tugni925
Mechanical
- Sep 14, 2020
- 107
- rank-n laminates
- plate lattice structures (PLS)
- open truss lattice structures (TLS)
This is the context in which it is mentioned:
A” stiff competition” [1] for architected materials has been going on for decades. Already in the 1980's, applied mathematicians found that microstructures meeting the upper Hashin-Shtrikman bounds [2] can be realized by so-called rank-n laminates [3–5]. These, however, are physically unrealistic since they require laminations at up to n = 6 widely differing length-scales, although they in the low volume fraction case can be simplified to one length scale [6]. Importantly, these optimally stiff microstructures are closed-walled, from now on denoted plate lattice structures (PLS). For intermediate volume fractions, PLS that are optimal in the low volume fraction limit may be thicknessscaled to yield practically realizable microstructures with Young's moduli within 10% of the theoretically achievable values [7–9]. If for reasons like manufacturability or permeability, one is restricted to open truss lattice structures (TLS), this comes at the cost of an up to three-fold decrease in attainable stiffnesses [6–8,10].
- plate lattice structures (PLS)
- open truss lattice structures (TLS)
This is the context in which it is mentioned:
A” stiff competition” [1] for architected materials has been going on for decades. Already in the 1980's, applied mathematicians found that microstructures meeting the upper Hashin-Shtrikman bounds [2] can be realized by so-called rank-n laminates [3–5]. These, however, are physically unrealistic since they require laminations at up to n = 6 widely differing length-scales, although they in the low volume fraction case can be simplified to one length scale [6]. Importantly, these optimally stiff microstructures are closed-walled, from now on denoted plate lattice structures (PLS). For intermediate volume fractions, PLS that are optimal in the low volume fraction limit may be thicknessscaled to yield practically realizable microstructures with Young's moduli within 10% of the theoretically achievable values [7–9]. If for reasons like manufacturability or permeability, one is restricted to open truss lattice structures (TLS), this comes at the cost of an up to three-fold decrease in attainable stiffnesses [6–8,10].
