Normal Interaction Force of Two Particles (Q6674527)

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force component acting normally at the contact interface between two particles

Language	Label	Description	Also known as
English	Normal Interaction Force of Two Particles	force component acting normally at the contact interface between two particles

Statements

mathematical expression

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in defining formula

D_{N}

symbol represents

Damping Coefficient

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E_{N}

symbol represents

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F_{i j}^{N}

symbol represents

Interaction Force

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v_{i} \in ℝ^{3}

symbol represents

Particle Velocity

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r_{i j}

symbol represents

Particle Radius

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n_{i j} \in ℝ^{3}

symbol represents

Unit Normal Vector

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x_{i} \in ℝ^{3}

symbol represents

Particle Position

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k_{i j}^{N}

symbol represents

Normal Stiffness

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m_{i}

symbol represents

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MaRDI profile type

MaRDI formula profile

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defining formula

\begin{aligned} F_{i j}^{N} & = (k_{i j}^{N} δ_{i j} + d_{i j}^{N} {\dot{δ}}_{i j}) n_{i j} \\ δ_{i j} & = ⟨ x_{i} - x_{j}, n_{i j} ⟩ \\ {\dot{δ}}_{i j} & = ⟨ v_{i} - v_{j}, n_{i j} ⟩ \\ r_{i j} & = (r_{i} + r_{j}) / 2 \\ k_{i j}^{N} & = E_{N} π r_{i j} / 2 \\ d_{i j}^{N} & = D_{N} 2 \sqrt{k_{i j}^{N} m_{i j}} \\ m_{i j} & = \frac{m_{i} m_{j}}{m_{i} + m_{j}} \\ n_{i j} & = \frac{x_{i} - x_{j}}{‖ x_{i} - x_{j} ‖} \end{aligned}

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Sitelinks

Mathematics(1 entry)

mardi Formula:6674527

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