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Data-based derivation of material response. (English) Zbl 1439.74050
Summary: This paper proposes a method to identify the strain-stress relation of non-linear elastic materials, without any underlying constitutive equation. The approach is based on the concept of Data Driven Computational Mechanics recently introduced by T. Kirchdoerfer and M. Ortiz [ibid. 304, 81–101 (2016; Zbl 1425.74503)]. From a collection of non-homogeneous strain fields, for example measured through Digital Image Correlation, the algorithm builds a database of strain-stress couples that sample the mechanical response of the material for the range of measured strains. The method is first derived for truss structures and then extended to the case of small-strain elasticity. The method accuracy, sensitivity to measurement noise and parameters are discussed using manufactured data.

MSC:
74B20 Nonlinear elasticity
74S05 Finite element methods applied to problems in solid mechanics
62N05 Reliability and life testing
62P30 Applications of statistics in engineering and industry; control charts
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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