Modeling and analysis of a phase field system for damage and phase\n separation processes in solids

2013/12/05 by E. Bonetti, Christian Heinemann, Bonetti, Elena +5
Computer Science · Engineering · Mathematics · #34A12 #35J50 #35K35 #35K55 #35K65 #35K85 #35K92 #49J40 #49S05 #74A45 #74G25 #82B26 #82C26 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1312.1623

openalex publication_date 2013/12/05 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

In this work, we analytically investigate a multi-component system for\ndescribing phase separation and damage processes in solids. The model consists\nof a parabolic diffusion equation of fourth order for the concentration coupled\nwith an elliptic system with material dependent coefficients for the strain\ntensor and a doubly nonlinear differential inclusion for the damage function.\nThe main aim of this paper is to show existence of weak solutions for the\nintroduced model, where, in contrast to existing damage models in the\nliterature, different elastic properties of damaged and undamaged material are\nregarded. To prove existence of weak solutions for the introduced model, we\nstart with an approximation system. Then, by passing to the limit, existence\nresults of weak solutions for the proposed model are obtained via suitable\nvariational techniques.\n

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