A geometric formulation of linear elasticity based on Discrete Exterior Calculus

Pieter Boom, Odysseas Kosmas, Lee Margetts, Andrey Jivkov

Mechanical and Aerospace Engineering

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15 Article

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2024
A discrete model for force-based elasticity and plasticity
Dassios, I., Tzounas, G., Milano, F. & Jivkov, A., 1 Jul 2024, In: Journal of Computational and Applied Mathematics. 444, 14 p., 115796.
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Discrete modelling of continuous dynamic recrystallisation by modified Metropolis algorithm
Zhu, S., Borodin, E. & Jivkov, A., 1 Feb 2024, In: Computational Materials Science. 234, 11 p., 112804.
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Triple junction disclinations in severely deformed Cu-0.4%Mg alloys
Zhu, S., Jivkov, A., Borodin, E. & Morozova, A., 1 Jan 2024, In: Acta Materialia. 264, 12 p., 119600.
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2023
Microstructures, physical processes, and discrete differential forms
Jivkov, A., Berbatov, K., Boom, P. D. & Hazel, A., 13 Jan 2023, In: Procedia Structural Integrity. 43, p. 15-22 8 p.
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ParaGEMS: Integrating discrete exterior calculus (DEC) into ParaFEM for geometric analysis of solid mechanics
Boom, P., Jivkov, A. & Margetts, L., 1 Feb 2023, In: SoftwareX. 21, 7 p., 101280.
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Topological characteristics of grain boundary networks during severe plastic deformations of copper alloys
Zhu, S., Borodin, E. & Jivkov, A., 15 Oct 2023, In: Acta Materialia. 259, 14 p., 119290.
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2022
Diffusion in multi-dimensional solids using Forman's combinatorial differential forms
Berbatov, K., Boom, P., Hazel, A. & Jivkov, A., 1 Oct 2022, In: Applied Mathematical Modelling. 110, p. 172-192 21 p.
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Parallelized discrete exterior calculus for three-dimensional elliptic problems
Boom, P., Seepujak, A., Kosmas, O., Margetts, L. & Jivkov, A., 1 Oct 2022, In: Computer Physics Communications. 279, 10 p., 108456.
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2021
A guide to the finite and virtual element methods for elasticity
Berbatov, K., Lazarov, B. & Jivkov, A., Nov 2021, In: Applied Numerical Mathematics. 169, p. 351-395 45 p.
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Boundary value problem on a weighted graph relevant to the static analysis of truss structures
Kodsi, C. & Jivkov, A., 17 Jun 2021, In: SIAM Journal of Applied Mathematics. 81, 3, p. 1190-1201 12 p.
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On the derivation of multisymplectic variational integrators for hyperbolic PDEs using exponential functions
Kosmas, O., Boom, P. & Jivkov, A., 25 Aug 2021, In: Applied Sciences. 11, 17, 11 p., 7837.
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On the geometric description of non linear elasticity via an energy approach using barycentric coordinates
Kosmas, O., Boom, P. & Jivkov, A., 19 Jul 2021, In: Mathematics. 9, 1689.
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Optimisation of rGO-enriched nanoceramics by combinatorial analysis
Borodin, E., Jivkov, A., Sheinerman, A. & Gutkin, M. Y., 15 Dec 2021, In: Materials & Design. 212, 11 p., 110191.
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Triple junctions network as the key pattern for characterisation of grain structure evolution in metals
Zhu, S., Borodin, E. & Jivkov, A., 1 Jan 2021, In: Materials & Design. 198, 6 p., 109352.
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2020
Geometric modelling of elastic and elastic-plastic solids by separation of deformation energy and Prandtl operators
Seruga, D., Kosmas, O. & Jivkov, A., 1 Aug 2020, In: International Journal of Solids and Structures. 198, p. 136-148 13 p.
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A geometric formulation of linear elasticity based on Discrete Exterior Calculus

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