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Deterministic mathematical models, such as those specified via differential equations, are a powerful tool to communicate scientific insight. However, such models are necessarily simplified descriptions of the real world. Generalised…
A conception of inhomogeneous locally random distribution of microdefects in crystalline solids is proposed. A method to calculate some physical properties of solids, containing inhomogeneously distributed defects, is developed. A…
Parametric statistical methods play a central role in analyzing risk through its underlying frequency and severity components. Given the wide availability of numerical algorithms and high-speed computers, researchers and practitioners often…
We consider microstructure as an arbitrary contamination of the underlying latent securities price, through a Markov kernel $Q$. Special cases include additive error, rounding and combinations thereof. Our main result is that, subject to…
Frailty models are essential tools in survival analysis for addressing unobserved heterogeneity and random effects in the data. These models incorporate a random effect, the frailty, which is assumed to impact the hazard rate…
Ensuring structural reliability remains a core concern in civil engineering, yet the quantitative effects of quality control measures on material variability and safety margins are not fully understood, especially for materials other than…
Motivated by results of the topological theory of glasses accounting for geometric frustration, we develop the simplest possible continuum mechanical model of defect dynamics in metallic glasses that accounts for topological, energetic, and…
Metal additive manufacturing has gained extensive attention from research institutes and companies to fabricate intricate parts and functionally graded materials. However, the porosity of the as-built part deteriorates the mechanical…
In this work we propose an Uncertainty Quantification methodology for sedimentary basins evolution under mechanical and geochemical compaction processes, which we model as a coupled, time-dependent, non-linear, monodimensional (depth-only)…
Granular materials can fail through spontaneous events like earthquakes or brittle fracture. However, measurements and analytic models which forecast failure in this class of materials, while of both fundamental and practical interest,…
In complex crystals close to melting or at finite temperatures, different types of defects are ubiquitous and their role becomes relevant in the mechanical response of these solids. Conventional elasticity theory fails to provide a…
Predicting the failure and plasticity of solids remains a longstanding challenge, with broad implications for materials design and functional reliability. Disordered solids like metallic glasses can fail either abruptly or gradually without…
The aim of this article is to analyze data from multiple repairable systems under the presence of dependent competing risks. In order to model this dependence structure, we adopted the well-known shared frailty model. This model provides a…
The origin of the anomalously compliant behavior of nanoporous gold is studied by comparing the elasticity obtained from molecular dynamics (MD) and finite element method (FEM) simulations. Both models yield a compliance, which is much…
Multiscale models of materials, consisting of upscaling discrete simulations to continuum models, are unique in their capability to simulate complex materials behavior. The fundamental limitation in multiscale models is the presence of…
In this paper, we present an approach for modeling bio-tissues that incorporates the variability in properties as part of their characteristics. This is achieved by considering the parameters of the model of a biomaterial to themselves be…
Uncertainty quantification (UQ) is crucial in machine learning, yet most (axiomatic) studies of uncertainty measures focus on classification, leaving a gap in regression settings with limited formal justification and evaluations. In this…
Rapid progress in additive manufacturing methods has created a new class of ultralight and strong architected metamaterials that resemble periodic truss structures. The mechanical performance of these metamaterials with a very large number…
Uncertainty quantification (UQ) has increasing importance in building robust high-performance and generalizable materials property prediction models. It can also be used in active learning to train better models by focusing on getting new…
Uncertainty quantification in Artificial Intelligence (AI)-based predictions of material properties is of immense importance for the success and reliability of AI applications in material science. While confidence intervals are commonly…