Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-29T00:10:19.162Z Has data issue: false hasContentIssue false
  • English
  • Français

A numerical study of a nonlocal model of damage propagation under chemical aggression

Published online by Cambridge University Press:  30 July 2003

R. NATALINI ,
C. NITSCH ,
G. PONTRELLI  and
S. SBARAGLIA
R. NATALINI
Affiliation:
Istituto per le Applicazioni del Calcolo “Mauro Picone”, Consiglio Nazionale delle Ricerche, Viale del Policlinico, 137, I-00161 Roma, Italy
C. NITSCH
Affiliation:
Istituto per le Applicazioni del Calcolo “Mauro Picone”, Consiglio Nazionale delle Ricerche, Viale del Policlinico, 137, I-00161 Roma, Italy Dipartimento di Matematica “G. Castelnuovo”, Università degli Studi di Roma “La Sapienza”, Piazzale Aldo Moro, 2, I-00161 Roma, Italy
G. PONTRELLI
Affiliation:
Istituto per le Applicazioni del Calcolo “Mauro Picone”, Consiglio Nazionale delle Ricerche, Viale del Policlinico, 137, I-00161 Roma, Italy
S. SBARAGLIA
Affiliation:
Istituto per le Applicazioni del Calcolo “Mauro Picone”, Consiglio Nazionale delle Ricerche, Viale del Policlinico, 137, I-00161 Roma, Italy Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università degli Studi di Roma “La Sapienza”, Via A. Scarpa 16, I-00161 Roma, Italy
Get access Rights & Permissions [Opens in a new window]

Abstract

We introduce a differential model to study damage accumulation processes in the presence of chemical reactions. The influence of micro-structure leads to a nonlinear parabolic system characterized by the presence of a characteristic length. Here, we first present an analytical description of the qualitative behaviour of solutions which blow-up in finite time. Numerical simulations are given to describe the shape of solutions near the rupture time and the influence of the chemical reagents. As in the non-reactive model, the failure of the material occurs in a region of positive measure, due to the diffusive effects of the micro-structure, although some localization phenomena are observed. Moreover, if we increase the chemical concentration beyond a given threshold, which depends upon the specific conditions of the material, we observe a strong acceleration in the damage process.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 14 , Issue 4 , August 2003 , pp. 447 - 464
Copyright
2003 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)