Simulating the Poisson effect in lattice models of elastic continua

Abstract

Lattice models provide discontinuous approximations of the displacement field over the computational domain, which facilitates the modeling of fracture and other discontinuous phenomena. By discretizing the domain with two-node elements, however, ordinary lattice models cannot simulate the Poisson effect in a local (intra-element) sense, which is problematic for some types of analyses.Furthermore, such methods are limited in the range of Poisson ratio values that can be simulated. We present a new approach to remedy such known, yet underappreciated, shortcomings of lattice models. In this approach, the Poisson effect is modeled through the introduction of fictitious stresses into a regular lattice. Capabilities of the new approach are demonstrated through compressive test simulations of homogeneous and heterogeneous materials. The simulation results are compared with theory and those of continuum finite element models. The comparisons show good agreement for arbitrary Poisson ratios (including ν ⩾ 1/3) with respect to nodal displacement, intra-element stress, and nodal stress. This form of discrete method, supplemented by the proposed fictitious measures of stress, retains the simplicity of collections of two-node elements.

Elastically-homogeneous lattice models of damage in geomaterials

“…The basic concept of the auxiliary (or fictitious) stress approach has been described in a previous study [3], for the special case of planar lattices composed of regular triangles. The extension to 3D irregular lattices, described herein, involves several generalizations.…”

“…4a). Asahina et al [3] derived asymptotic values of the auxiliary stress, such that iteration is not necessary, for planar cases. Herein, the derivation is extended to three dimensions.…”

“…The inability of lattice models to represent elasticity in a local sense is less appreciated [31,3]. Discrepancies with elastic continua appear in both regular and irregular lattice models.…”

“…This research involves the development of elasticallyhomogeneous 3D lattice models and their application to simulating brittle failure of geomaterials. The model formulation relies on the auxiliary (or fictitious) stress approach, which was originally proposed for the elastic analyses of planar, regular triangle lattices [3]. Herein, the approach is extended for use in random, three-dimensional assemblages of rigid-body-spring elements, which are a form of lattice model.…”

Spatial representation of fiber bridging forces in strain-hardening cement composites

“…Correct representation of the Poisson effect, both globally and in an element-local sense, has recently been accomplished [15]. …”