Le Research Group

Stochastic Localization Limiters for heterogeneous materials

This project aims to develop a mechanism-based adaptive mapping algorithm for random fields of material properties in stochastic finite-element (FE) analyses of damage and fracture in heterogeneous materials such as concrete, rock, and ceramics. The mapping of random constitutive properties onto the FE mesh is explicitly tied to the prevailing damage mechanism, which evolves throughout the loading process. The proposed adaptive mapping ensures that the stochastic representation of the FE tangential stiffness remains consistent with the current damage state and localization pattern. The model further predicts that, as a consequence of localization instabilities, the probability distributions of strength and fracture properties at Gauss integration points depend on the mesh size.

Probabilistic modeling of localization-induced failures

The investigation of statistical scaling in localization-induced failures dates back to da Vinci’s speculation on the length effect on rope strength in 1500s. The early mathematical description of statistical scaling emerged with the birth of the extreme value statistics. The most commonly known mathematical model for statistical scaling is the Weibull size effect, which is a direct consequence of the infinite weakest-link model. However, abundant experimental observations on various localization-induced failures have shown that the Weibull size effect is inadequate. Two mathematical models are developed to describe the statistical size effect in localization-induced failures. One is the finite weakest-link model, in which the random structural resistance is expressed as the minimum of a set of independent discrete random variables. The other is the level excursion model, a continuum description of the finite weakest-link model, in which the structural failure probability is calculated as the probability of the upcrossing of a random field over a barrier.

Stochastic buckling of hemispherical shells

This project investigates the stochastic buckling behavior of thin shells, with particular emphasis on how the coupling between localization mechanisms and geometric imperfections governs the statistics of the pressure required to induce buckling in a hemispherical shell. Geometric imperfections are modeled as random surface fields superimposed on the nominal hemispherical geometry. The resulting probability distribution of the buckling pressure is evaluated using stochastic finite element analysis. Monte Carlo simulations are carried out over a wide range of radius-to-thickness ratios and imperfection correlation lengths. The primary outcome of the analysis is the identification of a statistical size effect in the knockdown factor, governed by the dimensionless radius. These results provide new insight into the universal statistical role of the dimensionless radius in controlling the buckling behavior of geometrically imperfect hemispherical shells.

Experimental characterization of spatial randomness of elastic and strength properties of heterogeneous materials

This project aims to develop an integrated experimental–numerical framework for characterizing the spatial randomness of elastic and strength properties in heterogeneous materials. The proposed method combines digital image correlation (DIC) with finite element (FE) analysis. An iterative identification procedure is employed in which the FE model is calibrated to match the strain fields measured by DIC, thereby enabling the reconstruction of the spatially varying elastic constants. The identified fields are subsequently used to compute the probability distributions, spatial autocorrelation functions, and cross-correlation functions of the elastic properties. The methodology is applied to microcrystalline cellulose tablets subjected to diametral compression. The experimental results demonstrate a clear influence of compaction pressure on the statistical characteristics of the elastic constants.

Energy scaling in rock cutting

This project aims to address the fundamental problem of energy scaling in rock cutting, namely the dependence of specific energy on the depth of cut. The research focuses on the development of scaling laws governing distinct failure regimes. Both continuum and discrete computational models are used to simulate the cutting process over a range of cutting depths. The proposed scaling laws will be validated experimentally using data from the existing literature as well as from newly planned experiments.

Stochastic Localization Limiters for heterogeneous materials

Probabilistic modeling of localization-induced failures

Stochastic buckling of hemispherical shells

Experimental characterization of spatial randomness of elastic and strength properties of heterogeneous materials

Energy scaling in rock cutting

We gratefully acknowledge financial support from our research sponsors