Flexible plate and foundation modelling.
Hosking, R. J. (2000)
Journal of Applied Mathematics and Decision Sciences
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Hosking, R. J. (2000)
Journal of Applied Mathematics and Decision Sciences
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Roy, P.Pal, Debnath, L. (1988)
International Journal of Mathematics and Mathematical Sciences
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Alberto Carpinteri (1990)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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The nature of the crack and the structure behaviour can range from ductile to brittle depending on tensile strength and fracture toughness of the material, as well as on the size-scale of the solid body. Strength and toughness present in fact different physical dimensions and any consistent fracture criterion must consider energy dissipation both per unit of volume and per unit of crack area. A cohesive crack model is proposed aiming at describing the size effects of fracture mechanics,...
Mukherjee, S., Das, S. (2005)
Journal of Applied Mathematics
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Emilio Silva, Clemens Först, Ju Li, Xi Lin, Ting Zhu, Sidney Yip (2007)
ESAIM: Mathematical Modelling and Numerical Analysis
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Although the intellectual merits of computational modelling across various length and time scales are generally well accepted, good illustrative examples are often lacking. One way to begin appreciating the benefits of the multiscale approach is to first gain experience in probing complex physical phenomena at one scale at a time. Here we discuss materials modelling at two characteristic scales separately, the atomistic level where interactions are specified through classical potentials...
Crescentino Bosco, Alberto Carpinteri (1990)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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Whereas in elasticity and plasticity geometrically similar structures behave in the same way, when strain-softening and strain-localization are taken into account the structural behaviour ranges from ductile to brittle merely by increasing size and keeping material properties and geometrical shape unchanged. The size-scale of plain and reinforced concrete elements has often revealed a fundamental influence on the global structural behaviour. This has been theoretically predicted and...
Gérard A. Maugin (1999)
Extracta Mathematicae
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This paper outlines recent developments and prospects in the application of the continuum mechanics expressed intrinsically on the material manifold itself. This includes applications to materially inhomogeneous materials, physical effects which, in this vision, manifest themselves as quasi-inhomogeneities, and the notion of thermodynamical driving force of the dissipative progress of singular point sets on the material manifold with special emphasis on fracture, shock waves and phase-transition...