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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Lagrangian crumpling equations.

Mark A Peterson¹

¹Department of Physics, Mount Holyoke College South Hadley, Massachusetts 01075, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|October 2, 2009

Summary

This summary is machine-generated.

This study introduces a Lagrangian coordinate method to track moving surfaces efficiently. The technique simplifies complex calculations by using the initial surface geometry, proving useful in nonlinear elasticity problems.

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Area of Science:

Solid Mechanics
Nonlinear Elasticity
Surface Physics

Background:

Tracking evolving surface geometry in dynamic systems is computationally challenging.
Nonlinear elasticity problems often involve complex deformations and boundary conditions.
Understanding surface phenomena like capillary wrinkles requires accurate geometric modeling.

Purpose of the Study:

To present a concise Lagrangian coordinate method for analyzing moving surfaces.
To demonstrate the method's applicability to nonlinear elasticity problems.
To improve the accuracy of modeling surface tension-induced phenomena.

Main Methods:

Utilizing Lagrangian coordinates to follow surface evolution.
Performing all computations within the fixed initial surface geometry.
Applying the method to thin plate bulging, spherical shell buckling, and capillary wrinkling.

Main Results:

The method allows computations in a fixed initial geometry, simplifying complex moving surface analysis.
Successful application to three distinct nonlinear elasticity problems.
Inclusion of gravitational potential energy improved agreement with experimental data for capillary wrinkles.

Conclusions:

The described Lagrangian method offers an efficient approach for studying moving surfaces in nonlinear elasticity.
The technique provides a robust framework for analyzing phenomena like plate bulging, shell buckling, and capillary wrinkling.
Further refinement, such as incorporating gravitational effects, can enhance predictive accuracy.