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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
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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

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