このシステムは物理的なパラメータの変動と強い物質の異質性に対応します
数値シミュレーションは,収束特性を確認し,方法の精度を検証します.
この方法は,一般的な多層網をうまく処理します.

結論:

開発された不連続ガールキン法では,ケルビン-ヴォイグトの熱/ポロ-粘着性に対する安定的かつ正確な数値ツールを提供します.
このシステムの強さと柔軟性により,地質学的な応用に適しています.
この研究は,複雑な地下モデリングのための検証されたアプローチを提供します.

キーワード:

不連続ガレルキンポリトーパル法ポーロ粘着性熱粘弾性

さらに関連する動画

Studying Large Amplitude Oscillatory Shear Response of Soft Materials

Studying Large Amplitude Oscillatory Shear Response of Soft Materials

Published on: April 25, 2019

Sample Preparation in Quartz Crystal Microbalance Measurements of Protein Adsorption and Polymer Mechanics

Sample Preparation in Quartz Crystal Microbalance Measurements of Protein Adsorption and Polymer Mechanics

Published on: January 22, 2020

関連する概念動画

Generalized Hooke's Law

Generalized Hooke's Law

The generalized Hooke's Law is a broadened version of Hooke's Law, which extends to all types of stress and in every direction. Consider an isotropic material shaped into a cube subjected to multiaxial loading. In this scenario, normal stresses are exerted along the three coordinate axes. As a result of these stresses, the cubic shape deforms into a rectangular parallelepiped. Despite this deformation, the new shape maintains equal sides, and there is a normal strain in the direction of the...

Elastic Strain Energy for Shearing Stresses

Elastic Strain Energy for Shearing Stresses

As discussed in previous lessons, strain energy in a material is the energy stored when it is elastically deformed, a concept crucial in materials science and mechanical engineering. This energy results from the internal work done against the cohesive forces within the material. When a material undergoes shearing stress and corresponding shearing strain, the strain energy density, which is the energy stored per unit volume, is calculated. Within the elastic limit, where the stress is...

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.

Viscosity of Fluid

Viscosity of Fluid

Viscosity measures the resistance a fluid offers to flow and deformation. It results from internal friction between layers of fluid moving relative to one another. Dynamic viscosity, denoted by the Greek letter mu (μ), quantifies the force needed to move one fluid layer over another. For Newtonian fluids like water and air, the relationship between the shearing stress and the rate of shearing strain is linear, meaning their viscosity remains constant regardless of the applied stress.

Navier–Stokes Equations

Navier–Stokes Equations

For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...

Three-Dimensional Analysis of Strain

Three-Dimensional Analysis of Strain

Three-dimensional strain analysis is crucial for understanding how materials deform under stress, particularly in elastic, homogeneous materials. This method employs principal stress axes to simplify complex stress states into more understandable forms. Subjected to stress, a small cubic element within a material either expands or contracts along these axes, transforming into a rectangular parallelepiped. This transformation effectively illustrates the material's deformation. The principal...