TY - JOUR

T1 - Imprecise random field analysis for non-linear concrete damage analysis

AU - Dannert, Mona M.

AU - Faes, Matthias G.R.

AU - Fleury, Rodolfo M.N.

AU - Fau, Amelie

AU - Nackenhorst, Udo

AU - Moens, David

N1 - Funding Information: The support of the German Research Foundation (DFG) during the priority program SPP 1886 (NA330/12-1) is gratefully acknowledged. Matthias Faes acknowledges the support of the Research Foundation Flanders (FWO) under Grant No. 12P3519N. The support of the French-German University is acknowledged under the French-German doctoral college Sophisticated Numerical and Testing Approaches (SNTA), grant DFDK 04-19. This work was supported by the compute cluster, which is funded by the Leibniz University of Hannover, the Lower Saxony Ministry of Science and Culture (MWK) and the German Research Foundation (DFG).

PY - 2021/3

Y1 - 2021/3

N2 - Imprecise random fields consider both, aleatory and epistemic uncertainties. In this paper, spatially varying material parameters representing the constitutive parameters of a damage model for concrete are defined as imprecise random fields by assuming an interval valued correlation length. For each correlation length value, the corresponding random field is discretized by Karhunen-Loève expansion. In a first study, the effect of the series truncation is discussed as well as the resulting variance error on the probability box (p-box) that represents uncertainty on the damage in a concrete beam as a result of the imprecise random field. It is shown that a certain awareness for the influence of the truncation order on the local field variance is needed when the series is truncated according to a fixed mean variance error. In the following case study, the main investigation is on the propagation of imprecise random fields in the context of non-linear finite element problems, i.e. quasi-brittle damage of a four-point bended concrete beam. The global and local damage as the quantities of interest are described by a p-box. The influence of several imprecise random field input parameters to the resulting p-boxes is studied. Furthermore, it is examined whether correlation length values located within the interval, so-called intermediate values, affect the p-box bounds. It is shown that, from the engineering point of view, a pure vertex analysis of the correlation length intervals is sufficient to determine the p-box in this context.

AB - Imprecise random fields consider both, aleatory and epistemic uncertainties. In this paper, spatially varying material parameters representing the constitutive parameters of a damage model for concrete are defined as imprecise random fields by assuming an interval valued correlation length. For each correlation length value, the corresponding random field is discretized by Karhunen-Loève expansion. In a first study, the effect of the series truncation is discussed as well as the resulting variance error on the probability box (p-box) that represents uncertainty on the damage in a concrete beam as a result of the imprecise random field. It is shown that a certain awareness for the influence of the truncation order on the local field variance is needed when the series is truncated according to a fixed mean variance error. In the following case study, the main investigation is on the propagation of imprecise random fields in the context of non-linear finite element problems, i.e. quasi-brittle damage of a four-point bended concrete beam. The global and local damage as the quantities of interest are described by a p-box. The influence of several imprecise random field input parameters to the resulting p-boxes is studied. Furthermore, it is examined whether correlation length values located within the interval, so-called intermediate values, affect the p-box bounds. It is shown that, from the engineering point of view, a pure vertex analysis of the correlation length intervals is sufficient to determine the p-box in this context.

KW - Imprecise random fields

KW - Interval valued correlation length

KW - Karhunen-Loève expansion

KW - Non-linear stochastic finite element method

KW - Probability box approach

KW - Uncertainty quantification

UR - http://www.scopus.com/inward/record.url?scp=85095695796&partnerID=8YFLogxK

U2 - 10.1016/j.ymssp.2020.107343

DO - 10.1016/j.ymssp.2020.107343

M3 - Article

AN - SCOPUS:85095695796

VL - 150

JO - Mechanical Systems and Signal Processing

JF - Mechanical Systems and Signal Processing

SN - 0888-3270

M1 - 107343

ER -