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In this work we introduce and analyze a new multiscale method for strongly nonlinear monotone equations in the spirit of the Localized Orthogonal Decomposition. A problem-adapted multiscale space is constructed by solving linear local…
This paper presents a novel stochastic framework to quantify the knock down in strength from out-of-plane wrinkles at the coupon level. The key innovation is a Markov Chain Monte Carlo algorithm which rigorously derives the stochastic…
This paper presents a hybrid continuum discrete macro modelling strategy with a multiscale calibration procedure for realistic simulations of brick masonry bridges. The response of these structures is affected by the intrinsic nonlinearity…
Knowledge of the mechanical properties of materials is required for the design and analysis of engineering products, however, the characterisation of heterogeneous properties using traditional techniques is limited by spatial resolution or…
We develop estimation and inference methods for a stylized macroeconomic model with potentially multiple behavioural equilibria, where agents form expectations using a constant-gain learning rule. We first show geometric ergodicity of the…
In this paper we propose a novel numerical approach for the Boltzmann equation with uncertainties. The method combines the efficiency of classical direct simulation Monte Carlo (DSMC) schemes in the phase space together with the accuracy of…
We present a new method for stochastic shape optimisation of engineering structures. The method generalises an existing deterministic scheme, in which the structure is represented and evolved by a level-set method coupled with mathematical…
There is increasing interest in using high-energy collisions to probe the structure of nuclei, in particular with the high-precision data made possible by collisions performed with pairs of isobaric species. A systematic study requires a…
Sampling orthogonal polynomial bases via Monte Carlo is of interest for uncertainty quantification of models with high-dimensional random inputs, using Polynomial Chaos (PC) expansions. It is known that bounding a probabilistic parameter,…
A thresholded Gaussian random field model is developed for the microstructure of porous materials. Defining the random field as a solution to stochastic partial differential equation allows for flexible modelling of non-stationarities in…
In the analysis of composite materials with heterogeneous microstructures, full resolution of the heterogeneities using classical numerical approaches can be computationally prohibitive. This paper presents a micromechanics-enhanced finite…
A micromorphic computational homogenization framework has recently been developed to deal with materials showing long-range correlated interactions, i.e. displaying patterning modes. Typical examples of such materials are elastomeric…
We consider linearizations of stochastic differential equations with additive noise using the Karhunen-Lo\`eve expansion. We obtain our linearizations by truncating the expansion and writing the solution as a series of matrix-vector…
Presence of a high-dimensional stochastic parameter space with discontinuities poses major computational challenges in analyzing and quantifying the effects of the uncertainties in a physical system. In this paper, we propose a stochastic…
In this paper an asymptotic homogenization method for the analysis of composite materials with periodic microstructure in presence of thermodiffusion is described. Appropriate down-scaling relations correlating the microscopic fields to the…
Motivated by an application involving additively manufactured bioresorbable polymer scaffolds supporting bone tissue regeneration, we investigate the impact of uncertain geometry perturbations on the effective mechanical properties of…
The goal of this paper is to develop a reliable analytical approach to finding the effective elastic-plastic response of metal matrix composites (MMC) and porous metals (PM) with a predefined particle or void distribution, as well as to…
Stochastic approximation is a framework unifying many random iterative algorithms occurring in a diverse range of applications. The stability of the process is often difficult to verify in practical applications and the process may even be…
In this letter, we develop a framework to study the mechanical response of athermal amorphous solids via a coupling of mesoscale and microscopic models. Using measurements of coarse grained quantities from simulations of dense disordered…
The paper deals with optimization of the acoustic band gaps computed using the homogenized model of strongly heterogeneous elastic composite which is constituted by soft inclusions periodically distributed in stiff elastic matrix. We employ…