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A Geometric Formulation of Linear Elasticity Based on Discrete Exterior Calculus
- Source :
- Boom, P, Kosmas, O, Margetts, L & Jivkov, A 2022, ' A geometric formulation of linear elasticity based on Discrete Exterior Calculus ', International Journal of Solids and Structures, vol. 236-237, 111345 . https://doi.org/10.1016/j.ijsolstr.2021.111345
- Publication Year :
- 2021
-
Abstract
- A direct formulation of linear elasticity of cell complexes based on discrete exterior calculus is presented. The primary unknowns are displacements, represented by a primal vector-valued 0-cochain. Displacement differences and internal forces are represented by a primal vector-valued 1-cochain and a dual vector-valued 2-cochain, respectively. The macroscopic constitutive relation is enforced at primal 0-cells with the help of musical isomorphisms mapping cochains to smooth fields and vice versa. The balance of linear momentum is established at primal 0-cells. The governing equations are solved as a Poisson's equation with a non-local and non-diagonal material Hodge star. Numerical simulations of several classical problems with analytic solutions are presented to validate the formulation. Excellent agreement with known solutions is obtained. The formulation provides a method to calculate the relations between displacement differences and internal forces for any lattice structure, when the structure is required to follow a prescribed macroscopic elastic behaviour. This is also the first and critical step in developing formulations for dissipative processes in cell complexes.
- Subjects :
- Constitutive equation
Structure (category theory)
FOS: Physical sciences
010103 numerical & computational mathematics
01 natural sciences
Displacement (vector)
General Materials Science
0101 mathematics
Hodge dual
Mathematical Physics
Mathematics
Elastic materials
Applied Mathematics
Mechanical Engineering
Mathematical analysis
Linear elasticity
Mathematical Physics (math-ph)
Condensed Matter Physics
Cohomology
0104 chemical sciences
010404 medicinal & biomolecular chemistry
Discrete exterior calculus
Mechanics of Materials
Modeling and Simulation
Dissipative system
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Boom, P, Kosmas, O, Margetts, L & Jivkov, A 2022, ' A geometric formulation of linear elasticity based on Discrete Exterior Calculus ', International Journal of Solids and Structures, vol. 236-237, 111345 . https://doi.org/10.1016/j.ijsolstr.2021.111345
- Accession number :
- edsair.doi.dedup.....6bc2816b5d33aecfc48aea2d6f628f56