Lippmann‐Schwinger solvers for the computational homogenization of materials with pores

Summary We show that under suitable hypotheses on the nonporous material law and a geometric regularity condition on the pore space, Moulinec‐Suquet's basic solution scheme converges linearly. We also discuss for which derived solvers a (super)linear convergence behavior may be obtained, and fo...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2020-11, Vol.121 (22), p.5017-5041
Main Author: Schneider, Matti
Format: Article
Language:English
Subjects:
Basic converters
computational homogenization
Convergence
FFT‐based computational micromechanics
Homogenization
porous materials
Solvers
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Summary:Summary We show that under suitable hypotheses on the nonporous material law and a geometric regularity condition on the pore space, Moulinec‐Suquet's basic solution scheme converges linearly. We also discuss for which derived solvers a (super)linear convergence behavior may be obtained, and for which such results do not hold, in general. The key technical argument relies on a specific subspace on which the homogenization problem is nondegenerate, and which is preserved by iterations of the basic scheme. Our line of argument is based in the nondiscretized setting, and we draw conclusions on the convergence behavior for discretized solution schemes in FFT‐based computational homogenization. Also, we see how the geometry of the pores' interface enters the convergence estimates. We provide computational experiments underlining our claims.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.6508