2020
DOI: 10.1088/1361-6420/abbc76
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Nonlinear Cauchy problem and identification in contact mechanics: a solving method based on Bregman-gap

Abstract: This paper proposes a solution method for identification problems in the context of contact mechanics when overabundant data are available on a part Γm of the domain boundary while data are missing from another part of this boundary. The first step is then to find a solution to a Cauchy problem. The method used by the authors for solving Cauchy problems consists of expanding the displacement field known on Γm towards the inside of the solid via the minimization of a function that measures the gap between solut… Show more

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Cited by 6 publications
(3 citation statements)
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“…The perspectives of direct applications are numerous. In inverse problems, the symmetrized Bregman Gaps have been used, even if not always under this denomination, for nonlinear Cauchy problems in mechanics and the subsequent identification problems (nonlinear elasticity with small transformations, [9], plastic zones identification [10], cracks identification in contact mechanics [11]). As mentioned in the introduction, replacement of usual least-squares functionals in various algorithms or procedures in nonlinear mechanics and data-driven approaches can also be of interest and is seemingly straightforward.…”
Section: Discussionmentioning
confidence: 99%
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“…The perspectives of direct applications are numerous. In inverse problems, the symmetrized Bregman Gaps have been used, even if not always under this denomination, for nonlinear Cauchy problems in mechanics and the subsequent identification problems (nonlinear elasticity with small transformations, [9], plastic zones identification [10], cracks identification in contact mechanics [11]). As mentioned in the introduction, replacement of usual least-squares functionals in various algorithms or procedures in nonlinear mechanics and data-driven approaches can also be of interest and is seemingly straightforward.…”
Section: Discussionmentioning
confidence: 99%
“…For the simplicity of the presentation, we now limit ourselves to isothermal evolutions. The Euler implicit time incremental form of these constitutive equations reads: (11) showing that the (thermodynamically) conjugate couples for describing the thermodynamic state are [(σ + ∆σ,ε + ∆ε),(A + ∆A,α + ∆α)]. So, denoting:…”
Section: Generating Functions In Thermomechanics For Generalized Stan...mentioning
confidence: 99%
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