Specific modulus
Specific modulus is a materials property consisting of the elastic modulus per mass density of a material. It is also known as the stiffness to weight ratio or specific stiffness. High specific modulus materials find wide application in aerospace applications where minimum structural weight is required. The dimensional analysis yields units of distance squared per time squared. The equation can be written as:
where is the elastic modulus and is the density.
The utility of specific modulus is to find materials which will produce structures with minimum weight, when the primary design limitation is deflection or physical deformation, rather than load at breaking—this is also known as a "stiffness-driven" structure. Many common structures are stiffness-driven over much of their use, such as airplane wings, bridges, masts, and bicycle frames.
To emphasize the point, consider the issue of choosing a material for building an airplane. Aluminum seems obvious because it is "lighter" than steel, but steel is stronger than aluminum, so one could imagine using thinner steel components to save weight without sacrificing (tensile) strength. The problem with this idea is that there would be a significant sacrifice of stiffness, allowing, e.g., wings to flex unacceptably. Because it is stiffness, not tensile strength, that drives this kind of decision for airplanes, we say that they are stiffness-driven.
The connection details of such structures may be more sensitive to strength (rather than stiffness) issues due to effects of stress risers.
Specific modulus is not to be confused with specific strength, a term that compares strength to density.
Applications
[edit]Specific stiffness in tension
[edit]The use of specific stiffness in tension applications is straightforward. Both stiffness in tension and total mass for a given length are directly proportional to cross-sectional area. Thus performance of a beam in tension will depend on Young's modulus divided by density.
Specific stiffness in buckling and bending
[edit]Specific stiffness can be used in the design of beams subject to bending or Euler buckling, since bending and buckling are stiffness-driven. However, the role that density plays changes depending on the problem's constraints.
Beam with fixed dimensions; goal is weight reduction
[edit]Examining the formulas for buckling and deflection, we see that the force required to achieve a given deflection or to achieve buckling depends directly on Young's modulus.
Examining the density formula, we see that the mass of a beam depends directly on the density.
Thus if a beam's cross-sectional dimensions are constrained and weight reduction is the primary goal, performance of the beam will depend on Young's modulus divided by density.
Beam with fixed weight; goal is increased stiffness
[edit]By contrast, if a beam's weight is fixed, its cross-sectional dimensions are unconstrained, and increased stiffness is the primary goal, the performance of the beam will depend on Young's modulus divided by either density squared or cubed. This is because a beam's overall stiffness, and thus its resistance to Euler buckling when subjected to an axial load and to deflection when subjected to a bending moment, is directly proportional to both the Young's modulus of the beam's material and the second moment of area (area moment of inertia) of the beam.
Comparing the list of area moments of inertia with formulas for area gives the appropriate relationship for beams of various configurations.
Beam's cross-sectional area increases in two dimensions
[edit]Consider a beam whose cross-sectional area increases in two dimensions, e.g. a solid round beam or a solid square beam.
By combining the area and density formulas, we can see that the radius of this beam will vary with approximately the inverse of the square of the density for a given mass.
By examining the formulas for area moment of inertia, we can see that the stiffness of this beam will vary approximately as the fourth power of the radius.
Thus the second moment of area will vary approximately as the inverse of the density squared, and performance of the beam will depend on Young's modulus divided by density squared.
Beam's cross-sectional area increases in one dimension
[edit]Consider a beam whose cross-sectional area increases in one dimension, e.g. a thin-walled round beam or a rectangular beam whose height but not width is varied.
By combining the area and density formulas, we can see that the radius or height of this beam will vary with approximately the inverse of the density for a given mass.
By examining the formulas for area moment of inertia, we can see that the stiffness of this beam will vary approximately as the third power of the radius or height.
Thus the second moment of area will vary approximately as the inverse of the cube of the density, and performance of the beam will depend on Young's modulus divided by density cubed.
However, caution must be exercised in using this metric. Thin-walled beams are ultimately limited by local buckling and lateral-torsional buckling. These buckling modes depend on material properties other than stiffness and density, so the stiffness-over-density-cubed metric is at best a starting point for analysis. For example, most wood species score better than most metals on this metric, but many metals can be formed into useful beams with much thinner walls than could be achieved with wood, given wood's greater vulnerability to local buckling. The performance of thin-walled beams can also be greatly modified by relatively minor variations in geometry such as flanges and stiffeners.[1][2][3]
Stiffness versus strength in bending
[edit]Note that the ultimate strength of a beam in bending depends on the ultimate strength of its material and its section modulus, not its stiffness and second moment of area. Its deflection, however, and thus its resistance to Euler buckling, will depend on these two latter values.
Approximate specific stiffness for various materials
[edit]
| Material | Young's modulus (GPa) | Density (g/cm3) | Young's modulus per density; specific stiffness (106 m2s−2) | Young's modulus per density squared (103 m5kg−1s−2) | Young's modulus per density cubed (m8kg−2s−2) | Reference |
|---|---|---|---|---|---|---|
| Latex foam, low density, 10% compression[4] | 5.9×10−7 | 0.06 | 9.83×10−6 | 0.000164 | 0.00273 | |
| Reversible Assembled Cellular Composite Materials | 0.0123 | 0.0072 | 1.71 | 237 | 32,953 | [5][6] |
| Self Reprogrammable Mechanical Metamaterials | 0.0011129 | 0.0103 | 0.108 | 10.5 | 1,018 | [7][8] |
| Latex foam, low density, 40% compression[4] | 1.8×10−6 | 0.06 | 3×10−5 | 0.0005 | 0.00833 | |
| Latex foam, high density, 10% compression[4] | 1.3×10−5 | 0.2 | 6.5×10−5 | 0.000325 | 0.00162 | |
| Latex foam, high density, 40% compression[4] | 3.8×10−5 | 0.2 | 0.00019 | 0.00095 | 0.00475 | |
| Silica aerogel, medium density[9] | 0.00035 | 0.09 | 0.00389 | 0.0432 | 0.48 | |
| Rubber (small strain) | 0.055±0.045 | 1.055±0.145[10] | 0.059±0.051 | 0.06345±0.05655 | 0.0679±0.0621 | |
| Expanded polystrene (EPS) foam, low density (1 lb/ft3)[11] | 0.00137 | 0.016 | 0.086 | 5.35 | 334 | |
| Silica aerogel, high density[9] | 0.024 | 0.25 | 0.096 | 0.384 | 1.54 | |
| Expanded polystrene (EPS) foam, medium density (3 lb/ft3)[11] | 0.00524 | 0.048 | 0.11 | 2.3 | 47 | |
| Low-density polyethylene | 0.2 | 0.925±0.015 | 0.215±0.005 | 0.235±0.005 | 0.255±0.015 | |
| PTFE (Teflon) | 0.5 | 2.2 | 0.23 | 0.10 | 0.047 | |
| Duocel aluminum foam, 8% density[12] | 0.102 | 0.216 | 0.472 | 2.19 | 10.1 | |
| Extruded polystrene (XPS) foam, medium density (Foamular 400)[13][14] | 0.013789 | 0.0289 | 0.48 | 16.5 | 571 | |
| Extruded polystrene (XPS) foam, high density (Foamular 1000)[13][14] | 0.02551 | 0.0481 | 0.53 | 11 | 229 | |
| HDPE | 0.8 | 0.95[15] | 0.84 | 0.89 | 0.93 | |
| Duocel copper foam, 8% density[16] | 0.736 | 0.717 | 1.03 | 1.43 | 2 | |
| Polypropylene[17] | 1.2±0.3 | 0.9 | 1.33±0.33 | 1.48±0.37 | 1.65±0.41 | |
| Polyethylene terephthalate | 2.35±0.35 | 1.4125±0.0425 | 1.7±0.3 | 1.17±0.23 | 0.875±0.225 | |
| Nylon | 3.0±1.0 | 1.15 | 2.6±0.9 | 2.25±0.75 | 1.95±0.65 | |
| Polystyrene | 3.25±0.25 | 1.05 | 3.1±0.2 | 2.95±0.25 | 2.8±0.2 | |
| Biaxially-oriented Polypropylene[17] | 3.2±1.0 | 0.9 | 3.56±1.11 | 3.95±1.23 | 4.39±1.37 | |
| Medium-density fibreboard | 4 | 0.75[18] | 5.3 | 7.1 | 9.5 | |
| Titanium foam, low density[19] | 5.3 | 0.991 | 5.35 | 5.4 | 5.45 | |
| Titanium foam, high density[19] | 20 | 3.15 | 6.35 | 2.02 | 0.64 | |
| Foam glass[20] | 0.9 | 0.12 | 7.5 | 62.5 | 521 | |
| Copper (Cu) | 117 | 8.94 | 13 | 1.5 | 0.16 | |
| Brass and bronze | 112.5±12.5 | 8.565±0.165 | 13.0±2.0 | 1.55±0.25 | 0.18±0.03 | |
| Zinc (Zn) | 108 | 7.14 | 15 | 2.1 | 0.29 | |
| Oak wood (along grain) | 11 | 0.76±0.17[21] | 15.5±3.5 | 22.5±9.5 | 34.0±20.0 | |
| Concrete (under compression) | 40±10 | 2.4 | 17±4 | 6.95±1.75 | 2.9±0.7 | |
| Glass-reinforced plastic[22][23][24] | 31.65±14.45 | 1.8 | 18±8 | 9.65±4.35 | 5.4±2.5 | |
| Pine wood | 8.963 | 0.505±0.155[21] | 20±6 | 47±26 | 120±89 | |
| Balsa, low density (4.4 lb/ft3)[25] | 1.41 | 0.071 | 20 | 280 | 3,940 | |
| Tungsten (W) | 400 | 19.25 | 21 | 1.1 | 0.056 | |
| Sitka spruce green[26][27][28] | 8.7±0.7 | 0.37 | 23.5±2 | 64±5 | 172±13 | |
| Osmium (Os) | 550 | 22.59 | 24 | 1.1 | 0.048 | |
| Balsa, medium density (10 lb/ft3)[25] | 3.86 | 0.163 | 24 | 145 | 891 | |
| Steel | 200 | 7.9±0.15 | 25±0.5 | 3.2±0.1 | 0.41±0.02 | |
| Titanium alloys | 112.5±7.5 | 4.5 | 25±2 | 5.55±0.35 | 1.23±0.08 | |
| Balsa, high density (16 lb/ft3)[25] | 6.57 | 0.265 | 25 | 94 | 353 | |
| Wrought iron | 200±10 | 7.7±0.2 | 26±2 | 3.35±0.35 | 0.445±0.055 | |
| Magnesium metal (Mg) | 45 | 1.738 | 26 | 15 | 8.6 | |
| Sitka spruce dry[26][27][28] | 10.4±0.8 | 0.4 | 26±2 | 65±5 | 162±12 | |
| Macor machineable glass-ceramic[29] | 66.9 | 2.52 | 26.55 | 10.53 | 8.14 | |
| Cordierite[30] | 70 | 2.6 | 26.9 | 10.4 | 3.98 | |
| Glass | 70±20 | 2.6±0.2[31] | 28±10 | 11.2±4.8 | 4.4±2.1 | |
| Tooth enamel (largely calcium phosphate) | 83 | 2.8[32] | 30 | 11 | 3.8 | |
| E-Glass fiber[33][34] | 81 | 2.62 | 31 | 12 | 4.5 | |
| Molybdenum (Mo) | 329 | 10.28 | 32 | 3.1 | 0.30 | |
| Basalt fiber | 89 | 2.7 | 33 | 12 | 4.5 | |
| Zirconia[30] | 207 | 6.04 | 34.3 | 5.67 | 0.939 | |
| Tungsten carbide (WC) | 550±100 | 15.8 | 34.5±6.5 | 2.2±0.4 | 0.135±0.025 | |
| S-Glass fiber[33][35] | 89 | 2.5 | 36 | 14 | 5.7 | |
| Flax fiber[36][37][38][39] | 45±34 | 1.35±0.15 | 36.65±29.35 | 30±25 | 25±21 | |
| single-crystal Yttrium iron garnet (YIG) | 200 | 5.17[40] | 39 | 7.5 | 1.4 | |
| Kevlar 29[41] (tensile only[42]) | 70.5 | 1.44 | 49 | 34 | 24 | |
| Steatite L-5[30] | 138 | 2.71 | 50.9 | 18.8 | 6.93 | |
| Mullite[30] | 150 | 2.8 | 53.6 | 19.1 | 6.83 | |
| Dyneema SK25 Ultra-high-molecular-weight polyethylene (tensile only)[43] | 52 | 0.97 | 54 | 55 | 57 | |
| Beryllium, 30% porosity[44] | 76 | 1.3 | 58.5 | 45 | 34.6 | |
| Kevlar 49[41] (tensile only[42]) | 112.4 | 1.44 | 78 | 54 | 38 | |
| Silicon[45] | 185 | 2.329 | 79 | 34 | 15 | |
| Alumina fiber (Al2O3)[46][47][35] | 300 | 3.595±0.315 | 84±7 | 24±4 | 6.76±1.74 | |
| Syalon 501 Silicon nitride[48] | 340 | 4.01 | 84.8 | 21.1 | 5.27 | |
| Sapphire[30] | 400 | 3.97 | 101 | 25.4 | 6.39 | |
| Alumina[30] | 393 | 3.8 | 103 | 27.2 | 7.16 | |
| Carbon fiber reinforced plastic (70:30 fibre:matrix, unidirectional, along grain)[49] | 181 | 1.6 | 113 | 71 | 44 | |
| Dyneema SK78/Honeywell Spectra 2000 UHMWPE (tensile only)[43][50] | 121±11 | 0.97 | 125±11 | 128±12 | 132±12 | |
| Silicon carbide (SiC) | 450 | 3.21 | 140 | 44 | 14 | |
| Beryllium (Be) | 287 | 1.85 | 155 | 84 | 45 | |
| Boron fiber[51] | 400 | 2.54 | 157 | 62 | 24 | |
| Boron nitride[30] | 675 | 2.28 | 296 | 130 | 57 | |
| Diamond (C) | 1,220 | 3.53 | 347 | 98 | 28 | |
| Dupont E130 carbon fiber[52] | 896 | 2.15 | 417 | 194 | 90 |
| Material | Young's modulus (GPa) | Density (g/cm3) | Young's modulus per density; specific stiffness (106 m2s−2) | Young's modulus per density squared (103 m5kg−1s−2) | Young's modulus per density cubed (m8kg−2s−2) |
|---|---|---|---|---|---|
| Applewood or wild apple (Pyrus malus) | 8.76715 | 0.745 | 11.768 | 15.7959 | 21.2026 |
| Ash, black (Fraxinus nigra) | 11.0423 | 0.526 | 20.9929 | 39.9105 | 75.8755 |
| Ash, blue (quadrangulata) | 9.64974 | 0.603 | 16.0029 | 26.5388 | 44.0113 |
| Ash, green (Fraxinus pennsylvanica lanceolata) | 11.4738 | 0.610 | 18.8095 | 30.8352 | 50.5495 |
| Ash, white (Fraxinus americana) | 12.2485 | 0.638 | 19.1983 | 30.0914 | 47.1651 |
| Aspen (Populus tremuloides) | 8.21797 | 0.401 | 20.4937 | 51.1065 | 127.448 |
| Aspen, large tooth (Populus grandidentata) | 9.76742 | 0.412 | 23.7073 | 57.5421 | 139.665 |
| Basswood (Tilia glabra or Tilia americanus) | 10.091 | 0.398 | 25.3544 | 63.7045 | 160.061 |
| Beech (Fagus grandifolia or Fagus americana) | 11.5718 | 0.655 | 17.6669 | 26.9724 | 41.1793 |
| Beech, blue (Carpinus caroliniana) | 7.3746 | 0.717 | 10.2854 | 14.345 | 20.007 |
| Birch, gray (Betula populifolia) | 7.8159 | 0.552 | 14.1592 | 25.6508 | 46.4688 |
| Birch, paper (Betula papyrifera) | 10.9736 | 0.600 | 18.2894 | 30.4823 | 50.8039 |
| Birch, sweet (Betula lenta) | 14.9061 | 0.714 | 20.8769 | 29.2394 | 40.9515 |
| Buckeye, yellow (Aesculus octandra) | 8.12971 | 0.383 | 21.2264 | 55.4214 | 144.703 |
| Butternut (Juglans cinerea) | 8.13952 | 0.404 | 20.1473 | 49.8696 | 123.44 |
| Cedar, eastern red (Juniperus virginiana) | 6.00167 | 0.492 | 12.1985 | 24.7937 | 50.3938 |
| Cedar, northern white (Thuja occidentalis) | 5.57018 | 0.315 | 17.6831 | 56.1368 | 178.212 |
| Cedar, southern white (Chamaecyparis thvoides) | 6.42336 | 0.352 | 18.2482 | 51.8414 | 147.277 |
| Cedar, western red (Thuja plicata) | 8.03165 | 0.344 | 23.3478 | 67.8715 | 197.301 |
| Cherry, black (Prunus serotina) | 10.2578 | 0.534 | 19.2093 | 35.9724 | 67.3641 |
| Cherry, wild red (Prunus pennsylvanica) | 8.74753 | 0.425 | 20.5824 | 48.4292 | 113.951 |
| Chestnut (Castanea dentata) | 8.53179 | 0.454 | 18.7925 | 41.3931 | 91.1743 |
| Cottonwood, eastern (Populus deltoides) | 9.53206 | 0.433 | 22.014 | 50.8407 | 117.415 |
| Cypress, southern (Taxodium distichum) | 9.90472 | 0.482 | 20.5492 | 42.6332 | 88.4506 |
| Dogwood (flowering) (Cornus Florida) | 10.6402 | 0.796 | 13.3671 | 16.7928 | 21.0965 |
| Douglas fir (coast type) (Pseudotsuga taxifolia) | 13.3076 | 0.512 | 25.9915 | 50.7646 | 99.1495 |
| Douglas fir (mountain type) (Pseudotsuga taxifolia) | 9.62032 | 0.446 | 21.5702 | 48.3637 | 108.439 |
| Ebony, Andaman marble-wood (India) (Diospyros kursii) | 12.4544 | 0.978 | 12.7346 | 13.0211 | 13.314 |
| Ebony, Ebè marbre (Mauritius, E. Africa) (Diospyros melanida) | 9.8753 | 0.768 | 12.8585 | 16.7428 | 21.8005 |
| Elm, American (Ulmus americana) | 9.2967 | 0.554 | 16.7811 | 30.2907 | 54.6764 |
| Elm, rock (Ulmus racemosa or Ulmus thomasi) | 10.65 | 0.658 | 16.1854 | 24.5979 | 37.3829 |
| Elm, slippery (Ulmus fulva or pubescens) | 10.297 | 0.568 | 18.1285 | 31.9164 | 56.1908 |
| Eucalyptus, Karri (W. Australia) (Eucalyptus diversicolor) | 18.4855 | 0.829 | 22.2986 | 26.8982 | 32.4465 |
| Eucalyptus, Mahogany (New South Wales) (Eucalyptus hemilampra) | 15.7691 | 1.058 | 14.9046 | 14.0875 | 13.3153 |
| Eucalyptus, West Australian mahogany (Eucalyptus marginata) | 14.3373 | 0.787 | 18.2177 | 23.1483 | 29.4133 |
| Fir, balsam (Abies balsamea) | 8.62005 | 0.414 | 20.8214 | 50.2932 | 121.481 |
| Fir, silver (Abies amabilis) | 10.552 | 0.415 | 25.4264 | 61.2684 | 147.635 |
| Gum, black (Nyssa sylvatica) | 8.22778 | 0.552 | 14.9054 | 27.0025 | 48.9176 |
| Gum, blue (Eucalyptus globulus) | 16.5046 | 0.796 | 20.7344 | 26.0483 | 32.7239 |
| Gum, red (Liquidambar styraciflua) | 10.2479 | 0.530 | 19.3358 | 36.4826 | 68.835 |
| Gum, tupelo (Nyssa aquatica) | 8.71811 | 0.524 | 16.6376 | 31.7512 | 60.5939 |
| Hemlock eastern (Tsuga canadensis) | 8.29643 | 0.431 | 19.2492 | 44.6618 | 103.624 |
| Hemlock, mountain (Tsuga martensiana) | 7.8159 | 0.480 | 16.2831 | 33.9232 | 70.6733 |
| Hemlock, western (Tsuga heterophylla) | 9.95375 | 0.432 | 23.0411 | 53.3359 | 123.463 |
| Hickory, bigleaf shagbark (Hicoria laciniosa) | 13.0919 | 0.809 | 16.1828 | 20.0034 | 24.7261 |
| Hickory, mockernut (Hicoria alba) | 15.3964 | 0.820 | 18.7761 | 22.8977 | 27.9241 |
| Hickory, pignut (Hicoria glabra) | 15.7201 | 0.820 | 19.1708 | 23.379 | 28.511 |
| Hickory, shagbark (Hicoria ovata) | 14.9551 | 0.836 | 17.8889 | 21.3982 | 25.596 |
| Hornbeam (Ostrya virginiana) | 11.7582 | 0.762 | 15.4307 | 20.2502 | 26.5751 |
| Ironwood, black (Rhamnidium ferreum) | 20.594 | 1.077−1.30 | 17.48±1.64 | 14.97±2.78 | 12.93±3.56 |
| Larch, western (Larix occidentalis) | 11.6503 | 0.587 | 19.8472 | 33.8112 | 57.6 |
| Locust, black or yellow (Robinia pseudacacia) | 14.2 | 0.708 | 20.0565 | 28.3284 | 40.0119 |
| Locust honey (Gleditsia triacanthos) | 11.4247 | 0.666 | 17.1543 | 25.7572 | 38.6744 |
| Magnolia, cucumber (Magnolia acuminata) | 12.5133 | 0.516 | 24.2506 | 46.9972 | 91.0798 |
| Mahogany (W. Africa) (Khaya ivorensis) | 10.5814 | 0.668 | 15.8404 | 23.7131 | 35.4987 |
| Mahogany (E. India) (Swietenia macrophylla) | 8.01203 | 0.54 | 14.8371 | 27.4761 | 50.8817 |
| Mahogany (E. India) (Swietenia mahogani) | 8.72792 | 0.54 | 16.1628 | 29.9311 | 55.428 |
| Maple, black (Acer nigrum) | 11.1894 | 0.620 | 18.0474 | 29.1087 | 46.9495 |
| Maple, red (Acer rubrum) | 11.3267 | 0.546 | 20.7448 | 37.9942 | 69.5865 |
| Maple, silver (Acer saccharinum) | 7.89435 | 0.506 | 15.6015 | 30.833 | 60.9347 |
| Maple, sugar (Acer saccharum) | 12.6506 | 0.676 | 18.7139 | 27.6832 | 40.9515 |
| Oak, black (Quercus velutina) | 11.3071 | 0.669 | 16.9014 | 25.2637 | 37.7634 |
| Oak, bur (Quercus macrocarpa) | 7.09021 | 0.671 | 10.5666 | 15.7476 | 23.4688 |
| Oak, canyon live (Quercus chrysolepis) | 11.2678 | 0.838 | 13.4461 | 16.0455 | 19.1473 |
| Oak, laurel (Quercus Montana) | 10.9246 | 0.674 | 16.2086 | 24.0484 | 35.6801 |
| Oak, live (Quercus virginiana) | 13.543 | 0.977 | 13.8618 | 14.1881 | 14.5221 |
| Oak, post (Quercus stellata or Quercus minor) | 10.4245 | 0.738 | 14.1253 | 19.14 | 25.9349 |
| Oak, red (Quercus borealis) | 12.4937 | 0.657 | 19.0162 | 28.9441 | 44.0549 |
| Oak, swamp chestnut (Quercus Montana (Quercus prinus)) | 12.2289 | 0.756 | 16.1758 | 21.3965 | 28.3023 |
| Oak swamp white (Quercus bicolor or Quercus platanoides) | 14.1804 | 0.792 | 17.9046 | 22.6068 | 28.5439 |
| Oak, white (Quercus alba) | 12.2681 | 0.710 | 17.279 | 24.3367 | 34.277 |
| Paulownia (P. tomentosa) | 6.894 | 0.274 | 25.1606 | 91.8269 | 335.134 |
| Persimmon (Diospyros virginiana) | 14.151 | 0.776 | 18.2358 | 23.4998 | 30.2832 |
| Pine, eastern white (Pinus strobus) | 8.80637 | 0.373 | 23.6096 | 63.2964 | 169.696 |
| Pine, jack (Pinus banksiana or Pinus divericata) | 8.51217 | 0.461 | 18.4646 | 40.0533 | 86.8836 |
| Pine, loblolly (Pinus taeda) | 13.2782 | 0.593 | 22.3916 | 37.7598 | 63.6759 |
| Pine, longleaf (Pinus palustris) | 14.1706 | 0.638 | 22.211 | 34.8135 | 54.5665 |
| Pine, pitch (Pinus rigida) | 9.46342 | 0.542 | 17.4602 | 32.2144 | 59.4361 |
| Pine, red (Pinus resinosa) | 12.3956 | 0.507 | 24.4489 | 48.2227 | 95.1139 |
| Pine, shortleaf (Pinus echinata) | 13.1899 | 0.584 | 22.5855 | 38.6738 | 66.2223 |
| Poplar, balsam (Populus balsamifera or Populus candicans) | 7.02156 | 0.331 | 21.2132 | 64.0881 | 193.62 |
| Poplar, yellow (Liriodendron tulipifera) | 10.3754 | 0.427 | 24.2984 | 56.905 | 133.267 |
| Redwood (Sequoia sempervirens) | 9.39477 | 0.436 | 21.5476 | 49.4212 | 113.351 |
| Sassafras (Sassafras uariafolium) | 7.74725 | 0.473 | 16.379 | 34.6278 | 73.209 |
| Satinwood (Ceylon) (Chloroxylon swietenia) | 10.7971 | 1.031 | 10.4725 | 10.1576 | 9.85217 |
| Sourwood (Oxydendrum arboreum) | 10.6206 | 0.593 | 17.91 | 30.2023 | 50.9313 |
| Spruce, black (Picea mariana) | 10.4833 | 0.428 | 24.4937 | 57.2283 | 133.711 |
| Spruce, red (Picea rubra or Picea rubens) | 10.5029 | 0.413 | 25.4308 | 61.5758 | 149.094 |
| Spruce, white (Picea glauca) | 9.81646 | 0.431 | 22.776 | 52.8446 | 122.609 |
| Sycamore (Platanus occidentalis) | 9.82626 | 0.539 | 18.2305 | 33.8229 | 62.7512 |
| Tamarack (Larix laricina or Larix americana) | 11.3169 | 0.558 | 20.2811 | 36.3461 | 65.1364 |
| Teak (India) (Tectona grandis) | 11.7189 | 0.5892 | 19.8896 | 33.7569 | 57.2928 |
| Walnut, black (Juglans nigra) | 11.6209 | 0.562 | 20.6777 | 36.7931 | 65.4682 |
| Willow, black (Salix nigra) | 5.03081 | 0.408 | 12.3304 | 30.2216 | 74.0726 |
| Material | Young's modulus (GPa) | Density (g/cm3) | Young's modulus per density; specific stiffness (106 m2s−2) | Young's modulus per density squared (103 m5kg−1s−2) | Young's modulus per density cubed (m8kg−2s−2) |
|---|---|---|---|---|---|
| Thallium | 8 | 11.8 | 0.675 | 0.057 | 0.00481 |
| Cesium | 1.7 | 1.88 | 0.905 | 0.481 | 0.256 |
| Arsenic | 8 | 5.73 | 1.4 | 0.244 | 0.0426 |
| Lead | 16 | 11.3 | 1.41 | 0.124 | 0.011 |
| Indium | 11 | 7.31 | 1.5 | 0.206 | 0.0282 |
| Rubidium | 2.4 | 1.53 | 1.57 | 1.02 | 0.667 |
| Selenium | 10 | 4.82 | 2.08 | 0.431 | 0.0894 |
| Bismuth | 32 | 9.78 | 3.27 | 0.335 | 0.0342 |
| Europium | 18 | 5.24 | 3.43 | 0.655 | 0.125 |
| Ytterbium | 24 | 6.57 | 3.65 | 0.556 | 0.0846 |
| Barium | 13 | 3.51 | 3.7 | 1.06 | 0.301 |
| Gold | 78 | 19.3 | 4.04 | 0.209 | 0.0108 |
| Plutonium | 96 | 19.8 | 4.84 | 0.244 | 0.0123 |
| Cerium | 34 | 6.69 | 5.08 | 0.76 | 0.114 |
| Praseodymium | 37 | 6.64 | 5.57 | 0.839 | 0.126 |
| Cadmium | 50 | 8.65 | 5.78 | 0.668 | 0.0773 |
| Neodymium | 41 | 7.01 | 5.85 | 0.834 | 0.119 |
| Hafnium | 78 | 13.3 | 5.86 | 0.44 | 0.0331 |
| Lanthanum | 37 | 6.15 | 6.02 | 0.98 | 0.159 |
| Promethium | 46 | 7.26 | 6.33 | 0.872 | 0.12 |
| Thorium | 79 | 11.7 | 6.74 | 0.575 | 0.049 |
| Samarium | 50 | 7.35 | 6.8 | 0.925 | 0.126 |
| Lutetium | 67 | 9.84 | 6.81 | 0.692 | 0.0703 |
| Terbium | 56 | 8.22 | 6.81 | 0.829 | 0.101 |
| Tin | 50 | 7.31 | 6.84 | 0.936 | 0.128 |
| Tellurium | 43 | 6.24 | 6.89 | 1.1 | 0.177 |
| Gadolinium | 55 | 7.9 | 6.96 | 0.881 | 0.112 |
| Dysprosium | 61 | 8.55 | 7.13 | 0.834 | 0.0976 |
| Holmium | 64 | 8.79 | 7.28 | 0.827 | 0.0941 |
| Erbium | 70 | 9.07 | 7.72 | 0.852 | 0.0939 |
| Platinum | 168 | 21.4 | 7.83 | 0.365 | 0.017 |
| Thulium | 74 | 9.32 | 7.94 | 0.852 | 0.0914 |
| Silver | 85 | 10.5 | 8.1 | 0.772 | 0.0736 |
| Antimony | 55 | 6.7 | 8.21 | 1.23 | 0.183 |
| Lithium | 4.9 | 0.535 | 9.16 | 17.1 | 32 |
| Palladium | 121 | 12 | 10.1 | 0.837 | 0.0696 |
| Zirconium | 67 | 6.51 | 10.3 | 1.58 | 0.243 |
| Sodium | 10 | 0.968 | 10.3 | 10.7 | 11 |
| Uranium | 208 | 19.1 | 10.9 | 0.573 | 0.0301 |
| Tantalum | 186 | 16.6 | 11.2 | 0.671 | 0.0403 |
| Niobium | 105 | 8.57 | 12.3 | 1.43 | 0.167 |
| Calcium | 20 | 1.55 | 12.9 | 8.32 | 5.37 |
| Yttrium | 64 | 4.47 | 14.3 | 3.2 | 0.716 |
| Copper | 130 | 8.96 | 14.5 | 1.62 | 0.181 |
| Zinc | 108 | 7.14 | 15.1 | 2.12 | 0.297 |
| Silicon | 47 | 2.33 | 20.2 | 8.66 | 3.72 |
| Vanadium | 128 | 6.11 | 20.9 | 3.43 | 0.561 |
| Tungsten | 411 | 19.2 | 21.4 | 1.11 | 0.0576 |
| Rhenium | 463 | 21 | 22 | 1.05 | 0.0499 |
| Rhodium | 275 | 12.4 | 22.1 | 1.77 | 0.143 |
| Nickel | 200 | 8.91 | 22.5 | 2.52 | 0.283 |
| Iridium | 528 | 22.6 | 23.4 | 1.04 | 0.046 |
| Cobalt | 209 | 8.9 | 23.5 | 2.64 | 0.296 |
| Scandium | 74 | 2.98 | 24.8 | 8.31 | 2.78 |
| Titanium | 116 | 4.51 | 25.7 | 5.71 | 1.27 |
| Magnesium | 45 | 1.74 | 25.9 | 14.9 | 8.54 |
| Aluminum | 70 | 2.7 | 25.9 | 9.6 | 3.56 |
| Manganese | 198 | 7.47 | 26.5 | 3.55 | 0.475 |
| Iron | 211 | 7.87 | 26.8 | 3.4 | 0.432 |
| Molybdenum | 329 | 10.3 | 32 | 3.11 | 0.303 |
| Ruthenium | 447 | 12.4 | 36.1 | 2.92 | 0.236 |
| Chromium | 279 | 7.19 | 38.8 | 5.4 | 0.751 |
| Beryllium | 287 | 1.85 | 155 | 84 | 45.5 |
See also
[edit]References
[edit]- ^ "Archived copy" (PDF). Archived from the original (PDF) on 2011-06-27. Retrieved 2010-11-22.
{{cite web}}: CS1 maint: archived copy as title (link) - ^ "Flange Local Buckling". Archived from the original on 2010-05-27. Retrieved 2010-11-22.
- ^ Bonanni, David L.; Johnson, Eric R.; Starnes, James H. (31 July 1988). Local buckling and crippling of composite stiffener sections. Nasa-Tm. College of Engineering, Virginia Polytechnic Institute and State University – via National Library of Australia (new catalog).
- ^ a b c d "A Density — Compression Modulus Relationship For Latex Foam".
- ^ "Toylike blocks make lightweight, strong structures". 2013-08-16. Retrieved 2024-03-21.
- ^ Schaedler, Tobias A.; Jacobsen, Alan J.; Carter, Wiliam B. (2013-09-13). "Toward Lighter, Stiffer Materials". Science. 341 (6151): 1181–1182. Bibcode:2013Sci...341.1181S. doi:10.1126/science.1243996. ISSN 0036-8075. PMID 24031005.
- ^ Coldewey, Devin (2024-01-17). "NASA's robotic, self-assembling structures could be the next phase of space construction". TechCrunch. Retrieved 2024-03-21.
- ^ "Robot Team Builds High-Performance Digital Structure for NASA - NASA". 2024-01-17. Retrieved 2024-03-21.
- ^ a b Alaoui, Adil Hafidi; Woignier, Thierry; Scherer, George W.; Phalippou, Jean (2008). "Comparison between flexural and uniaxial compression tests to measure the elastic modulus of silica aerogel". Journal of Non-Crystalline Solids. 354 (40–41): 4556–4561. Bibcode:2008JNCS..354.4556A. doi:10.1016/j.jnoncrysol.2008.06.014. ISSN 0022-3093.
- ^ "Densities of Solids". www.engineeringtoolbox.com.
- ^ a b "Polystyrene Foam (EPS) Physical Data Sheet".
- ^ "Physical Characteristics of Duocel® Aluminum Foam* (8% Nominal Density 6101-T6)".
- ^ a b "FOAMULAR® Extruded Polystyrene (XPS) Insulation SI and I-P Units for Selected Properties - Technical Bulletin" (PDF).
- ^ a b "High Density Extruded Polystyrene Rigid Insulation" (PDF).
- ^ "Archived copy". dynalabcorp.com. Archived from the original on 18 November 2003. Retrieved 15 January 2022.
{{cite web}}: CS1 maint: archived copy as title (link) - ^ "Physical Characteristics of Duocel® Copper Foam* (8% Nominal Density C10100)".
- ^ a b www.goodfellow.com. "Polypropylene - online catalogue source - supplier of research materials in small quantities - Goodfellow". www.goodfellow.com.
- ^ "Material Properties Data: Medium Density Fiberboard (MDF)". Archived from the original on 2011-05-19. Retrieved 2010-11-11.
- ^ a b Dunand, D. C. (2004). "Processing of Titanium Foams" (PDF). Advanced Engineering Materials. 6 (6): 369–376. doi:10.1002/adem.200405576. ISSN 1438-1656. S2CID 15118192.
- ^ "PHYSICAL AND THERMAL PROPERTIES OF FOAMGLAS® ONE™ INSULATION" (PDF).
- ^ a b "Mass, Weight, Density or Specific Gravity of Wood". www.simetric.co.uk.
- ^ "Polyester Matrix Composite reinforced by glass fibers (Fiberglass) [SubsTech]". www.substech.com.
- ^ "MatWeb - The Online Materials Information Resource". www.matweb.com.
- ^ VROD. "V-Rod fiberglass rebar - Retaining walls".
- ^ a b c Sabate, Borrega; Gibson, Lorna J. (May 2015). "Mechanics of balsa (Ochroma pyramidale) wood". Mechanics of Materials. 84: 75–90. Bibcode:2015MechM..84...75B. doi:10.1016/j.mechmat.2015.01.014. hdl:1721.1/108580. S2CID 54736632. Retrieved 2019-08-09.
- ^ a b "Touchwood BV - Sitka Spruce". www.sitkaspruce.nl.
- ^ a b [1][dead link]
- ^ a b "Sitka Spruce". Archived from the original on 2011-07-16. Retrieved 2010-11-11.
- ^ "Archived copy" (PDF). Archived from the original (PDF) on 2015-04-13. Retrieved 2015-04-13.
{{cite web}}: CS1 maint: archived copy as title (link) - ^ a b c d e f g "Ceramic Industry 2013 Material Properties Chart" (PDF). Archived from the original (PDF) on 2016-02-22. Retrieved 2019-08-12.
- ^ Storm, Shaye (2004). Elert, Glenn (ed.). "Density of glass". The Physics Factbook. Retrieved 2022-01-24.
- ^ Weatherell, J. A. (1 May 1975). "Composition of Dental Enamel". British Medical Bulletin. 31 (2): 115–119. doi:10.1093/oxfordjournals.bmb.a071263. PMID 1164600.
- ^ a b "Reinforcement types". Archived from the original on 2010-12-20. Retrieved 2010-11-11.
- ^ "E-Glass Fibre". AZoM.com. 30 August 2001.
- ^ a b "S-Glass Fibre". AZoM.com. 30 August 2001.
- ^ "Metapress - A Fast Growing Resource for Young Entrepreneurs". 14 December 2017. Archived from the original on 12 March 2012. Retrieved 11 November 2010.
- ^ [2][dead link]
- ^ "Microsoft PowerPoint - Ulven Natural Fiber Presentation.ppt" (PDF). Retrieved 2018-08-01.
- ^ "Archived copy" (PDF). Archived from the original (PDF) on 2011-07-07. Retrieved 2010-11-11.
{{cite web}}: CS1 maint: archived copy as title (link) - ^ "YIG properties" (PDF). Archived from the original (PDF) on 2009-02-25. Retrieved 2010-11-11.
- ^ a b admin. "Kevlar® Properties - Kevlar® Technical Guide - DuPont USA" (PDF). www2.dupont.com.
- ^ a b Piggott, M. R.; Harris, B. (1980). "Compression strength of carbon, glass and Kevlar-49 fibre reinforced polyester resins". Journal of Materials Science. 15 (10): 2523–2538. Bibcode:1980JMatS..15.2523P. doi:10.1007/BF00550757. S2CID 133594285.
- ^ a b "Home - Dyneema®" (PDF). www.dyneema.com.
- ^ Billone, M.C; Donne, M.Dalle; Macaulay-Newcombe, R.G (1995). "Status of beryllium development for fusion applications" (PDF). Fusion Engineering and Design. 27: 179–190. Bibcode:1995FusED..27..179B. doi:10.1016/0920-3796(95)90125-6. ISSN 0920-3796.
- ^ "Physical properties of Silicon (Si)". www.ioffe.ru.
- ^ "Alumina (Al2O3) - Physical and Mechanical Properties of Aluminium Oxide Ceramics by Superior Technical Ceramics". www.azom.com. Archived from the original on 21 July 2012. Retrieved 3 February 2022.
- ^ "saffil". www.saffil.com.
- ^ "Physical property data for Syalon 501". 18 October 2017.
- ^ "Epoxy Matrix Composite reinforced by 70% carbon fibers [SubsTech]". www.substech.com.
- ^ "Product info" (PDF). www51.honeywell.com. 2000.
- ^ "Boron Fiber Properties". www.specmaterials.com.
- ^ Lavin, J. Gerard; Kogure, Kei; Sines, G. (1995). "Mechanical and physical properties of post-creep, pitch-based carbon filaments". Journal of Materials Science. 30 (9): 2352–2357. Bibcode:1995JMatS..30.2352L. doi:10.1007/BF01184586. S2CID 137212713.
- ^ "Physical Properties of Common Woods". Archived from the original on 2010-06-09. Retrieved 2010-11-22.
- ^ "Young Modulus of the elements".
- ^ "Density of the elements".
