Related papers: A Hybrid-High Order method for fracture modelling
We propose a hybrid neural network and physics framework for reduced-order modeling of elastoplasticity and fracture. State-of-the-art scientific computing models like the Material Point Method (MPM) faithfully simulate large-deformation…
In this article, we design and analyze a hybrid high-order (HHO) finite element approximation for the solution of a nonlocal nonlinear problem of Kirchhoff type. The HHO method involves arbitrary-order polynomial approximations on…
This paper proposes the use of a Spectral method to simulate diffusive moisture transfer through porous materials as a Reduced-Order Model (ROM). The Spectral approach is an a priori method assuming a separated representation of the…
The favored phase field method (PFM) has encountered challenges in the finite strain fracture modeling of nearly or truly incompressible hyperelastic materials. We identified that the underlying cause lies in the innate contradiction…
We develop a cut finite element method (CutFEM) for convection-diffusion problems posed on mixed-dimensional domains, i.e., unions of manifolds of different dimensions arranged in a hierarchical structure where lower-dimensional components…
We present a novel, generalised formulation to treat coupled structural integrity problems by combining phase field and multi-physics modelling. The approach exploits the versatility of the heat transfer equation and is therefore well…
This document contains lecture notes from the Ph.D. course given at Scuola Superiore Meridionale by Daniele Di Pietro in February 2025. The goal of the course is to provide an overview of polytopal methods, focusing on the Hybrid High-Order…
The fracture simulation of random particle reinforced composite structures remains a challenge. Current techniques either assumed a homogeneous model, ignoring the microstructure characteristics of composite structures, or considered a…
This paper presents an overview of the theories and computer implementation aspects of phase field models (PFM) of fracture. The advantage of PFM over discontinuous approaches to fracture is that PFM can elegantly simulate complicated…
We propose a novel approach to optimize the design of heterogeneous materials, with the goal of enhancing their effective fracture toughness under mode-I loading. The method employs a Gaussian processes-based Bayesian optimization framework…
This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach…
The purpose of this study is to investigate morphology of simultaneously propagating hydraulic fractures. Simultaneous propagation of hydraulic fractures occurs during stimulation of horizontal wells, and, in particular, several initiation…
The analysis of wave propagation problems in linear damped media must take into account both propagation features and attenuation process. To perform accurate numerical investigations by the finite differences or finite element method, one…
We introduce a framework for the design of finite element methods for two-dimensional moving boundary problems with prescribed boundary evolution that have arbitrarily high order of accuracy, both in space and in time. At the core of our…
In this work, we present numerical studies of fixed-stress iterative coupling for solving flow and geomechanics with propagating fractures in a porous medium. Specifically, fracture propagations are described by employing a phase-field…
The problem of a plane strain hydraulic fracture propagating in a layered formation is considered. Fracture toughness, in-situ stress, and leak-off coefficient are assumed to vary by layer, while the elastic properties are kept constant…
Multiscale problems are computationally costly to solve by direct simulation because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and analyzed new numerical methods…
The purpose of this research is to describe an efficient iterative method suitable for obtaining high accuracy solutions to high frequency time-harmonic scattering problems. The method allows for both refinement of local polynomial degree…
We design, analyse and implement an arbitrary order scheme applicable to generic meshes for a coupled elliptic-parabolic PDE system describing miscible displacement in porous media. The discretisation is based on several adaptations of the…
In the last ten years, the phase-field method has gained much attention as a novel method to simulate fracture due to its straightforward way allowing to cover crack initiation and propagation without additional conditions. More recently,…