Related papers: Phase-field approximation of a vectorial, geometri…
We obtain a cohesive fracture model as a $\Gamma$-limit of scalar damage models in which the elastic coefficient is computed from the damage variable $v$ through a function $f_k$ of the form $f_k(v)=min\{1,\varepsilon_k^{1/2} f(v)\}$, with…
We study an approximation scheme for a variational theory of cohesive fracture in a one-dimensional setting. Here, the energy functional is approximated by a family of functionals depending on a small parameter $0 < \varepsilon \ll 1$ and…
Variational models for cohesive fracture are based on the idea that the fracture energy is released gradually as the crack opening grows. Recently, [Conti, Focardi, and Iurlano, Ann. Inst. H. Poincar\'e C Anal. Non Lin\'eaire, 2016]…
Reproducing the key features of fracture behavior under multiaxial stress states is essential for accurate modeling. Experimental evidence indicates that three intrinsic material properties govern fracture nucleation in elastic materials:…
We extend a phase-field/gradient damage formulation for cohesive fracture to the dynamic case. The model is characterized by a regularized fracture energy that is linear in the damage field, as well as non-polynomial degradation functions.…
The main aim of this three-part work is to provide a unified consistent framework for the phase-field modeling of cohesive fracture. In this first paper we establish the mathematical foundation of a cohesive phase-field model by proving a…
We propose a variational phase-field model of fracture capable of accounting for arbitrary closed convex strength domains. Unlike traditional models based on Ambrosio and Tortorelli regularization, the phase-field variable does not affect…
We study the $\Gamma$-limit of Ambrosio-Tortorelli-type functionals $D_\varepsilon(u,v)$, whose dependence on the symmetrised gradient $e(u)$ is different in $\mathbb{A} u$ and in $e(u)-\mathbb{A} u$, for a $\mathbb{C}$-elliptic symmetric…
We consider a free-boundary and free-discontinuity energy connecting phase separation and fracture in an elastic material. The energy excludes the contribution of phase boundaries in the cracked region, providing a heuristic approximation…
Phase-field approaches to fracture based on energy minimization principles have been rapidly gaining popularity in recent years, and are particularly well-suited for simulating crack initiation and growth in complex fracture networks. In…
In this paper we propose a notion of irreversibility for the evolution of cracks in presence of cohesive forces, which allows for different responses in the loading and unloading processes, motivated by a variational approximation with…
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…
This paper concludes a three-part effort aimed at developing a consistent and unified framework for the phase-field modeling of cohesive fracture. Building on the theoretical foundations established in the first two parts, which included a…
This is the second paper of a three-part work the main aim of which is to provide a unified consistent framework for the phase-field modelling of cohesive fracture. Building on the theoretical foundations of the first paper, where…
Standard phase-field fracture methods are rooted in brittle fracture theory and therefore do not inherently prescribe a material strength for crack nucleation, while also struggling to capture cohesive fracture behaviour. Recent…
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…
We propose a novel variational phase-field model for fracture in anisotropic materials. The model is specifically designed to allow a more flexible calibration of crack nucleation than existing anisotropic fracture formulations, while…
The goal of the current work is to explore direction-dependent damage initiation and propagation within an arbitrary anisotropic solid. In particular, we aim at developing anisotropic cohesive phase-field (PF) damage models by extending the…
We consider second order phase field functionals, in the continuum setting, and their discretization with isogeometric tensor product B-splines. We prove that these functionals, continuum and discrete, $\Gamma$-converge to a brittle…
We present a continuum theory to describe elastically induced phase transitions between coherent solid phases. In the limit of vanishing elastic constants in one of the phases, the model can be used to describe fracture on the basis of the…