SPH method applied to compression of solid materials for a variety of loading conditions

•SPH modelling for three different sets of common solid mechanical tests – uniaxial, biaxial and triaxial loading.•A new numerical treatment is introduced to deal with these boundary conditions.•The numerical method is robust to large strain (30%).•The sample deforms in shape which is readily and ac...

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Bibliographic Details
Published in:Applied Mathematical Modelling 2017-04, Vol.44, p.72-90
Main Authors: Pereira, G.G., Cleary, P.W., Lemiale, V.
Format: Article
Language:English
Subjects:
Biaxial
Boundary conditions
Compression
Computational fluid dynamics
Deformation
Fluid flow
Fluid mechanics
Numerical analysis
Partial differential equations
Robustness (mathematics)
Smooth particle hydrodynamics
Smoothed particle hydrodynamics
Solid materials
Solid mechanics
Triaxial
Uniaxial
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Summary:•SPH modelling for three different sets of common solid mechanical tests – uniaxial, biaxial and triaxial loading.•A new numerical treatment is introduced to deal with these boundary conditions.•The numerical method is robust to large strain (30%).•The sample deforms in shape which is readily and accurately captured by SPH.•Both elastic and more complex (elasto-plastic) materials are considered. Smoothed Particle Hydrodynamics (SPH) is a numerical method that does not use a mesh or grid when solving a set of partial differential equations. This makes it particularly useful in application to solid mechanics problems where the sample undergoes large deformation. Whereas mesh-based methods have difficulty when the sample becomes severely distorted, SPH naturally deals with this important engineering scenario. We implement the SPH method for compressional deformation of solid samples and focus on uniaxial, biaxial and triaxial loading. We develop numerical procedures that naturally deal with these three different sets of boundary conditions and apply it to both small and larger strains in elastic and more complex materials. The method is shown to be robust up to large strains of 30%. Under uniaxial loading, a cylindrical sample tends to deform by bulging while under triaxial loading the cylindrical sample will remain cylindrical, but the diameter of the sample increases accordingly.
ISSN:0307-904X
1088-8691
0307-904X
DOI:10.1016/j.apm.2016.12.009