Projects per year
Abstract
The deformation of a solid in Euclidean space, caused by the change of boundary conditions, can be fully described via a deformation gradient. For reversible (conservative) solid behaviour, the work done by changing boundary conditions is stored as a potential (elastic) energy, a function of the deformation gradient invariants. Using this, we present a discrete energy formulation that uses maps between nodal positions, which are linked via standard barycentric coordinates. A derivation is provided for domains tessellated by tetrahedrons, where the energy functionals are constrained with prescribed boundary conditions via Lagrange multipliers. Analysis of such domains is performed via energy minimisation, where the constraints and eliminated via premultiplication of the discrete equations by a discrete nullspace matrix of the constraint gradients. Numerical examples are provided to verify the accuracy of the proposed technique. The definition of standard barycentric coordinates is restricted to three dimensional convex polygons. We show that for an explicit energy expression, applicable also to nonconvex polytopes, general barycentric coordinates can be a fundamental tool. We define the discrete energy via a gradient for general polytopes, which is a natural extension of the definition for discrete domains tessellated by tetrahedra. We finally prove that the resulting expressions can fully define the deformation of solids.
Original language  English 

Article number  1689 
Journal  Mathematics 
Volume  9 
DOIs  
Publication status  Published  19 Jul 2021 
Keywords
 nonlinear elasticity
 general barycentric coordinates
 energy minimization
 Lagrange multipliers
 nullspace method
Fingerprint
Dive into the research topics of 'On the geometric description of non linear elasticity via an energy approach using barycentric coordinates'. Together they form a unique fingerprint.Projects
 1 Finished

Geometric Mechanics of Solids: new analysis of modern engineering materials  GEMS
1/11/16 → 31/10/21
Project: Research
Research output
 7 Article

A discrete model for forcebased 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.Research output: Contribution to journal › Article › peerreview
Open AccessFile20 Downloads (Pure) 
A geometric formulation of linear elasticity based on Discrete Exterior Calculus
Boom, P., Kosmas, O., Margetts, L. & Jivkov, A., 1 Feb 2022, In: International Journal of Solids and Structures. 236237, 12 p., 111345.Research output: Contribution to journal › Article › peerreview
Open AccessFile93 Downloads (Pure) 
Diffusion in multidimensional solids using Forman's combinatorial differential forms
Berbatov, K., Boom, P., Hazel, A. & Jivkov, A., 1 Oct 2022, In: Applied Mathematical Modelling. 110, p. 172192 21 p.Research output: Contribution to journal › Article › peerreview
Open AccessFile73 Downloads (Pure)