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Geometric modelling of elastic and elastic-plastic solids by separation of deformation energy and Prandtl operators
ID Šeruga, Domen (Author), ID Kosmas, Odysseas (Author), ID Jivkov, Andrey P. (Author)

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Abstract
A geometric method for analysis of elastic and elastic-plastic solids is proposed. It involves operators on naturally discrete domains representing a material's microstructure, rather than the classical discretisation of domains for solving continuum boundary value problems. Discrete microstructures are considered as general cell complexes, which are circumcentre-dual to simplicial cell complexes. The proposed method uses the separation of the total deformation energy into volumetric and distortional parts as a base for introducing elastoplastic material behaviour. Volumetric parts are obtained directly from volume changes of dual cells, and the distortional parts are calculated from the distance changes between primal and dual nodes. First, it is demonstrated that the method can accurately reproduce the elastic behaviour of solids with Poisson's ratios in the thermodynamically admissible range from -0.99 to 0.49. Further verification of the method is demonstrated by excellent agreement between analytical results and simulations of the elastic deformation of a beam subjected to a vertical displacement. Second, the Prandtl operator approach is used to simulate the behaviour of the solid during cyclic loading, considering its elastoplastic material properties. Results from simulations of cyclic behaviour during alternating and variable load histories are compared to expected macroscopic behaviour as further support to the applicability of the method to elastic-plastic problems.

Language:English
Keywords:geometric modelling, lattice model, discrete exterior calculus, Prandtl operator, critical raw materials, elasticity, plasticity
Work type:Article
Typology:1.01 - Original Scientific Article
Organization:FS - Faculty of Mechanical Engineering
Publication status:Published
Publication version:Version of Record
Year:2020
Number of pages:Str. 136-148
Numbering:Vol. 198
PID:20.500.12556/RUL-116661 This link opens in a new window
UDC:519.876.5:539(045)
ISSN on article:0020-7683
DOI:10.1016/j.ijsolstr.2020.04.019 This link opens in a new window
COBISS.SI-ID:17592323 This link opens in a new window
Publication date in RUL:01.06.2020
Views:948
Downloads:408
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Record is a part of a journal

Title:International journal of solids and structures
Shortened title:Int. j. solids struct.
Publisher:Elsevier
ISSN:0020-7683
COBISS.SI-ID:997903 This link opens in a new window

Licences

License:CC BY 4.0, Creative Commons Attribution 4.0 International
Link:http://creativecommons.org/licenses/by/4.0/
Description:This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

Language:Slovenian
Keywords:geometrijsko modeliranje, model na mreži, diskretni infinitezimalni račun, Prandtlov operator, kritični materiali, elastičnost, plastičnost

Projects

Funder:Other - Other funder or multiple funders
Funding programme:COST
Project number:CA15102
Acronym:CRM Extreme

Funder:ARRS - Slovenian Research Agency
Project number:P2-0182
Name:Razvojna vrednotenja

Funder:RCUK - Research Council UK
Funding programme:EPSRC
Project number:EP/N026136/1
Name:Geometric mechanics of solids: new analysis of modern engineering materials

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