A constrained-optimization methodology for the detection phase in contact mechanics simulations

• Published in: International journal for numerical methods in engineering Vol. 96; no. 5; pp. 323 - 338
• Main Authors: Aragón, Alejandro M., Yastrebov, Vladislav A., Molinari, Jean-François
• Format: Journal Article
• Language: English
• Published: Chichester Blackwell Publishing Ltd 02.11.2013; Wiley; Wiley Subscription Services, Inc
• Subjects: collision detection; constrained optimization; Contact; contact detection; contact mechanics; Copyrights; Engineering Sciences; Exact sciences and technology; Finite element method; Fundamental areas of phenomenology (including applications); Inequalities; Materials; Mathematical analysis; Mathematical models; Mechanical contact (friction...); Optimization; Physics; Reproduction; Solid mechanics; Structural and continuum mechanics; collision detection; Local search; contact detection; Constraint; Collision; Linear programming; Mechanical contact; contact mechanics; Automatic mesh generation; Modeling; Differentiable manifold; Global local method; Constrained optimization; Finite element method; Computational geometry; Quadratic approximation; Inequality; constrained optimization
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.4561

SUMMARY The detection phase in computational contact mechanics can be subdivided into a global search and a local detection. When potential contact is detected by the former, a rigorous local detection determines which surface elements come or may come in contact in the current increment. We first introduce a rigorous definition of the closest point for non‐differentiable lower‐dimensional manifolds. We then simplify the detection by formulating an optimization problem subject to inequality constraints. The formulation is then solved using different techniques from the field of mathematical optimization, for both linear and quadratic finite element meshes. The resulting general and robust detection scheme is tested on a set of problems and compared with other techniques commonly used in computational geometry. Copyright © 2013 John Wiley & Sons, Ltd.