English
Related papers

Related papers: Size effects on quasistatic growth of fractures

200 papers

We propose a discontinuous finite element approximation for a model of quasi-static growth of brittle fractures in linearly elastic bodies formulated by Francfort and Marigo, and based on the classical Griffith's criterion. We restrict our…

Analysis of PDEs · Mathematics 2007-05-23 A. Giacomini , M. Ponsiglione

We propose a time-space discretization of a general notion of quasistatic growth of brittle fractures in elastic bodies proposed in [13] by G. Dal Maso, G.A. Francfort, and R. Toader, which takes into account body forces and surface loads.…

Analysis of PDEs · Mathematics 2025-10-20 Alessandro Giacomini , Marcello Ponsiglione

We give a precise mathematical formulation of a variational model for the irreversible quasi-static evolution of brittle fractures proposed by G.A. Francfort and J.-J. Marigo, and based on Griffith's theory of crack growth. In the…

Analysis of PDEs · Mathematics 2009-11-07 Gianni Dal Maso , Rodica Toader

We give a precise mathematical formulation of a variational model for the irreversible quasi-static evolution of a brittle fracture proposed by G.A. Francfort and J.-J. Marigo, and based on Griffith's theory of crack growth. In the…

Analysis of PDEs · Mathematics 2007-05-23 Gianni Dal Maso , Rodica Toader

We present some recent existence results for the variational model of crack growth in brittle materials proposed by Francfort and Marigo in 1998. These results, obtained in collaboration with Francfort and Toader, cover the case of…

Analysis of PDEs · Mathematics 2007-05-23 Gianni Dal Maso

In this paper, we prove a new existence result for a variational model of crack growth in brittle materials proposed in [15]. We consider the case of $n$-dimensional finite elasticity, for an arbitrary $n\ge1$, with a quasiconvex bulk…

Analysis of PDEs · Mathematics 2007-05-23 Gianni Dal Maso , Gilles A. Francfort , Rodica Toader

Recently the scaling laws describing the roughness development of fracture surfaces was proposed to be related to the macroscopic elastic energy released during crack propagation [Mor00]. On this basis, an energy-based asymptotic analysis…

Materials Science · Physics 2009-11-07 S. Morel , E. Bouchaud , G. Valentin

We prove a linearization result for quasistatic fracture evolution in nonlinear elasticity. As the stiffness of the material tends to infinity, we show that rescaled displacement fields and their associated crack sets converge to a solution…

Analysis of PDEs · Mathematics 2024-11-21 Manuel Friedrich , Pascal Steinke , Kerrek Stinson

We present the main existence result for quasistatic crack growth in the model proposed by Dal Maso, Francfort, and Toader, and prove some qualitative properties of the solutions.

Functional Analysis · Mathematics 2008-08-19 Gianni Dal Maso , Alessandro Giacomini , Marcello Ponsiglione

We study a variant of the variational model for the quasi-static growth of brittle fractures proposed by Francfort and Marigo. The main feature of our model is that, in the discrete-time formulation, in each step we do not consider absolute…

Analysis of PDEs · Mathematics 2007-05-23 Gianni Dal Maso , Rodica Toader

In this paper we prove the existence of quasistatic evolutions for a cohesive fracture on a prescribed crack surface, in small-strain antiplane elasticity. The main feature of the model is that the density of the energy dissipated in the…

Analysis of PDEs · Mathematics 2018-02-13 Vito Crismale , Giuliano Lazzaroni , Gianluca Orlando

In this paper we prove a two-dimensional existence result for a variational model of crack growth for brittle materials in the realm of linearized elasticity. Starting with a time-discretized version of the evolution driven by a prescribed…

Analysis of PDEs · Mathematics 2018-07-10 Manuel Friedrich , Francesco Solombrino

Nonlocal quasistatic fracture evolution for interacting cracks is developed and supporting numerical examples are presented. The approach is implicit and is based on local stationarity and fixed point methods. It is proved that the fracture…

Numerical Analysis · Mathematics 2023-01-18 Debdeep Bhattacharya , Robert Lipton , Patrick Diehl

We study a variational model for the quasistatic growth of cracks with fractional di- mension in brittle materials. We give a minimal set of properties of the collection of admissible cracks which ensure the existence of a quasistatic…

Optimization and Control · Mathematics 2016-02-29 Gianni Dal Maso , Marco Morandotti

We study an approximation scheme for a variational theory of quasi-static crack growth based on an eigendeformation approach. We consider a family of energy functionals depending on a small parameter $\varepsilon$ and on two fields, the…

Analysis of PDEs · Mathematics 2026-02-13 Ba Duc Duong , Manuel Friedrich

We provide an adaptive finite element approximation for a model of quasi-static crack growth in dimension two. The discrete setting consists of integral functionals that are defined on continuous, piecewise affine functions, where the…

Analysis of PDEs · Mathematics 2025-03-25 Vito Crismale , Manuel Friedrich , Joscha Seutter

We propose a model for quasistatic growth of cavities and cracks in two-dimensional nonlinear elasticity. Cavities and cracks are modeled as discrete and compact subsets of a planar domain, respectively, and deformations are defined only…

Analysis of PDEs · Mathematics 2025-07-22 Marco Bresciani , Manuel Friedrich

It has been claimed that quasistatic granular materials, as well as nanoscale materials, exhibit departures from elasticity even at small loadings. It is demonstrated, using 2D and 3D models with interparticle harmonic interactions, that…

Statistical Mechanics · Physics 2007-05-23 C. Goldenberg , I. Goldhirsch

We show the existence of quasistatic evolutions in a fracture model for brittle materials by a vanishing viscosity approach, in the setting of planar linearized elasticity. The crack is not prescribed a priori and is selected in a class of…

Analysis of PDEs · Mathematics 2019-06-07 Stefano Almi , Giuliano Lazzaroni , Ilaria Lucardesi

This work investigated how the structure size affects the quasi-static and fatigue behaviors of graphene polymer nanocomposites, a topic that has been often overlooked. The results showed that both quasi-static and fatigue failure of these…

Applied Physics · Physics 2023-03-13 Yao Qiao , Kaiwen Guo , Marco Salviato
‹ Prev 1 2 3 10 Next ›