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Analysis of staggered evolutions for nonlinear energies in phase field fracture

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Stefano Almi, Matteo Negri

Analysis of PDEs · Submitted 3 Apr 2019

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim By a careful study of the energy balance we deduce that time-continuous evolutions may still exhibit an alternate behavior in discontinuity times.

how it is stated · hedged possibility 0.99 read the record →

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arXiv ID1904.01895 (version 1)
Pith IDOBNAYXPH, Pith's permanent record of this paper and its review
CitationMatteo Negri, Stefano Almi. "Analysis of staggered evolutions for nonlinear energies in phase field fracture." arXiv:1904.01895 (2019). https://pith.science/paper/OBNAYXPH
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,742 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.71 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.08 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; .

We consider a class of separately convex phase field energies employed in fracture mechanics, featuring non-interpenetration and a general softening behavior. We analyze the time-discrete evolutions generated by a staggered minimization scheme, where fracture irreversibility is modeled by a monotonicity constraint on the phase field variable. After recasting the staggered scheme by means of gradient flows, we characterize the time-continuous limits of the discrete solutions in terms of balanced viscosity evolutions, parametrized by their arc-length with respect to the L2-norm (for the phase field) and the H1-norm (for the displacement field). By a careful study of the energy balance we deduce that time-continuous evolutions may still exhibit an alternate behavior in discontinuity times.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We consider a class of separately convex phase field energies employed in fracture mechanics, featuring non-interpenetration and a general softening behavior. background 0.72 0.28 0.02 asserted 0.93
s1 We analyze the time-discrete evolutions generated by a staggered minimization scheme, where fracture irreversibility is modeled by a monotonicity constraint on the phase field variable. method 0.73 0.90 0.05 asserted 0.99
s2 After recasting the staggered scheme by means of gradient flows, we characterize the time-continuous limits of the discrete solutions in terms of balanced viscosity evolutions, parametrized by their arc-length with respect to the L2-norm (for the phase field) and the H1-norm (for the displacement field). result 0.55 0.92 0.32 asserted 1.00
s3 By a careful study of the energy balance we deduce that time-continuous evolutions may still exhibit an alternate behavior in discontinuity times. result 0.99 0.93 0.44 hedged possibility 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We consider a class of separately convex phase field energies employed in fracture mechanics, featuring non-interpenetration and a general softening behavior. We analyze the time-discrete evolutions generated by a staggered minimization scheme, where fracture irreversibility is modeled by a monotonicity constraint on the phase field variable. After recasting the staggered scheme by means of gradient flows, we characterize the time-continuous limits of the discrete solutions in terms of balanced viscosity evolutions, parametrized by their arc-length with respect to the L2-norm (for the phase field) and the H1-norm (for the displacement field). By a careful study of the energy balance we deduce that time-continuous evolutions may still exhibit an alternate behavior in discontinuity times.

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2 arXiv papers cite this in 2 sentences

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