Energy-Based Coarse Graining of the Lattice-Discrete Particle Model

Homogenization of discrete mesoscale model of concrete for coupled mass transport and mechanics by asymptotic expansion

“…The primary variables p, u and θ are now considered to be approximated by several components, especially by the macroscopic component, • (0) , and the microscopic component, • (1) . Expansion of the pressure and displacements is straightforward.…”

“…( 12) into ∇ = ∇ X + η −1 ∇ y . The three asymptotic expansion equations read p(X, y) = η −1 p (−1) (X, y) + p (0) (X, y) + ηp (1) (X, y) + . .…”

“…There are several known and widely used techniques available for reducing computational complexity of numerical models. The techniques applicable for mechanical discrete mesoscale models spans from (i) coarse graining [50,46,1], (ii) adaptivity [25,58,19,15], (iii) model order reduction such as Proper orthogonal decomposition [61,18,44,13] and (iv) homogenization.…”

Discrete modeling of deterministic size effect of normal-strength and ultra-high performance concrete under compression

“…CG is widely used in the field of atomistic simulations and molecular dynamics [66]. Moreover, CG was also successfully adopted in many LDPM numerical studies [55], and its efficiency and accuracy has been verified by simulating several examples, see [67,68]. The adopted values for the LDPM mesoscale parameters are compressive yielding strength = 500 MPa, initial hardening modulus ratio = 0.36, densification ratio = 2.5, transitional strain ratio = 2, shear strength ratio = 17, initial friction = 0.5, softening exponent = 0.2, transitional stress = 300 MPa, tensile strength = 4, and tensile characteristic length = 150 mm [55].…”

Recent Advances in Computational Methods in Engineering Mechanics

“…They employ the naturally stabilized nodal integration (NSNI) technique to achieve a stable and efficient reproducing kernel mixed formulation. Abdellatef and Alnaggar (2020) present a formulation for calibration-free coarse graining approach within the framework of the lattice-discrete particle model (LDPM). They validate their approach against various test cases, showing success in replicating similar fine-scale response and failure patterns at a fraction of the fine-scale computational cost.…”