Simulation and the monte carlo method

http://www.ukm.my/kamal3/psm/pfpstochastics.pdf

The stochastic finite element method: Past, present and future

Statistical learning of materials properties or functions so far starts with a largely silent, nonchallenged step: the choice of the set of descriptive parameters (termed descriptor). However, when the scientific connection between the descriptor and the actuating mechanisms is unclear, the causality of the learned descriptor-property relation is uncertain. Thus, a trustful prediction of new promising materials, identification of anomalies, and scientific advancement are doubtful. We analyze this issue and define requirements for a suitable descriptor. For a classic example, the energy difference of zinc blende or wurtzite and rocksalt semiconductors, we demonstrate how a meaningful descriptor can be found systematically.

Big Data of Materials Science -- Critical Role of the Descriptor

In this paper the authors derive a higher-order shear deformation theory for modeling functionally graded plates accounting for extensibility in the thickness direction. The explicit governing equations and boundary conditions are obtained using the principle of virtual displacements under Carrera’s Unified Formulation. The static and eigenproblems are solved by collocation with radial basis functions. The efficiency of the present approach is assessed with numerical results including deflection, stresses, free vibration, and buckling of functionally graded isotropic plates and functionally graded sandwich plates.

/pdf/static-free-vibration-and-buckling-analysis-of-isotropic-and-3kzg33vvlb.pdf

Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique

Digital image correlation for surface deformation measurement: historical developments, recent advances and future goals

Digital image correlation analysis of interfacial debonding properties and fracture behavior in concrete

A stochastic computational method for evaluation of global and local behavior of random elastic media

Stochastic simulation of non-Gaussian/non-stationary properties in a functionally graded plate

In this work a spectral stochastic computational scheme is proposed that links the global properties of multi-phase periodic composites to the geometry and random material properties of their microstructural components. To propagate the uncertainties associated with the material properties to the microstructural response the scheme benefits from a combination of homogenization theory built into a finite element framework and the spectral representation of uncertainty based on Hermite Chaos where a probabilistic characterization of the solutions to a set of local problems defined on the period cell is first sought. A full stochastic description of the global (effective) properties is then obtained by averaging the solutions to the forgoing set of local problems over the unit cell. A representative subset of results is compared with the results obtained using Monte Carlo simulation to demonstrate the accuracy of the proposed procedure. Copyright © 2010 John Wiley & Sons, Ltd.

A multi‐scale spectral stochastic method for homogenization of multi‐phase periodic composites with random material properties

We perform two-dimensional dynamic fracture simulations of a specimen in biaxial tension, incorporating various distributions of pre-existing microcracks. The simulations consider the spatial distribution of flaws while modeling the discrete failure processes of crack interactions and coalescence, and predict the macroscopic variability in failure strength. The model quantitatively predicts the effect (on the dynamic failure strength) of different shapes of the flaw size distribution function, the random spatial distribution of flaws, and the random local resistance to crack growth (i.e. strength) associated with each flaw. The effect of changing material volumes on the variability in failure strengths is also examined in relation to the flaw size distribution. The effect of loading rate on the variability in failure strengths is presented in a form that will enable improved constitutive modeling using non-local formulations at the continuum scale. (C) 2010 Elsevier Ltd. All rights reserved.

Lori Graham-Brady

Papers

Digital image correlation analysis of interfacial debonding properties and fracture behavior in concrete

A stochastic computational method for evaluation of global and local behavior of random elastic media

Stochastic simulation of non-Gaussian/non-stationary properties in a functionally graded plate

A multi‐scale spectral stochastic method for homogenization of multi‐phase periodic composites with random material properties

Predicting variability in the dynamic failure strength of brittle materials considering pre-existing flaws