Related papers: Phase-Field Peridynamics
This work reports an extensive study of three-dimensional topological ordered phases that, in one of the directions behave like usual topological order concerning mobility of excitations, but in the perpendicular plane manifest type-II…
Phase field crystal (PFC) models constitute a field theoretical approach to solidification, melting and related phenomena at atomic length and diffusive time scales. One of the advantages of these models is that they naturally contain…
Recent years have seen a significant interest in using phase field approaches to model hydraulic fracture, so as to optimise a process that is key to industries such as petroleum engineering, mining and geothermal energy extraction. Here,…
Exploiting the framework of peridynamics, a dimensionally-reduced plate formulation is developed that allows for the through-thickness nucleation and growth of fracture surfaces, enabling the treatment of delamination in a lower-dimensional…
We present a new multiphase-field theory for describing pattern formation in multi-domain and/or multi-component systems. The construction of the free energy functional and the dynamic equations is based on criteria that ensure mathematical…
In this contribution, a novel framework for simulating mixed-mode failure in rock is presented. Based on a hybrid phase-field model for mixed-mode fracture, separate phase-field variables are introduced for tensile (mode I) and shear (mode…
Soft-walled microchannels arise in many applications, ranging from organ-on-a-chip platforms to soft-robotic actuators. However, despite extensive research on their static and dynamic response, the potential failure of these devices has not…
Cracking of rocks and rock-like materials exhibits a rich variety of patterns where tensile (mode I) and shear (mode II) fractures are often interwoven. These mixed-mode fractures are usually cohesive (quasi-brittle) and frictional.…
Variational phase-field models of brittle fracture are powerful tools for studying Griffith-type crack propagation in complex scenarios. However, as approximations of Griffith's theory-which does not incorporate a strength criterion-these…
We consider a quantum many-body model describing a system of electrons interacting with themselves and hopping from one ion to another of a one dimensional lattice. We show that the ground state energy of such system, as a functional of the…
In this paper we develop a new set of results based on a nonlocal gradient jointly inspired by the Riesz s-fractional gradient and Peridynamics, in the sense that its integration domain depends on a ball of radius delta > 0 (horizon of…
We derive the variational formulation of a gradient damage model by applying the energetic formulation of rate-independent processes and obtain a regularized formulation of fracture. The model exhibits different behavior at traction and…
Data driven approaches have the potential to make modeling complex, nonlinear physical phenomena significantly more computationally tractable. For example, computational modeling of fracture is a core challenge where machine learning…
The quantum dynamics of a subset of interacting bosons in a subspace of fixed particle number is described in terms of symmetrized many-particle states. A suitable partial trace operation over the von Neumann equation of an $N$-particle…
As phase-field modeling (PFM) is booming across various disciplines and has been proven fitted for numerically modeling interfacial problems, we aim at taking a step back to revisit its fundamental validity, in the light of non-equilibrium…
In order to meet the requirements of practical applications, a model of deforming manifold in the embedded space is proposed. The deforming vector and deforming field are presented to precisely describe the deforming process, which have…
We develop a novel nonlocal model of dislocations based on the framework of peridynamics. By embedding interior discontinuities into the nonlocal constitutive law, the displacement jump in the Volterra dislocation model is reproduced,…
The Fredkin model describes a spin-half chain segment subject to three-body, correlated-exchange interactions and twisted boundary conditions. The model is frustration-free, and its ground state wave function is known exactly. Its…
Many geo-engineering applications, e.g., enhanced geothermal systems, rely on hydraulic fracturing to enhance the permeability of natural formations and allow for sufficient fluid circulation. Over the past few decades, the phase-field…
In this work we aim to develop a unified mathematical framework and a reliable computational approach to model the brittle fracture in heterogeneous materials with variability in material microstructures, and to provide statistic metrics…