2020/04/01 by Sören Bartels, Bartels, Sören, Christian Palus +1 · 1 citation
Computer Science · Engineering · #65N12 #65N30 #74K20 #Advanced Materials and Mechanics #Advanced Numerical Analysis Techniques #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2004.00341
openalex publication_date 2020/04/01 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
Bilayer plates are compound materials that exhibit large bending deformations\nwhen exposed to environmental changes that lead to different mechanical\nresponses in the involved materials. In this article a new numerical method\nwhich is suitable for simulating the isometric deformation induced by a given\nmaterial mismatch in a bilayer plate is discussed. A dimensionally reduced\nformulation of the bending energy is discretized generically in an abstract\nsetting and specified for discrete Kirchhoff triangles; convergence towards the\ncontinuous formulation is proved. A practical semi-implicit discrete gradient\nflow employing a linearization of the isometry constraint is proposed as an\niterative method for the minimization of the bending energy; stability and a\nbound on the violation of the isometry constraint are proved. The incorporation\nof obstacles is discussed and the practical performance of the method is\nillustrated with numerical experiments involving the simulation of large\nbending deformations and investigation of contact phenomena.\n