English
Related papers

Related papers: Energy consistent framework for continuously evolv…

200 papers

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 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 present a continuum phase-field model of crack propagation. It includes a phase-field that is proportional to the mass density and a displacement field that is governed by linear elastic theory. Generic macroscopic crack growth laws…

Materials Science · Physics 2009-11-07 L. O. Eastgate , J. P. Sethna , M. Rauscher , T. Cretegny , C. -S. Chen , C. R. Myers

We discuss steady state crack growth in the spirit of a free boundary problem. It turns out that mode I and mode III situations are very different from each other: In particular, mode III exhibits a pronounced transition towards unstable…

Materials Science · Physics 2009-11-13 R. Spatschek , E. A. Brener , D. Pilipenko

We investigate the fracture of Li-ion battery cathodic particles using a thermodynamically consistent phase-field approach that can describe arbitrarily complex crack paths and captures the full coupling between Li-ion diffusion, stress,…

Materials Science · Physics 2019-08-23 Ataollah Mesgarnejad , Alain Karma

While we fundamentally understand the dynamics of 'simple' cracks propagating in brittle solids within perfect (homogeneous) materials, we do not understand how paths of moving cracks are determined. We experimentally study strongly…

Soft Condensed Matter · Physics 2020-10-28 Lital Rozen-Levy , John M. Kolinski , Gil Cohen , Jay Fineberg

We present a continuum theory which predicts the steady state propagation of cracks. The theory overcomes the usual problem of a finite time cusp singularity of the Grinfeld instability by the inclusion of elastodynamic effects which…

Materials Science · Physics 2009-11-11 Robert Spatschek , Miks Hartmann , Efim Brener , Heiner Mueller-Krumbhaar , Klaus Kassner

In this letter we address the fragmentation of thin, brittle layers due to the impact of high-velocity projectiles. Our approach is a geometric statistical one, with lines and circles playing the role of cracks, randomly distributed over…

Soft Condensed Matter · Physics 2014-09-30 Rebeca C. Falcão , Fernando Parisio

Motivated by recent experiments, we present a study of the dynamics of cracks in thin sheets. While the equations of elasticity for thin plates are well known, there remains the question of path selection for a propagating crack. We invoke…

Materials Science · Physics 2015-05-18 Yossi Cohen , Itamar Procaccia

By a combination of geometrical and configurational analysis we study the properties of absolute minimal and equilibrium states of general Mumford-Shah functionals, with applications to models of quasistatic brittle fracture propagation.…

Analysis of PDEs · Mathematics 2008-03-14 Marius Buliga

A field theory is presented for predicting damage and fracture in quasi brittle materials incorporating effects of irreversible (plastic) deformation as well as elastic moduli that soften with damage. The new observation made here is that…

Materials Science · Physics 2026-03-17 Hayden Bromley , Robert Lipton

This work presents a novel three-dimensional Crack Element Method (CEM) designed to model transient dynamic crack propagation in quasi-brittle materials efficiently. CEM introduces an advanced element-splitting algorithm that enables…

Computational Engineering, Finance, and Science · Computer Science 2025-08-07 Yuxi Xie , C. T. Wu , Wei Hu , Lu Xu , Tinh Q. Bui , Shaofan Li

The modeling of cracks is an important topic - both in engineering as well as in mathematics. Since crack propagation is characterized by a free boundary value problem (the geometry of the crack is not known beforehand, but part of the…

Computational Engineering, Finance, and Science · Computer Science 2024-03-13 Felix Rörentrop , Samira Boddin , Dorothee Knees , Jörn Mosler

The problem of crack pattern formation due to thermal shock loading at the surface of half-space is solved numerically using two-dimensional boundary element method. The results of numerical simulations with 100-200 random simultaneously…

Materials Science · Physics 2022-02-09 Sergejs Tarasovs , Ahmad Ghassemi

J integral based criterion is widely used in elastic-plastic fracture mechanics. However, it is not rigorously applicable when plastic unloading appears during crack propagation. One difficulty is that the energy density with plastic…

Other Condensed Matter · Physics 2015-10-28 Si Xiao , HeLing Wang , Bin Liu

Fatigue crack growth is usually a three-dimensional problem, but it is often simplified to two dimensions to reduce complexity. However, this study investigates the relationships between microscopic effects such as crack kinking, shear…

Materials Science · Physics 2024-04-03 Vanessa Schöne , Florian Paysan , Eric Breitbarth

While of paramount importance in material science, the dynamics of cracks still lacks a complete physical explanation. The transition from their slow creep behavior to a fast propagation regime is a notable key, as it leads to full material…

A dynamic crack will travel in a straight path up to a material-dependent critical speed beyond which its path becomes erratic. Predicting this critical speed and discovering the origin of this instability are two outstanding problems in…

Materials Science · Physics 2015-06-25 Farid F. Abraham

Finite element calculations of dynamic fracture based on embedding cohesive surfaces in a continuum indicate that the predictions are sensitive to the cohesive law used. Simulations were performed on a square block in plane strain with an…

Materials Science · Physics 2007-05-23 Michael L. Falk , Alan Needleman , James R. Rice

We propose a minimal nonlinear model of brittle crack propagation by considering only the motion of the crack-tip atom. The model captures many essential features of steady-state crack velocity and is in excellent quantitative agreement…

Materials Science · Physics 2009-10-28 Brad Lee Holian , Raphael Blumenfeld , Peter Gumbsch