Effect of minimal defects in periodic cellular solids

Abstract

We study the relationship between the geometry of a point defect and the spatial distribution of the strain energy in an otherwise regular two-dimensional cellular solid. Sites of concentrated strain energy are potential sites for failure initiation in the cellular solid. For simplicity, a hexagonal honeycomb structure is chosen for our analysis. In our description, the basic building block of the honeycomb is not a beam, but rather a three-armed ''joint'', with the three beams meeting at a junction point. A minimal defect is introduced in an otherwise regular hexagonal honeycomb by exchanging one joint of the regular honeycomb with a joint of varying geometry. Finite element methods and micromechanical models are used to calculate the spatial distribution of the strain energy density (SED). Two different scenarios are found depending on the external loading. For hydrostatic loading, the SED is concentrated in the defect. Uniaxial loading resulted in intricate distribution of the SED, with its highest values not in the defect but in the nearer environment of the defect. The study demonstrates the complexity of SED patterns occurring around defects, which change their characteristics depending on the loading conditions.

Mechanical regulation of bone formation and resorption around implants in a mouse model of osteopenic bone

“…We also observed clear layer-specific differences in the strain levels where (re)modelling events occurred: average strains of bone formation and resorption were significantly different among the three layers, with L1 featuring the smallest values and L3 the highest. This could be due to the presence of the implant with a Young's modulus much higher than bone, which caused peak stresses at some distance from the bone -implant interface due to a complex load redistribution, in analogy to inclusions inside cellular solids [63,64]. Concerning the reduced mechano-responsiveness observed within peri-implant bone (especially in L3), our results are in agreement with previous studies reporting the effect of mechanical stimulation being confined around the implant [65,66].…”

The role of geometrical disorder on swelling anisotropy of cellular solids

“…The deformation localization due to structural disorder and different kinds of structural irregularities in two-dimensional (Ruffoni et al, 2010) and three-dimensional (Luxner et al, 2009) cellular structures under external mechanical loads have been widely investigated using finite element methods and micro-mechanical models. However, the swelling (expansion) behavior of cellular solids has not been studied to the same extent.…”

Pressurized honeycombs as soft-actuators: a theoretical study

“…These models estimate the macroscopic 'continuum' mechanical properties of a regular cellular material from microscopic parameters like nodal connectivity, cell shape, relative density and mechanical properties of the cell wall material [21,[25][26][27]. Moreover, the influence of cell-size distribution, irregularity and point defects on the elastic and failure properties of honeycombs and foams has also been extensively studied [28][29][30]. In these studies, the mechanical properties of the cellular material are discussed by simulating 'simple' boundary value problems (uniaxial, biaxial or pure shearing loading).…”