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Stochastic modeling and identification of a hyperelastic constitutive model for laminated composites

Publication ,  Journal Article
Staber, B; Guilleminot, J; Soize, C; Michopoulos, J; Iliopoulos, A
Published in: Computer Methods in Applied Mechanics and Engineering
April 15, 2019

In this paper, we investigate the construction and identification of a new random field model for representing the constitutive behavior of laminated composites. Here, the material is modeled as a random hyperelastic medium characterized by a spatially dependent, stochastic and anisotropic strain energy function. The latter is parametrized by a set of material parameters, modeled as non-Gaussian random fields. From a probabilistic standpoint, the construction is first achieved by invoking information theory and the principle of maximum entropy. Constraints related to existence theorems in finite elasticity are, in particular, accounted for in the formulation. The identification of the parameters defining the random fields is subsequently addressed. This issue is attacked as a two-step problem where the mean model is calibrated in a first step, by imposing a match between the linearized model and nominal values proposed in the literature. The remaining parameters controlling the fluctuations are next estimated by solving an inverse problem in which principal component analysis and the maximum likelihood method are combined. The whole framework is illustrated considering an experimental database where multi-axial measurements are performed on a carbon-epoxy laminate. This work constitutes a first step towards the development of an integrated framework that will support decision making under uncertainty for the design, certification and qualification of composite materials and structures.

Duke Scholars

Published In

Computer Methods in Applied Mechanics and Engineering

DOI

ISSN

0045-7825

Publication Date

April 15, 2019

Volume

347

Start / End Page

425 / 444

Related Subject Headings

  • Applied Mathematics
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 01 Mathematical Sciences
 

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Staber, B., Guilleminot, J., Soize, C., Michopoulos, J., & Iliopoulos, A. (2019). Stochastic modeling and identification of a hyperelastic constitutive model for laminated composites. Computer Methods in Applied Mechanics and Engineering, 347, 425–444. https://doi.org/10.1016/j.cma.2018.12.036
Staber, B., J. Guilleminot, C. Soize, J. Michopoulos, and A. Iliopoulos. “Stochastic modeling and identification of a hyperelastic constitutive model for laminated composites.” Computer Methods in Applied Mechanics and Engineering 347 (April 15, 2019): 425–44. https://doi.org/10.1016/j.cma.2018.12.036.
Staber B, Guilleminot J, Soize C, Michopoulos J, Iliopoulos A. Stochastic modeling and identification of a hyperelastic constitutive model for laminated composites. Computer Methods in Applied Mechanics and Engineering. 2019 Apr 15;347:425–44.
Staber, B., et al. “Stochastic modeling and identification of a hyperelastic constitutive model for laminated composites.” Computer Methods in Applied Mechanics and Engineering, vol. 347, Apr. 2019, pp. 425–44. Scopus, doi:10.1016/j.cma.2018.12.036.
Staber B, Guilleminot J, Soize C, Michopoulos J, Iliopoulos A. Stochastic modeling and identification of a hyperelastic constitutive model for laminated composites. Computer Methods in Applied Mechanics and Engineering. 2019 Apr 15;347:425–444.
Journal cover image

Published In

Computer Methods in Applied Mechanics and Engineering

DOI

ISSN

0045-7825

Publication Date

April 15, 2019

Volume

347

Start / End Page

425 / 444

Related Subject Headings

  • Applied Mathematics
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 01 Mathematical Sciences