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H. Askes et alii, Frattura ed Integrità Strutturale, 25 (2013) 87-93; DOI: 10.3221/IGF-ESIS.25.13 92 C ONCLUSIONS he validation exercise summarised in the present paper strongly supports the idea that gradient-enriched crack tip stresses can successfully be used to perform the static assessment of cracked components. The GM based design methodology proposed and validated in the present paper by post-processing a large number of experimental results generated by testing engineering ceramics has the potential to turn into an important step forward in developing alternative methods to model the detrimental effect of cracks and defects in engineering components and structures. In particular, since, according to GM’s modus operandi , gradient enriched stresses can directly be calculated at any material points (crack tips included), components containing both cracks and defects could directly be designed against static loading by following the same strategy as the one commonly adopted to perform, as suggested by continuum mechanics, the fatigue assessment of un-cracked bodies. R EFERENCES [1] Irwin, G.R., Structural aspects of brittle fracture, Applied Materials Research, 3 (1964) 65-81. [2] Mindlin, R.D., Micro-structure in linear elasticity, Arch. Rat. Mech. Analysis, 16 (1964) 52–78. [3] Aifantis, E.C., On the role of gradients in the localization of deformation and fracture, Int. J. Engng. Sci., 30 (1992) 1279–1299. [4] Altan, S.B., Aifantis, E.C., On the structure of the mode III crack-tip in gradient elasticity, Scripta Metall. Mater., 26 (1992) 319–324. [5] Ru, C.Q., Aifantis, E.C., A simple approach to solve boundary-value problems in gradient elasticity, Acta Mech., 101 (1993) 59–68. [6] Askes, H., Gutiérrez, M.A., Implicit gradient elasticity, Int. J. Numer. Meth. Engng., 67 (2006) 400-416. [7] Askes, H., Morata I., Aifantis E.C., Finite element analysis with staggered gradient elasticity, Comput. Struct., 86 (2008) 1266-1279. [8] Askes, H., Gitman, I.M., Non-Singular Stresses in Gradient Elasticity at Bi-Material Interface with Transverse Crack, Int. J. Fract., 156 (2009) 217-222. [9] Askes, H., Aifantis, E.C., Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results, Int. J. Solids Struct., 48 (2011) 1962–1990. [10] Taylor, D., The Theory of Critical Distances: A new perspective in fracture mechanics, Elsevier, Oxford, UK (2007). [11] Susmel, L., Taylor, D., On the use of the Theory of Critical Distances to predict static failures in ductile metallic materials containing different geometrical features, Engng. Fract. Mech., 75 (2008) 4410-4421. [12] Susmel, L., Taylor, D., The Theory of Critical Distances to estimate the static strength of notched samples of Al6082 loaded in combined tension and torsion. Part I: Material cracking behaviour, Engng. Fract. Mech., 77 (2010) 452–469. [13] Susmel L., Taylor D., The Theory of Critical Distances to estimate the static strength of notched samples of Al6082 loaded in combined tension and torsion. Part II: Multiaxial static assessment, Engng. Fract. Mech., 77 (2010) 470– 478. [14] Whitney, J.M., Nuismer, R.J., Stress fracture criteria for laminated composites containing stress concentrations, J. Composite Mater., 8 (1974) 253-265. [15] Taylor, D., Predicting the fracture strength of ceramic materials using the theory of critical distances, Engng. Fract. Mech., 71 (2004) 2407-2416. [16] Susmel, L., Taylor, D., The theory of critical distances to predict static strength of notched brittle components subjected to mixed-mode loading, Eng Frac Mech, 75 3-4 (2008) 534-550. [17] Susmel, L., Askes, H., Material length scales in fracture analysis: from Gradient Elasticity to the Theory of Critical Distances, Computational Technology Reviews, 6 (2012) 63-80. [18] Susmel, L., Askes, H., Bennett, T., Taylor, D., Theory of Critical Distances vs. Gradient Mechanics in modelling the transition from the short- to long-crack regime at the fatigue limit, Fatigue Fract. Engng. Mater. Struct., (2013) – in press. [19] Neuber, H., Theory of Notch Stresses. Springer, Berlin, (1958). [20] Peerlings, R.H.J., de Borst, R., Brekelmans, W.A.M., de Vree, J.H.V., Gradient enhanced damage for quasi-brittle materials, Int. J. Numer. Meth. Engng., 39 (1996) 3391–3403. T