Gradient Damage Models for Heterogeneous Materials

Annika Bach; Teresa Esposito; Roberta Marziani; Caterina Ida Zeppieri

doi:10.1137/22M1499145

Gradient Damage Models for Heterogeneous Materials

Annika Bach (Corresponding author-nrf)
, Teresa Esposito
, Roberta Marziani
, Caterina Ida Zeppieri

Research output: Contribution to journal › Article › Academic › peer-review

3 Citations (Scopus)

Abstract

In this paper we study the asymptotic behaviour of phase-field functionals of Ambrosio and Tortorelli type allowing for small-scale oscillations both in the volume and in the diffuse surface term. The functionals under examination can be interpreted as an instance of a static gradient damage model for heterogeneous materials. Depending on the mutual vanishing rate of the approximation and of the oscillation parameters, the effective behaviour of the model is fully characterised by means of Γ -convergence.

Original language	English
Pages (from-to)	3567-3601
Journal	SIAM Journal on Mathematical Analysis
Volume	55
Issue number	4
DOIs	https://doi.org/10.1137/22M1499145
Publication status	Published - 31 Aug 2023
Externally published	Yes

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title = "Gradient Damage Models for Heterogeneous Materials",

abstract = "In this paper we study the asymptotic behaviour of phase-field functionals of Ambrosio and Tortorelli type allowing for small-scale oscillations both in the volume and in the diffuse surface term. The functionals under examination can be interpreted as an instance of a static gradient damage model for heterogeneous materials. Depending on the mutual vanishing rate of the approximation and of the oscillation parameters, the effective behaviour of the model is fully characterised by means of Γ -convergence.",

author = "Annika Bach and Teresa Esposito and Roberta Marziani and Zeppieri, \{Caterina Ida\}",

year = "2023",

month = aug,

day = "31",

doi = "10.1137/22M1499145",

language = "English",

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T1 - Gradient Damage Models for Heterogeneous Materials

AU - Esposito, Teresa

AU - Marziani, Roberta

AU - Zeppieri, Caterina Ida

A2 - Bach, Annika

PY - 2023/8/31

Y1 - 2023/8/31

N2 - In this paper we study the asymptotic behaviour of phase-field functionals of Ambrosio and Tortorelli type allowing for small-scale oscillations both in the volume and in the diffuse surface term. The functionals under examination can be interpreted as an instance of a static gradient damage model for heterogeneous materials. Depending on the mutual vanishing rate of the approximation and of the oscillation parameters, the effective behaviour of the model is fully characterised by means of Γ -convergence.

AB - In this paper we study the asymptotic behaviour of phase-field functionals of Ambrosio and Tortorelli type allowing for small-scale oscillations both in the volume and in the diffuse surface term. The functionals under examination can be interpreted as an instance of a static gradient damage model for heterogeneous materials. Depending on the mutual vanishing rate of the approximation and of the oscillation parameters, the effective behaviour of the model is fully characterised by means of Γ -convergence.

U2 - 10.1137/22M1499145

DO - 10.1137/22M1499145

M3 - Article

SN - 0036-1410

VL - 55

SP - 3567

EP - 3601

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 4

ER -

Gradient Damage Models for Heterogeneous Materials

Abstract

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