Related papers: Probabilistic failure mechanisms via Monte Carlo s…
This paper concerns with finite element approximations of a quasi-static poroelasticity model in displacement-pressure formulation which describes the dynamics of poro-elastic materials under an applied mechanical force on the boundary. To…
While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with random coefficients enjoy great popularity, combinations with spatial adaptivity seem to be rare. We present an adaptive MLMC…
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 statistical learning approach for parametric PDEs related to Uncertainty Quantification is derived. The method is based on the minimization of an empirical risk on a selected model class and it is shown to be applicable to a broad range…
Multilevel sampling methods, such as multilevel and multifidelity Monte Carlo, multilevel stochastic collocation, or delayed acceptance Markov chain Monte Carlo, have become standard uncertainty quantification (UQ) tools for a wide class of…
Fracture is a ubiquitous phenomenon in most composite engineering structures, and is often the responsible mechanism for catastrophic failure. Over the past several decades, many approaches have emerged to model and predict crack failure.…
In this paper we derive a new two-dimensional brittle fracture model for thin shells via dimension reduction, where the admissible displacements are only normal to the shell surface. The main steps include to endow the shell with a small…
In studies of the dynamic failure of brittle hydrogels, a bound has been placed on the process zone scale - the scale where material separation and ultimate failure occur. For the polyacrylamide hydrogel system under study, this bound is…
Practical structural engineering problems are often characterized by significant uncertainties. Historically, one of the prevalent methods to account for this uncertainty has been the standard Monte Carlo (MC) method. Recently, improved…
The multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty quantification in PDE models. It combines approximations at different levels of accuracy using a hierarchy of…
This paper presents a computational framework for quasi-static brittle fracture in three dimensional solids. The paper set outs the theoretical basis for determining the initiation and direction of propagating cracks based on the concept of…
An electro-chemo-mechanical phase-field formulation is developed to simulate pitting and stress corrosion in polycrystalline materials. The formulation incorporates dependencies of mechanical properties and corrosion potential on…
We investigate compressive failure of heterogeneous materials on the basis of a continuous progressive damage model. The model explicitely accounts for tensile and shear local damage and reproduces the main features of compressive failure…
Brittle solids are often toughened by adding a second-phase material. This practice often results in composites with material heterogeneities on the meso scale: large compared to the scale of the process zone but small compared to that of…
Fracture growth in a material is strongly influenced by the presence of inhomogeneities, which deviate crack trajectories from rectilinearity and deeply affect failure. Increasing crack tortuosity is connected to enhancement of fracture…
Compressive-shear fracture is commonly observed in rock-like materials. However, this fracture type cannot be captured by current phase field models (PFMs), which have been proven an effective tool for modeling fracture initiation,…
The two principal ingredients determining the failure modes of disordered solids are the level of heterogeneity and the length scale of the region affected in the solid following a local failure. While the latter facilitates damage…
Phase-field models of fracture introduce smeared cracks of width commensurate with a regularisation length parameter $\epsilon$ and obeying a minimum energy principle. Mesh adaptivity naturally suggests itself as a means of supplying…
Fracture processes in multi-phase solids are inherently complex due to multiple competing mechanisms. Here, we investigate the elastic and fracture behaviour of two-phase solids, comprising a fragile phase and a tough phase using a…
The local geometrical randomness of metal foams brings complexities to the performance prediction of porous structures. Although the relative density is commonly deemed as the key factor, the stochasticity of internal cell sizes and shapes…