PSI - Issue 23

Jiří Vala et al. / Procedia Structural Integrity 23 (2019) 328 – 333 Ji ří Vala, Vladislav Kozák / Structural Integrity Procedia 00 (2019) 000 – 000

329

2

manifested by fracture process zones, in brittle materials like glass or welds in metal structures by discrete crack discontinuities, in elasto-plastic ductile metal or similar materials by shear (localization) bands, see Sumi (2014). Advanced building structures frequently use silicate composites reinforced by metal, plastic or other fibres, prevent ing undesirable micro- an macro-cracking effects. Mechanical behaviour of such composites is conditioned by the suitable choice of fibre properties, their concentration, localization and orientation in a silicate matrix, influenced by their early-age treatment, see Kom árková et al (2017) . Non-destructive testing of material structure is offered by image processing (2D radiographic, 3D tomographic, etc.) and stationary magnetic and non-stationary electromagnetic approaches. The macroscopic material homogeni zation, Vala (2016), relies then on the semi-analytical mixing formulae for special particle shapes (acceptable name ly for their low volume fractions), two-scale homogenization of periodic structures, or alternative results from the asymptotic analysis ( G -convergence, H -convergence, Γ -convergence, etc.), up to very general (both deterministic and stochastic) results for σ -convergence on homogenization structures, with numerous open problems uncovered by Roubíček (2013) . A unified scale-bridging approach covering elastic and plastic behavior together with fracture and other defects results in concept of structured deformation, see Morandotti (2018). The dissipative particle dynamics, Steinhauser (2008), referring up to the atomistic or molecular scale, can be adopted to handle certain super-particles; this results in the discrete element method, applied namely in soil, rock and concrete mechanics, in the analysis of granular materials and in the dynamic process of initiation and propagation of micro-cracks. The inheritance from dissipative particle dynamics, manifested in the limited offer of particle shapes and sizes, can be overcome with help of two- or three-dimensional reference volume elements, using the combination of finite and discrete element ap proaches, Munjiza (2004). An autonomous problem is the reliable identification of material parameters at various scales: the relevant computational approaches, Vala (2014), typically suffer from mathematical ill-possedness, nu merical instability and need of artificial regularization, together with uncertain or insufficient input data. These diffi culties have to be overcome by careful organization of experiments and various special problem-oriented algorithms, Shen et al (2010), Buljak et al (2013). The extensive use of brittle matrix composite materials requires also appropriate computational models to de scribe, with adequate accuracy, their mechanical behaviour. From a micromechanical model some macroscopic constitutive equations are derived for intentionally or random oriented fibres Park et al (2010), Brighenti et al (2013), Cerrone et al (2014), Sanjayan et al (2015), accounting for such physical processes as matrix/fibre debond ing and fibre rupture. One of possible ways is to adopt a discontinuous-like FE approach to a lattice model, see Brighenti & Scorza (2012). An alternative approach refers to special constitutive relations, inspired by continuum mechanics, where crack opening and contact surface sliding are included into the model of plastic damage, using smeared cracking, Jir á sek (2011), Edalat-Behbahani et al (2017), together with mesh objective strain localization due to material softening, referring to the thermodynamically irreversible continuum damage mechanics, Le et al (2019), compatible with Nair (2009, especially Chap.14) and open to more general analysis working with tensor calculus and differential geometry, Epstein (2007), Clayton (2015), in particular that leading to a smeared represen tation of the crack path, Kaliske et al (2012). At least for the practically significant application of self-compacting concrete, supported by both experimental methods and numerical simulations, smeared cracking can be combined with Monte Carlo simulations, which results in the Variational Multiscale Cohesive Method, Su et al (2010), whose various implementations differs in the choice of basis functions. Another approach to the same problems presents the eXtended Finite Element Method ( XFEM briefly), Khoei (2015), covering both strong geometrical discontinuities (in function values) and weak ones (in gradients), with the aim of enrichment of the approximation space by all needed types if (especially locally) discontinuous functions, and similar approaches, derived from the Partition of Unity Method , namely the Partition of Unity Finite Element Meth od, Babu ška & Melenk (1997), the Generalized Finite Element Me t hod, Duarte et al (2001), or the Discontinuous Galerkin XFEM, Aduloju & Truster (2019). Especially XFEM adds some degrees of freedom in relevant regions during the computation, typically along all curves and surfaces of discontinuities and in singular points, exploiting the Moving Least Squares technique: the usual extrinsic XFEM works with additional variables and functions, whereas the intrinsic XFEM developed by Fries & Belytchko (2006) tries to avoid them, only with one additional shape function in each relevant node. However, although no singularity exist at the tip of cohesive crack, the stresses obtained by differentiation of the displacement are not accurate, and cannot be used to predict accurately the growth of the tip, Fert é et al (2016 ), Li & Chen (2017).