A comment on the article "The Schwarz alternating method in solid mechanics" by Alejandro Mota, Irina Tezaur and Coleman Alleman [Comput. Methods Appl. Mech. Engrg. 319 (2017) 1951]

TL;DR

This paper critically reviews a recent extension of the Schwarz alternating method to finite-deformation solid mechanics, highlighting significant errors in the original work's mechanics and mathematical foundations.

Contribution

It provides a detailed critique of the original paper's theoretical and practical claims, emphasizing the importance of correct mechanics and elasticity principles.

Findings

Identifies serious errors in the original work's mechanics assumptions

Highlights flaws in the mathematical elasticity proofs

Underscores the need for rigorous validation in computational mechanics methods

Abstract

Recently, in the paper "The Schwarz alternating method in solid mechanics" by Alejandro Mota, Irina Tezaur and Coleman Alleman [Comput. Methods Appl. Mech. Engrg. 319 (2017) 1951] the authors extended the well known Schwarz alternating method from linear to finite-deformation solid mechanics. They developed and introduced four variants of the Schwarz alternating method, presented proof of geometric convergence of the method and prepared parallel implementation applied to some examples. Unfortunately, the work contains serious errors, both from the point of view of finite-deformation solid mechanics as well as mathematical elasticity.