Uncertainty quantification in computational stochastic multiscale analysis of nonlinear elastic materials

Uncertainty quantification in computational stochastic multiscale analysis of nonlinear elastic materials

This paper is devoted to a computational stochastic multiscale analysis of nonlinear structures made up of heterogeneous hyperelastic materials. At the microscale level, the nonlinear constitutive equation of the material is characterized by a stochastic potential for which a polynomial chaos representation is used. The geometry of the microstructure is random and characterized by a high number...

An Efficient Computational Framework for Uncertainty Quantification in Multiscale Systems

Uncertainty Quantification in Computational Electromagnetics : The stochastic approach

— Models in electromagnetism are more and more accurate. In some applications, the gap between the experience and the model comes from the deviation on input data of the model which are not perfectly known. The stochastic approach can be used to quantify the effect of these input data uncertainties on the outputs of the model. In this article, the application of such approach in computational e...

Stochastic Toolkit for Uncertainty Quantification in complex nonlinear systems

1 Prliminaries 2 1.1 Basic Probability concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Stochastic Differential Equations (SDE’s) . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.1 Langevin equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.2 Ito integral and basics of Ito calculus . . . . . . . . . . . . . . ....

Multiscale Evaluation of the Nonlinear Elastic Properties of Carbon Nanotubes Under Finite Deformation

This paper deals with the calculation of the elastic properties for single-walled carbon nanotubes (SWCNTs) under axial deformation and hydrostatic pressure using the atomistic-based continuum approach and the deformation mapping technique. A hyperelastic model based on the higher-order Cauchy-Born (HCB) rule being applicable at finite strains and accounting for the chirality and material nonli...