Boundary Layer Effect on Behavior of Discrete Models

Abstract

Abstract:The paper studies systems of rigid bodies with randomly generated geometry interconnected by normal and tangential bonds. The stiffness of these bonds determines the macroscopic elastic modulus while the macroscopic Poisson's ratio of the system is determined solely by the normal/tangential stiffness ratio. Discrete models with no directional bias have the same probability of element orientation for any direction and therefore the same mechanical properties in a statistical sense at any point and direction. However, the layers of elements in the vicinity of the boundary exhibit biased orientation, preferring elements parallel with the boundary. As a consequence, when strain occurs in this direction, the boundary layer becomes stiffer than the interior for the normal/tangential stiffness ratio larger than one, and vice versa. Nonlinear constitutive laws are typically such that the straining of an element in shear results in higher strength and ductility than straining in tension.Since the boundary layer tends, due to the bias in the elemental orientation, to involve more tension than shear at the contacts, it also becomes weaker and less ductile. The paper documents these observations and compares them to the results of theoretical analysis.

On macroscopic elastic properties of isotropic discrete systems: effect of tessellation geometry

“…Decreasing γ towards zero yields relations for discrete system with n = t as derived in e.g. [6] under assumption of perpendicularity of contact vector and contact facet. They are also identical to those from microplane theory [4].…”

“…where 1 is the identity matrix of size 2. Because the symmetry implied by equality t = n is no longer present, tensor T is different from definition in [6,8].…”

“…It has been shown that three fundamental assumptions are needed to derive the Poisson's ratio limits, namely the isotropy of geometrical structure, space tessellation into discrete Jan Eliáš units without any voids or overlaps and perpendicularity between contact facets and contact vectors [6]. The third assumption is relaxed here and implications are studied.…”

Simulations of Split Hopkinson Pressure Bar by Discrete Mesoscale Model

“…The model from [4] is further simplified by neglecting confinement effect. Reader interested in detailed description is referred to [5]. Anisotropic nature of concrete fracture is captured thanks to random geometry of particle system.…”

Lattice Modeling of Early-Age Behavior of Structural Concrete

“…The stiffness coefficients of the axial springs are: where is the Voronoi facet area; is the distance between nodes i and j ; factor ξ relates the normal and shear spring stiffnesses, which can be adjusted to simulate macroscopic Poisson ratio of the material [ 18 ]. In most cases of random discretization, there will be boundary layer effects on the mechanical properties [ 54 ]. For ξ = 1, which is used herein, the lattice is elastically homogeneous under uniform modes of straining [ 55 , 56 ], although Poisson ratio ν = 0.…”