TY - JOUR
T1 - Nonlinear convergence in contact mechanics
T2 - Immersed boundary finite volume
AU - Mehmani, Yashar
AU - Castelletto, Nicola
AU - Tchelepi, Hamdi A.
N1 - Funding Information:
Funding for this work was provided by the Stanford University Petroleum Research Institute (SUPRI-B affiliates), USA . We acknowledge the Center for Mechanistic Control of Unconventional Formations (CMC-UF), an Energy Frontier Research Center funded by the U.S. Department of Energy under Contract number DE-SC0019165 . We are grateful to the Center for Computational Earth & Environmental Science (CEES) at Stanford University for access to computational resources. Portions of this work were performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07-NA27344. The authors thank Joshua White for encouragements and fruitful discussions.
Publisher Copyright:
© 2021 Elsevier B.V.
PY - 2021/9/1
Y1 - 2021/9/1
N2 - 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.
AB - 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.
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U2 - 10.1016/j.cma.2021.113929
DO - 10.1016/j.cma.2021.113929
M3 - Article
AN - SCOPUS:85106388238
VL - 383
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0374-2830
M1 - 113929
ER -