PSI - Issue 64

Nicola Nisticò et al. / Procedia Structural Integrity 64 (2024) 2238–2245 Author name / Structural Integrity Procedia 00 (2019) 000–000

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3. Structural Modelling The Discrete Element Method (DEM) is particularly suitable for studying the mechanical behavior of a set of bodies free to move and interact with each other over time. Unlike traditional approaches, DEM does not assume a priori connections between bodies. Instead, it allows bodies to undergo large displacement motions solved by explicit algorithms, enabling various types of interactions, including atomic, gravitational, and mechanical interactions. For each body, a two-phase volume is defined, comprising an external and internal phase. For example, this could represent a planet and its gravitational orbit. As far as multibody dynamic simulations are concerned , key challenges (Williams and O’Connor 1999) include object representation, contact detection, physics, and visualization. Regarding contact detection and interacting forces evaluation, six contact conditions can be defined (see Figure 5). Contact forces can be simulated using mutually orthogonal forces, traditionally referred to as normal and shear forces, which interact through Coulomb's law. Zubelewicz and Bažant (1987), tracing the origins of discrete element methods back to the work of Serrano and Rodriguez- Orti (1973), proposed a similar model for simulating fracture within the interface of aggregate composites, such as Portland cement conc rete or mortar. This model, inspired by Cundall (1971), involves a random generation of circular discs with varying radii ( ). Each disc is characterized by an annular surface, with a greater diameter ( =1.2 ) where interacting forces are defined to capture interface crack propagation. The discs interact through forces acting along directions orthogonal to the center-to-center line. Ba žant (1984) , Ba žant and Oh (1985), proposed the microplanes to capture the property of aggregate materials that exhibit strain softening. Microplanes , in the framekork of continuos models, are independent planes of various orientation where the nonlinear stress-strain relationship is defined. Each plane can be interpreted as the lattice plane reported in Figure 3. Main difference is that lattice plane are usually randomly distributed, while microplanes are regularly distributed around a point (gauss point) and the randomness could be introduced opportunely adapting the stress-strain relationships. Both lattice and microplane models ( Bažant and Ožbolt , 1990) fall under the category of non-tensorial models and employ simplified stress-strain relationships to capture the micromechanics of deformation. These models provide a valuable framework for understanding and simulating the mechanical behavior of materials, particularly in scenarios involving strain softening. In the microplane model proposed by (O ž bolt et al, 2001) microplane strains, with the exception of the volumetric component ( ), are components of the macroscopic strain. Normal ( ) and shear strain ( ) components are determined, leading to the evaluation of the deviatoric ( ). Shear strain is decomposed in two ( , ) tangential vectors. Volumetric (Fig. 6b), deviatoric (Fig. 6c) and tangential (Fig. 6d) stresses, denoted as , and , stress, are evaluated through calibrated function that depend on three damage function ( , , ) and seven empirical parameters (O ž bolt et al., 2001). Figure 5. Discrete element method. Contact typologies: (a) vertex-face; (b) edge-face; (c) face-face; (d) vertex-vertex; (e) vertex-edge; (f) edge edge (Nisticò, 1994)

Figure 6. Microplane stress-strain relationship. Components: (a) Schematization of aggregate interfaces through micro planes ; (b) Volumetric component; (c) Deviatoric deviatoric component ; (d) Shear component. (Gambarelli et al., 2016a)