Adaptive multigrid methods for Signorini's problem in linear elasticity

We derive globally convergent multigrid methods for the discretized Signorini problem in linear elasticity. Special care has to be taken in the case of spatially varying normal directions. In numerical experiments for 2 and 3 space dimensions we observed similar convergence rates as for corresponding linear problems

The normal parameterization and its application to collision detection

Collision detection is a central task in the simulation of multibody systems. Depending on the description of the geometry, there are many efficient algorithms to address this need. A widespread approach is the common normal concept: potential contact points on opposing surfaces have antiparallel normal vectors. However, this approach leads to implicit equations that require iterative solutions when the geometries are described by implicit functions or the common parameterizations. We introduce the normal parameterization to describe the boundary of a strictly convex object as a function of the orientation of its normal vector. This parameterization depends on a scalar function, the so-called generating potential from which all properties are derived: points on the boundary, continuity/differentiability of the boundary, curvature, offset curves or surfaces. An explicit solution for collisions with a planar counterpart is derived and four iterative algorithms for collision detection between two arbitrary objects with the normal parametrization are compared. The application of this approach for collision detection in multibody models is illustrated in a case study with two ellipsoids and several planes

Adaptive finite elements for variational inequalities with non-smooth coefficients.

We consider an elliptic variational inequality with discontinuous coefficients arising in unilateral contact mechanics in linearized elasticity. The contact zone is an internal boundary separating sub-domains with difference elastic properties. We study some discrete formulations with mixed finite element methods and we give optimal error estimates in appropriate norms, independent of the variation of the elasticity coefficients. The focus of the article is the a posteriori analysis with residual error indicators. It is achieved both for the conforming and nonconforming discretization, in a unified framework. The residual error indicators are well suited to handle non-matching meshes and the contact conditions, and they allow us to obtain sharp and robust a posteriori estimates. An adaptive solution algorithm is proposed and few numerical experiments confirming the theory are presented.Nous considérons des discrétisations par éléments finis, conformes et non-conformes pour résoudre le problème de Signorini en contact unilatéral. Nous effectuons l'analyse a postériori avec des indicateurs d'erreur par résidu adaptés aux inéquations variationnelles. Nous obtenons des estimateurs optimaux. Un algorithme numérique mettant en oeuvre l'adaption de maillages avec ces indicateurs est proposé et quelques expériences numériques sont faites

Contact Detection and Constraints Enforcement for the Simulation of Pellet/Clad Thermo-Mechanical Contact in Nuclear Fuel Rods

As fission process heats up the fuel rods, UO2 pellets stacked on top of each other swell both radially and axially, while the surrounding Zircaloy cladding creeps down, so that the pellets eventually come into contact with the clad. This exacerbates chemical degradation of the protective cladding and high stress values may enable the formation and propagation of cracks, thus threatening the integrity of the clad. Along these lines, pellet-cladding interaction establishes itself as a major concern for fuel rod design and core operation in light water reactors. Accurately modeling fuel behavior is challenging because the mechanical contact problem strongly depends on temperature distribution and the pellet-clad coupled heat transfer problem is, in turn, affected by changes in geometry induced by body deformations and stresses generated at the contact interface. Our work focuses on active set strategies to determine the actual contact area in high-fidelity coupled physics fuel performance codes. The approach consists of two steps: in the first one, we determine the boundary region on standard finite element meshes where the contact conditions shall be enforced to prevent objects from occupying the same space. For this purpose, we developed and implemented an efficient parallel search algorithm for detecting mesh inter-penetration and vertex/mesh overlap. The second step deals with solving the mechanical equilibrium taking into account the contact conditions computed in the first step. To do so, we developed a modified version of the multi-point constraint strategy. While the original algorithm was restricted to the Jacobi preconditioned conjugate gradient method, our approach works with any Krylov solver and does not put any restriction on the type of preconditioner used. The multibody thermo-mechanical contact problem is tackled using modern numerics, with continuous finite elements and a Newton-based monolithic strategy to handle nonlinearities (the one stemming from the contact condition itself as well as the one due to the temperature-dependence of the fuel thermal conductivity, for instance) and coupling between the various physics components (gap conductance sensitive to the clad-pellet distance, thermal expansion coefficient or Young’s modulus affected by temperature changes, etc.). We will provide different numerical examples for contact problems using one and multiple bodies in order to demonstrate the performance of the method