Abstract
Advances in manufacturing techniques may now realize virtually any imaginable microstructures, paving the way for architected materials with properties beyond those found in nature. This has lead to a quest for closing gaps in property-space by carefully designed metamaterials. Development of mechanical metamaterials has gone from open truss lattice structures to closed plate lattice structures with stiffness close to theoretical bounds. However, the quest for optimally stiff and strong materials is complex. Plate lattice structures have higher stiffness and (yield) strength but are prone to buckling at low volume fractions. Hence here, truss lattice structures may still be optimal. To make things more complicated, hollow trusses or structural hierarchy bring closed-walled microstructures back in the competition. Based on analytical and numerical studies of common microstructures from the literature, we provide higher order interpolation schemes for their effective stiffness and (buckling) strength. Furthermore, we provide a case study based on multi-property Ashby charts for weight-optimal porous beams under bending, that demonstrates the intricate interplay between structure and microarchitecture that plays the key role in the design of ultimate load carrying structures. The provided interpolation schemes may also be used to account for microstructural yield and buckling in multiscale design optimization schemes.
Highlights
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We provide a case study based on multi-property Ashby charts for weightoptimal porous beams under bending, that demonstrates the intricate interplay between structure and microarchitecture that plays the key role in the design of ultimate load carrying structures
Where all coefficients (0 < < 1) and exponent n0 are estimated from analytical and/or numerical studies. As it will turn out, n0 = 2 for truss lattice structures (TLS) and n0 = 3 for plate lattice structures (PLS), which means that the buckling strengths of the two kinds of microstructures are notably different in terms of volume fraction dependence
Summary
Hashin-Shtrikman (HS) bounds provide upper limits on attainable Young's moduli for porous microstructures [2] These are rather complex expressions given in terms of base material properties: Poisson's ratio ν0 and Young's modulus E0, as well as volume fraction f (see Appendix A). Variability in terms of Poisson's ratio is small in the range of usual (compressible) base material values ν0 ∈ [0, 1/2[, selecting a value of ν0 = 1/3 at most gives an error of 1% in aforementioned interval With this assumption, HS bounds for isotropic and cubic symmetric materials become. An assumption behind the Castañeda bound is that it ignores stress concentrations and approaches the solid material yield strength σ0 as volume fraction approaches one. A simplified bound that takes some of this stress concentration the linear function σ uyat1⁄4h∂i∂σgfuyhef 1⁄4r 0vfoσlu0 m1⁄4e2pf2r3ffi6affi9ffifficftσio0n≈s into account
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