Nonlinear convergence in contact mechanics: Immersed boundary finite volume

We present an immersed boundary finite volume (IBM) method for simulating quasistatic contact mechanics of linearly elastic domains at small strains. In IBM, all external boundaries and internal contacts of an object are represented by embedded surfaces inside a Cartesian mesh, which need not confor...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2021-09, Vol.383 (C), p.113929, Article 113929
Main Authors: Mehmani, Yashar, Castelletto, Nicola, Tchelepi, Hamdi A.
Format: Article
Language:English
Subjects:
Cartesian coordinates
Contact mechanics
Convergence
Finite element method
Finite volume
Immersed boundary
Interpolation
Mechanics (physics)
Newton methods
Newton solver
Nonlinear convergence
Nonlinear systems
Parameter modification
Pattern analysis
Porous media
Solvers
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Summary:We present an immersed boundary finite volume (IBM) method for simulating quasistatic contact mechanics of linearly elastic domains at small strains. In IBM, all external boundaries and internal contacts of an object are represented by embedded surfaces inside a Cartesian mesh, which need not conform to the grid lines. The contact constraints consist of the non-penetrability condition and Coulomb’s friction law, which are discretized using special interpolation stencils and enforced via penalty parameters. The resulting nonlinear system depends on displacement unknowns only. To solve it, we use the Newton method but find that it diverges frequently. To understand the divergence pattern, we analyze a simplified 2-cell problem and show that the global convergence of Newton cannot be ensured for any choice of penalty parameters. We thus propose a modified Newton solver, which guarantees convergence for the 2-cell problem and is numerically verified to converge for all the challenging simulations considered herein. While both 1st- and 2nd-order variants of IBM, in displacement unknowns, are proposed, the modified Newton solver applies only to the 1st-order variant. •Immersed boundary finite volume method proposed for contact mechanics.•Contact equations are enforced using a penalty formulation.•Newton convergence analyzed for a 2N-cell problem in 2D and 3D.•No choice of penalty parameters guarantees convergence to an accurate solution.•Newton solver is modified to guarantee convergence to an accurate solution.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2021.113929