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A general model is formulated for elasto-plastic materials undergoing linear kinematic hardening to describe microstructure evolution associated with phase transformations. Using infinitesimal strain theory, the model is based on…
This work proposes a novel theoretical framework of robust limit analysis i.e. the computation of limit loads of structures in presence of uncertainties using limit analysis and robust optimization theories. We first derive generic robust…
We quantify the uncertainty of the L\"ammer model of damage evolution when fitted to (noisy) observations of damage evolution in cyclic fatigue experiments with and without dwell time. We therefore develop a bootstrap method by sampling…
Robust optimization is a method for optimization under uncertainties in engineering systems and designs for applications ranging from aeronautics to nuclear. In a robust design process, parameter variability (or uncertainty) is incorporated…
Amorphous materials exhibit complex material proprteties with strongly nonlinear behaviors. Below a yield stress they behave as plastic solids, while they start to yield above a critical stress $\Sigma_c$. A key quantity controlling…
ML models have errors when used for predictions. The errors are unknown but can be quantified by model uncertainty. When multiple ML models are trained using the same training points, their model uncertainties may be statistically…
Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…
We present a novel approach to understand geometric-incompatibility-induced rigidity in under-constrained materials, including sub-isostatic 2D spring networks and 2D and 3D vertex models for dense biological tissues. We show that in all…
We address the problem of uncertainty quantification and propose measures of total, aleatoric, and epistemic uncertainty based on a known decomposition of (strictly) proper scoring rules, a specific type of loss function, into a divergence…
Recent advancements in machine learning-based methods have demonstrated great potential for improved property prediction in material science. However, reliable estimation of the confidence intervals for the predicted values remains a…
Uncertainty quantification (UQ) plays a major role in verification and validation of computational engineering models and simulations, and establishes trust in the predictive capability of computational models. In the materials science and…
In engineering applications almost all processes are described with the help of models. Especially forming machines heavily rely on mathematical models for control and condition monitoring. Inaccuracies during the modeling, manufacturing…
To control part quality, it is critical to analyze pore generation mechanisms, laying theoretical foundation for future porosity control. Current porosity analysis models use machine setting parameters, such as laser angle and part pose.…
The finite element method (FEM) is used to study the influence of porosity and pore shape on the elastic properties of model porous ceramics. The Young's modulus of each model was found to be practically independent of the solid Poisson's…
Numerical simulations of concrete fracture performed with a probabilistic mesoscale discrete model are presented. The model represents a substantial part of material randomness by assigning random locations to the largest aggregates. The…
Heterogeneity of many building materials complicates numerical modelling of structural behaviour. The material randomicity can be manifested by different values of material parameters of each material specimen. To capture inherent…
Methods for model parameter estimation, uncertainty quantification and experimental design are summarized in this paper. They are based on the generalized least squares estimator and different approximations of its covariance matrix using…
Based on existing ideas in the field of imprecise probabilities, we present a new approach for assessing the reliability of the individual predictions of a generative probabilistic classifier. We call this approach robustness…
Atomistic simulations often rely on interatomic potentials to access greater time- and length- scales than those accessible to first principles methods such as density functional theory (DFT). However, since a parameterised potential…
Recent research reveals that machine learning (ML) models are highly sensitive to minor changes in their training procedure, such as the inclusion or exclusion of a single data point, leading to conflicting predictions on individual data…