The equilibrium problem for a hyperelastic body with a crack crossing the boundary at zero angle
Abstract
We study the equilibrium problem for a hyperelastic body containing a crack that crosses the boundary at zero angle. First, we consider the case where the crack and the boundary form a regular cusp. The problem is formulated as minimization of an energy functional over a set of admissible deformations and we prove an existence theorem. Then we address the general case of an irregular cusp. For this case, we develop an approach based on the fictitious domain method, which allows us to relax the restrictive geometric assumptions on the cusp sharpness and to prove an existence theorem for the corresponding variational problem.
Fields of Study & Subjects
Contact Mechanics and Variational Inequalities
Nonlinear Partial Differential Equations
Optimization and Variational Analysis
Publication details
- Journal / source
- Журнал «Математические заметки СВФУ»
- Publisher
- North-Eastern Federal University
- Volume
- 33
- Issue
- 1
- Pages
- 56–72
- Publication date
- 13 April 2026