Lattice approaches have emerged as a powerful tool to capture the effective mechanical behavior of heterogeneous materials using harmonic interactions inspired from beam-type stretch and rotational interactions between a discrete number of mass points. In this paper, the lattice element method (LEM) is reformulated within the conceptual framework of empirical force fields employed at the lattice scale. Within this framework, because classical harmonic formulations are but a Taylor expansion of nonharmonic potential expressions, they can be used to model both the linear and the nonlinear response of discretized material systems. Specifically, closed-form calibration procedures for such interaction potentials are derived for both the isotropic and the transverse isotropic elastic cases on cubic lattices, in the form of linear relations between effective elasticity properties and energy parameters that define the interactions. The relevance of the approach is shown by an application to the classical Griffith crack problem. In particular, it is shown that continuum-scale quantities of linear-elastic fracture mechanics, such as stress intensity factors (SIFs), are well captured by the method, which by its very discrete nature removes geometric discontinuities that provoke stress singularities in the continuum case. With its strengths and limitations thus defined, the proposed LEM is well suited for the study of multiphase materials whose microtextural information is obtained by, e.g., X-ray micro-computed tomography.with the current understanding of the link between texture (here lattice) and the deformation behavior of materials (Greaves et al. 2011). In order to overcome this limitation, several authors suggested the addition of beam-type interactions between mass points in 2D (e.g., Garboczi 1996, 1997;Bolander and Saito 1998) and 3D with or without rotational degrees of freedom (Zhao et al. 2011), with up to 178 interactions for each node in the (random lattice) system (Lilliu et al. 1999;Lilliu and van Mier 2003). While the preceding approaches allowed removing some of the earlier limitations of the central-force model, a search of the relevant literature was not conclusive in finding a rational framework that clearly defines the different elements of the method, from the local interactions that link the lattice's mass points to the macroscopic properties of the assembly of links, which is, in short, the focus of this paper. Such a framework is needed though not only for elastic (i.e., reversible) phenomena, but also for extending the method to poroelasticity (Monfared et al. 2016) or dissipative phenomena, related to plastic deformation, fracture, and so on, for which the method is frequently applied (e.g., Affes et al.

a b s t r a c tThe effective mechanical behavior of multiphase solid materials is generally modeled by means of homogenization techniques that account for phase volume fractions and elas-tic moduli without considering the spatial distribution of the different phases. By means of extensive numerical simulations of randomly generated porous materials using the lat-tice element method, the role of local textural properties on the effective elastic proper-ties of disordered porous materials is investigated and compared with different continuum micromechanics-based models. It is found that the pronounced disorder-induced stiffness degradation originates from stress concentrations around pore clusters in highly disordered porous materials. We identify a single disorder parameter, ϕs a , which combines a measure of the spatial disorder of pores (the clustering index, s a ) with the pore volume fraction (the porosity, ϕ) to scale the disorder-induced stiffness degradation. Thus, we conclude that the classical continuum micromechanics models with one spherical pore phase, due to their underlying homogeneity assumption fall short of addressing the clustering effect, unless additional texture information is introduced, e.g. in form of the shift of the perco-lation threshold with disorder, or other functional relations between volume fractions and spatial disorder; as illustrated herein for a differential scheme model representative of a twophase (solid-pore) composite model material.

Cell layers eliminate unwanted cells through the extrusion process, which underlines healthy versus flawed tissue behaviors. Although several biochemical pathways have been identified, the underlying mechanical basis including the forces involved in cellular extrusion remain largely unexplored. Utilizing a phase-field model of a three-dimensional cell layer, we study the interplay of cell extrusion with cell-cell and cell-substrate interactions, in a monolayer. Independent tuning of cell-cell versus cell-substrate adhesion forces in the model reveals that a higher cell-substrate adhesion leads to a lower number of total extrusion events. We find extrusion events to be linked to both half-integer topological defects in the orientation field of the cells and to five-fold disclinations in cellular arrangements. We also show that increasing the relative cell-cell adhesion forces translates into a higher likelihood for an extrusion event to be associated with a five-fold disclination and a weaker correlation with +1/2 topological defects. We unify our findings by accessing mechanical stress fields: an extrusion event acts as a mechanism to relieve localized stress concentration.

7Poromechanics of heterogeneous media is reformulated in a discrete framework using Lattice

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