# Metal foam **A metal foam** is a metal containing a large volume fraction of gas-filled pores, so that most of what occupies its outline is empty space held open by a network of metal struts or cell walls. It is a cellular solid in the same sense as cork, cancellous [[Bone|bone]] or bread, but made of [[Aluminium|aluminium]], steel, [[Titanium|titanium]] or [[Nickel|nickel]], and it keeps enough of the metal's own behaviour — conduction, melting point, weldability, resistance to fire — to go where a polymer foam cannot.[^banhart2001] Almost everything about it follows from one number, the relative density `rho*/rho_s`: the [[Density|density]] of the foam divided by that of the solid it is made from. Commercial metal foams run from about 0.02 to 0.5.[^ashby-designguide] In the microsim below the reader sets that one number, sweeping `rho*/rho_s` from 0.02 to 0.5, and an open-cell strut network thickens or thins in response. Two scaling laws answer. The stiffness follows `E*/E_s = C·(rho*/rho_s)^2` and the plateau strength `sigma*/sigma_s = 0.3·(rho*/rho_s)^(3/2)`, the Gibson–Ashby relations for a bending-dominated foam, with `C` near 1 for an open cell.[^gibson-ashby] Beside the model the sim draws the compressive [[Stress–strain_curve|stress–strain curve]] — a short elastic rise, a long flat plateau, then a steep rise as the cells close on themselves — and the area under that plateau, the energy absorbed per unit volume, grows and shortens as the struts thicken. A marker tracks where the foam sits on the flagship's stiffness–density map. On the [[Materials_science]] flagship this page serves Part X, Emerging technologies, in the section *Cellular solids*, next to the designed lattices of [[Metamaterial|metamaterials]]. The two are the same idea approached from opposite ends: a foam takes whatever cells the process gives it, a lattice is drawn cell by cell, and the scaling laws below say what each gains for its weight. ## Definitions A metal foam is classified first by whether its cells are connected, then by whether its cell pattern is random or designed. The classification matters because it decides which of the scaling laws applies, and the scaling laws decide what the material is good for. Relative density is the master variable, and its complement is the porosity. The reason it dominates is geometric. In an ordinary open-cell foam the cell edges carry load mainly by bending, like little beams; a beam's bending stiffness goes as the fourth power of its thickness and inversely as the cube of its length, and expressing both through the relative density gives the square law the sim plots.[^gibson-ashby] Nothing in that argument names a metal, so the same exponent describes an aluminium foam and a nickel one, the metal entering only through `E_s`, `sigma_s` and `rho_s`. ### Open-cell In an open-cell foam the cell faces are absent and only the edges survive, so every pore connects to its neighbours and a fluid can pass right through the block. Open cells are what make a foam useful as a [[Heat_exchanger|heat exchanger]] core, a filter, a support for a [[Catalysis|catalyst]], a wick, or a sound absorber, because all of those need access to the internal surface — which for a millimetre-cell foam is many times the external surface of the same block.[^banhart2001] Mechanically the open cell is the bending-dominated case, and the square law for stiffness is at its most accurate here.[^gibson-ashby] ### Closed-cell In a closed-cell foam each cell is sealed by a thin membrane of metal, so gas is trapped and the block is impermeable and buoyant. Load is carried partly by bending of the edges and partly by stretching of the faces, and the stiffness picks up a term linear in relative density: `E*/E_s = phi^2·(rho*/rho_s)^2 + (1 - phi)·(rho*/rho_s)`, with `phi` the fraction of solid in the edges rather than the faces.[^gibson-ashby] Because the linear term dominates at low density, an ideal closed-cell foam should be much stiffer than an open one of the same weight. Real ones fall well short: the faces are wrinkled, uneven and often torn, and measured stiffnesses sit close to the open-cell square law.[^ashby-designguide] ### Stochastic foam A stochastic foam has cells random in size, shape and position, which is what any melt-foaming or gas-injection process produces. The scaling laws still hold on average, but scatter is large and strength is set not by the average cell but by the weakest band across the block: collapse begins in one layer and spreads, which is why the plateau is often serrated rather than smooth.[^gibson-ashby] Density gradients left by drainage of the liquid metal before it froze are a common source of that weak band. ### Regular foam A regular, or periodic, foam is a designed lattice — a honeycomb, a Kelvin cell, an octet truss — repeated exactly. The gain is not tidiness but topology. If a lattice has enough struts meeting at each node to be rigid by Maxwell's counting rule, its members carry load by stretching rather than bending, and stiffness then scales *linearly* with relative density instead of quadratically: at `rho*/rho_s` = 0.05 a stretch-dominated lattice is roughly an order of magnitude stiffer than a bending-dominated foam of the same weight.[^deshpande2001] The cost is that a stretch-dominated lattice collapses abruptly once a strut buckles, where a bending-dominated foam yields gently, so the two trade stiffness against the long, forgiving plateau that absorbs energy. ### Hybrid foam A hybrid combines a foam with something else so the pair does what neither does alone. A foam core between two face sheets makes a sandwich panel whose bending stiffness comes from the separation of the faces and whose weight comes mostly from the core; a foam-filled tube resists crushing far better than an empty one because the filling suppresses the folding mode; a foam infiltrated with polymer or a phase-change compound adds [[Damping|damping]] or heat storage. Syntactic foams, hollow spheres embedded in a solid matrix rather than in gas, are the limiting case.[^ashby-designguide] ## Manufacturing No single process makes metal foams well over the whole density range, and the route chosen fixes the cell type, the achievable relative density and the cost. All of them face the same difficulty: liquid metal has a high surface tension and a low viscosity, so bubbles in it rise and drain far faster than bubbles in a polymer melt, and the foam must be stabilised and frozen before it collapses.[^banhart2001] ### Open-cell The commonest route to a well-controlled open cell is replication. A polymer foam with the desired cell structure is used as a pattern: it is invested in a slurry that sets, the polymer is burned out, and molten metal is drawn into the cavity it leaves and allowed to freeze, after which the mould is removed. The result is a faithful metal replica of the polymer cells, with the struts hollow or solid depending on the route.[^ashby-designguide] A second family uses a space-holder: metal powder is packed around beads of salt or another soluble solid, the compact is sintered, and the beads are leached out, which gives good control of pore size and is well suited to [[Titanium_alloys|titanium alloys]] for implants. [[Sintering|Sintering]] of hollow metal spheres, and vapour deposition onto a burnt-out template, fill in the remaining corners of the map.[^banhart2001] ### Closed-cell Closed cells come from foaming the metal itself. In the melt route, gas is blown directly into a molten aluminium alloy that has been thickened with a few per cent of ceramic particles — silicon carbide or alumina — which collect at the bubble surfaces and stop them from draining and merging; the foam floats to the top of the [[Casting|melt]] and is drawn off as a continuous slab.[^banhart2001] In the blowing-agent route a powder that decomposes on heating, usually titanium hydride, is stirred into the melt and releases hydrogen as the temperature rises through the range where the metal is fluid. The powder-compact route reverses the order: metal powder and hydride are mixed, compacted to a dense precursor billet which can be rolled or cut to shape, and only then heated above the solidus, so the precursor expands in place and can fill a hollow part with foam.[^banhart2001][^ashby-designguide] ## Composite metal foam Composite metal foam is a construction rather than a process variant: hollow metal spheres of chosen wall thickness are packed into a mould and the space between them filled with a second metal, by casting or powder metallurgy, giving a foam whose pores are engineered individually and whose matrix is fully dense. Because sphere wall and matrix are chosen separately, the plateau stress can be set without changing the pore size, which a stochastic foam does not allow. Reports of its ballistic and thermal performance come mainly from one research group, and Wikitube has not yet pinned them.[citation needed] ### High-speed impact/blast/ballistics testing What a cellular solid offers against a fast impact is not strength but a long stroke at nearly constant force. A dense plate stops a projectile by a short, violent deceleration and passes the peak force straight through; a foam crushes progressively at its plateau stress, and the energy absorbed is that stress times the stroke, so the transmitted force stays flat while the projectile is brought to rest over a far longer distance.[^gibson-ashby] Ballistic and blast tests measure that trade: depth of penetration, momentum transmitted behind the panel, and panel mass for a given threat. Composite metal foam is tested in this role because its uniform spheres give a flatter, more repeatable plateau than a stochastic foam. ### Fire/extreme heat testing A metal foam does not burn, does not outgas and does not lose its shape below the melting point of its metal, which already separates it from every polymer foam. Against a flame or a radiant source its advantage is that the closed pores break the conduction path: heat crossing the block must travel along a tortuous network of struts whose cross-section is a small fraction of the block's, while the trapped gas conducts poorly and [[Convection|convection]] inside a cell millimetres across is negligible.[^gibson-ashby-thermal] The result is a barrier that is simultaneously structural and insulating — a combination [[Thermal_insulation|thermal insulation]] normally cannot supply. ### Other abilities The same structure that absorbs mechanical energy also absorbs acoustic energy, because [[Sound|sound]] entering an open-cell foam is dissipated by viscous friction in the narrow passages, which makes metal foams useful in [[Noise_control|noise control]] where temperature or fire rules out fibre and polymer absorbers.[^banhart2001] Metal foams damp structural [[Vibration|vibration]], shield electromagnetic fields as a conducting mesh does, and, being made of metal, can be welded, machined and recycled by ordinary means. ## Regular foams gallery A gallery of regular foams shows what the periodic cells of the previous section look like when built: hexagonal honeycombs, the truncated-octahedron Kelvin cell that tiles space with the least surface area for equal-volume cells, the octet truss and its stretch-dominated relatives, gyroid and other triply periodic minimal surfaces, and graded lattices in which cell size changes across a part.[^gibson-ashby-structure] Wikitube carries no image gallery here; the pair's *Regular foams gallery* holds the photographs, and the geometry is better met in the microsim, where the strut network is the object the reader turns. What limits a printed regular foam is the process, not the drawing. Strut diameters must clear the minimum wall a process can build — above 0.016 in (0.41 mm) on metal powder-bed fusion, 0.028 in (0.71 mm) on selective laser sintering and 0.047 in (1.19 mm) on fused deposition — so a 0.030 in (0.76 mm) strut is legal on a powder bed and illegal on a desktop extruder.[^am-rules] The file is a limit too: a lattice approximated by triangles needs far more of them than a solid part of the same size, and balancing file size against accuracy is hardest for exactly these cellular models.[^am-stl] ## Applications Metal foams are specified when two requirements meet that a dense metal cannot satisfy together — stiffness with lightness, strength with a controlled crush, conduction with permeability. Where only one requirement is in play, a solid is usually cheaper. ### Design Selection follows the material indices, and for foams the indices give a clear verdict. A light, stiff panel loaded in bending is governed by `E^(1/3)/rho`; substituting the square law `E* ∝ (rho*)^2` makes this index proportional to `(rho*)^(-1/3)`, so it *improves* as the foam is made lighter, and foam-cored panels beat solid ones.[^ashby-selection] A light, stiff beam of free square section is governed by `E^(1/2)/rho`, which the same substitution makes independent of density: a foam is neither better nor worse than the solid. A tie loaded in tension is governed by `E/rho`, proportional to `rho*`, so foaming a tie only makes it worse (derived).[^ashby-selection][^gibson-ashby] The rule of thumb that follows is short: foam panels, not rods. ### Mechanical The mechanical section is the one the microsim draws. Its control is the relative density `rho*/rho_s` over 0.02 to 0.5; as the slider moves, the struts of the open-cell network thicken and three readouts change together. The stiffness follows `E*/E_s = C·(rho*/rho_s)^2`; the plateau stress follows `sigma*/sigma_s = 0.3·(rho*/rho_s)^(3/2)`; and the strain at which the cells touch and the curve turns upward follows the densification relation `eps_D ≈ 1 - 1.4·(rho*/rho_s)`.[^gibson-ashby] Take an aluminium foam with `E_s` = 70 GPa, `sigma_ys` = 150 MPa and `rho_s` = 2700 kg/m³.[^ashby-selection] At `rho*/rho_s` = 0.1 the foam weighs 270 kg/m³, its modulus is 0.70 GPa, its plateau stress 1.4 MPa and its densification strain 0.86, so it absorbs about 1.2 MJ per cubic metre before it bottoms out. Double the relative density to 0.2 and the modulus quadruples to 2.8 GPa, the plateau stress rises to 4.0 MPa, but the plateau shortens to a strain of 0.72 and the energy absorbed rises only to about 2.9 MJ/m³ (derived).[^gibson-ashby] That is the trade the sim is built to show: stiffness rewards density steeply, energy absorption does not, and a foam chosen for crash protection is deliberately made lighter than one chosen for stiffness. ILLUSTRATIVE: the exponents and the constants `C` ≈ 1 and 0.3 are fits to data across many cellular solids, not measured properties of any one foam, and real metal foams scatter around them by a factor of two or more because of cell-wall curvature, density gradients and missing struts.[^gibson-ashby][^ashby-designguide] ### Thermal For heat, a foam is a diluted conductor with a large internal surface. [[Thermal_conduction|Conduction]] through the solid dominates whenever the metal's conductivity vastly exceeds the gas's, and since only about a third of the struts in a random network lie along the heat flux, an open-cell foam's [[Thermal_conductivity_and_resistivity|conductivity]] is roughly one-third of the relative density times that of the solid; for aluminium at `rho*/rho_s` = 0.1 that estimates about 8 W/m·K against 237 for the solid (derived).[^gibson-ashby-thermal] Losing conductivity by a factor of thirty while gaining an enormous wetted area is a good bargain for a compact heat exchanger, where the limit is not conduction through the fin but transfer from the fin to the fluid — which is why open-cell aluminium and copper foams are used as cores in electronics cooling and in [[Heat_exchanger|heat exchangers]] that must be light.[^banhart2001] ## See also - [[Aerogel]] — the same scaling at a relative density near 0.01 - [[Honeycomb_structure]] - [[Foam]] - [[Amorphous_metal]] - [[Self-healing_material]] - [[Programmable_matter]] - [[Metamaterial]] — the designed-lattice neighbour on the flagship's Emerging technologies part - [[Composite_material]] - [[Sintering]] - [[3D_printing]] ## References [^gibson-ashby]: Gibson, L. J.; Ashby, M. F. *Cellular Solids: Structure and Properties*, 2nd ed. (Cambridge University Press, 1997), the chapter on the mechanics of foams (page to pin): relative density as the master variable, the bending-dominated derivation of `E*/E_s = C·(rho*/rho_s)²` and `sigma*/sigma_ys = C·(rho*/rho_s)^(3/2)` with `C` ≈ 1 and 0.3, the closed-cell edge/face expression, the densification strain `eps_D ≈ 1 − 1.4·(rho*/rho_s)`, and the plateau as the energy-absorbing regime. [^gibson-ashby-structure]: Gibson, L. J.; Ashby, M. F. *Cellular Solids: Structure and Properties*, 2nd ed. (Cambridge University Press, 1997), the chapter on the structure of cellular solids (page to pin): the geometry of two- and three-dimensional cells, the tetrakaidecahedral (Kelvin) cell and the relation between cell edge, cell size and relative density. [^gibson-ashby-thermal]: Gibson, L. J.; Ashby, M. F. *Cellular Solids: Structure and Properties*, 2nd ed. (Cambridge University Press, 1997), the chapter on thermal, electrical and acoustic properties of cellular solids (page to pin): solid conduction along a fraction of the struts, the negligible contribution of convection within cells of millimetre size, and acoustic dissipation in open cells. [^ashby-designguide]: Ashby, M. F.; Evans, A. G.; Fleck, N. A.; Gibson, L. J.; Hutchinson, J. W.; Wadley, H. N. G. *Metal Foams: A Design Guide* (Butterworth-Heinemann, 2000), the chapters on making metal foams, on properties, and on design (page to pin): the commercial relative-density range, the shortfall of measured closed-cell stiffness against the edge/face model, sandwich and foam-filled hybrids, and the replication and space-holder routes. [^banhart2001]: Banhart, J. (2001). "Manufacture, characterisation and application of cellular metals and metal foams." *Progress in Materials Science* 46 (6): 559–632 (DOI to pin) — the survey of melt foaming with ceramic particles, blowing-agent and powder-compact routes, the stability problem of liquid-metal foams, and the filter, catalyst-support, heat-exchanger and sound-absorption applications. [^deshpande2001]: Deshpande, V. S.; Ashby, M. F.; Fleck, N. A. (2001). "Foam topology: bending versus stretching dominated architectures." *Acta Materialia* 49 (6): 1035–1040 (DOI to pin) — Maxwell's rigidity criterion applied to lattices, and the linear stiffness scaling of stretch-dominated architectures. [^ashby-selection]: Ashby, M. F. *Materials Selection in Mechanical Design*, 4th ed. (Butterworth-Heinemann, 2011), the chapter on material indices and the appendix of material property data (page to pin): the indices `E/rho`, `E^(1/2)/rho` and `E^(1/3)/rho` for a tie, a beam and a panel, and the room-temperature data for aluminium used here (`E_s` = 70 GPa, `sigma_ys` ≈ 150 MPa for a common alloy, `rho_s` = 2700 kg/m³, `lambda_s` = 237 W/m·K). [^am-rules]: Barnes, J.; Simpson, T. *Additive Manufacturing Essentials* (2025), Ch. 4 Design for Additive Manufacturing, Table 4.6, PDF pp. 85–86 (Portal Book 110; sub-manual 12 §6.3): minimum wall greater than 0.016 in for powder-bed fusion, 0.028 in for selective laser sintering and 0.047 in for fused deposition, from which the manual derives that a 0.030 in wall passes powder-bed fusion and selective laser sintering but fails fused deposition. [^am-stl]: Barnes, J.; Simpson, T. *Additive Manufacturing Essentials* (2025), Ch. 4 Design for Additive Manufacturing, PDF pp. 78–79 (Portal Book 110; sub-manual 12 §6.4): tessellation approximates a boundary with triangles, "the more triangles created, the more accurate the tessellation, but the larger the .STL file size", and balancing size against accuracy is hardest for cellular models. ## External links - The Wikipedia pair's *External links* section lists the manufacturers' and research groups' pages; none is reproduced here until its URL has been checked. The quantitative sources behind this page are the two Gibson–Ashby books, the Banhart survey and Portal Book 110, all cited in full under References. <!-- MATTERSIM:BEGIN g24 — Matter & Energy Cluster microsim (framework build, specs/sims/Metal_foam.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework), pending deploy:** *Metal foam* will play here once `https://wikitube-3d-microsims.netlify.app/matter/Metal_foam.html` is live. <!-- pending: <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Metal_foam.html" data-title="Metal foam"></div> --> <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Metal_foam) : [Wikitube](https://en.wikitube.io/wiki/Metal_foam) · pinned revision [1368990793](https://en.wikipedia.org/w/index.php?oldid=1368990793) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Materials_science]]. --- *Matter & Energy Cluster child articles, wave 1 · 2026-09-11 · drafted · Materials_science row M65 · sim pending (matter/Metal_foam).*