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Non-local damage modelling of quasi-brittle composites

Jiří Vala, Vladislav Kozák (2021)

Applications of Mathematics

Most building materials can be characterized as quasi-brittle composites with a cementitious matrix, reinforced by some stiffening particles or elements. Their massive exploitation motivates the development of numerical modelling and simulation of behaviour of such material class under mechanical, thermal, etc. loads, including the evaluation of the risk of initiation and development of micro- and macro-fracture. This paper demonstrates the possibility of certain deterministic prediction, applying...

Note critiche sui carichi di collasso dei continui bidimensionali isotropi

Giuseppe Creazza, Arturo Natali (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Nei continui bidimensionali isotropi in fase fessurata si dimostra, nella sola ipotesi che le linee di rottura rappresentino univocamente il meccanismo di collasso, la impossibilità di ottenere un moltiplicatore ottimale del carico. La configurazione reale può essere definita considerando anche la capacità deformativa del continuo in esame.

Numerical approach to a rate-independent model of decohesion in laminated composites

Zeman, Jan, Gruber, Pavel (2010)

Programs and Algorithms of Numerical Mathematics

In this paper, we present a numerical approach to evolution of decohesion in laminated composites based on incremental variational problems. An energy-based framework is adopted, in which we characterize the system by the stored energy and dissipation functionals quantifying reversible and irreversible processes, respectively. The time-discrete evolution then follows from a solution of incremental minimization problems, which are converted to a fully discrete form by employing the conforming finite...

Numerical approaches to rate-independent processes and applications in inelasticity

Alexander Mielke, Tomáš Roubíček (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

A conceptual numerical strategy for rate-independent processes in the energetic formulation is proposed and its convergence is proved under various rather mild data qualifications. The novelty is that we obtain convergence of subsequences of space-time discretizations even in case where the limit problem does not have a unique solution and we need no additional assumptions on higher regularity of the limit solution. The variety of general perspectives thus obtained is illustrated on several...

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