Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Lagrangian Solid Modeling

Version 1 : Received: 13 March 2017 / Approved: 14 March 2017 / Online: 14 March 2017 (08:36:58 CET)
Version 2 : Received: 19 November 2017 / Approved: 20 November 2017 / Online: 20 November 2017 (09:06:40 CET)

A peer-reviewed article of this Preprint also exists.

Marko, M. A Discrete Approach to Meshless Lagrangian Solid Modeling. Computation 2017, 5, 33. Marko, M. A Discrete Approach to Meshless Lagrangian Solid Modeling. Computation 2017, 5, 33.


The author demonstrates a stable Lagrangian solid modeling method, tracking the interactions of solid mass particles, rather than using a meshed grid. This numerical method avoids the problem of tensile instability often seen with Smooth Particle Applied Mechanics by having the solid particles apply stresses expected with Hooke's law, as opposed to using a smoothing function for neighboring solid particles. This method has been tested successfully with a bar in tension, compression, and shear, as well as a disk compressed into a flat plate, and the numerical model consistently matched the analytical Hooke's law as well as Hertz contact theory for all examples. The solid modeling numerical method was then built into a 2-D model of a pressure vessel, which was tested with liquid water particles under pressure and simulated with Smoothed Particle Hydrodynamics. This simulation was stable, and demonstrated the feasibility of Lagrangian specification modeling for Fluid Solid Interactions.


Lagrangian, continuum mechanics, solid modeling, smoothing function, SPAM, SPH


Engineering, Mechanical Engineering

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