Material science

xTATTEREDx · +FINE+ · *SUPERIOR* · ≡EXCEPTIONAL≡ · ☼MASTERWORK☼

v50.14 · v0.47.05

This article is about the current version of DF.
Note that some content may still need to be updated.

Materials have a number of properties representing real world variables that describe how they respond to inputs. In particular, the game now has a number of variables that describe what happens to a material when it's put under stress.

What is stress?

In the real world, an object is stressed when a force is applied to the object. Depending on the nature of the force applied, this stress can take a number of forms, and the object can respond differently based on its material and how that material handles different stresses.

In the material raws, whenever you see 'yield', 'fracture', or 'strain at yield', that property is a stress-related quality.

When does Dwarf Fortress make stress calculations?

At present, DF seems to only apply forces during combat, and thus only stresses objects (generally armor and various body layers) at that time.

There's a lot of stress-related properties, what do they mean?

The first thing you'll notice is that the second word in each stress variable is one of Yield, Fracture, or strain at yield. These are mechanical performance terms.

The first set of words are things like Impact, Bending, and so forth. These describe modes of applying force.

The following explanations assumes real world physics sort of apply (since Toady One chose real world properties). The game doesn't use all of these properties yet, and may not be applying them according to real world physics.

Mechanical Performance Properties

Yield: This is almost certainly 'Yield Strength', which is the amount of stress needed to cause a material to go from elastic deformation to plastic deformation. (That is, if you cease stressing the object, does it revert to its original shape or not). Since most objects only elastically deform over small distances of deformation, high Yield values generally means it takes a lot of force to noticeably 'stretch' them (but see strain at yield).

Fracture: The fracture point is the amount of stress or force necessarily to cause the material to fail, or in other words, to break.

Strain at yield (sometimes incorrectly referred to as 'elasticity'): This variable tells you how much deformation occurs to the material while it is deforming elastically. That is, as long as the force is less than the yield strength, stress * strain at yield = deformation distance. The smaller the strain at yield, the less deformation occurs under stress. Strain is measured as parts-per-100000, meaning that 100000 strain is 100% deformation.

Note: Strain at yield is the inverse of the relevant elastic modulus, thus a highly elastic material has low elastic modulus, and engages in less elastic collisions.

Modes of Applying Force

Impact: Force applied by a sudden strike, like a hammer.

Compressive: Force applied by exerting pressure on an object, like trying to squish something between your hands.

Tensile: Force applied by pulling on something, like suspending one object via another. (e.g., if you suspend an elf from a metal pole, you are applying a tensile force to the pole).

Torsion: Force applied by twisting something. Note that you're twisting some portion of the object relative to itself to cause a torsion stress to be applied to it. (Consider trying to twist a metal rod by grasping at either end and attempting to wring it - yes, you'd have to apply a lot of force to succeed).

Shear: Force applied by pushing part of the material so it tries to slide relative to another part of it. Ie, pushing at the top of an object when the bottom part is fixed to the ground is going to primarily apply a shear stress to it (the top part will try to move in the direction you push, and the lower part will resist this shear stress).

Bending: Force applied by bending a material.

Effects on Combat

The Dwarf Fortress combat system does not use all material properties at present (0.40.05). Weapon and armor damage/wear/decay is not tracked.

The formulae below have been reverse-engineered [1] [2] and experimentally proven [3] [4] by several independent researchers. Below are the simplified results; for more details see links above.

Attack Types

Both creatures and items can have [ATTACK] tokens. A creature can execute any of its natural attacks plus any attacks of the items it holds. The attacks marked with [EDGE] flag deliver edged damage which is governed by [SHEAR_*] tokens; they can be further differentiated by attack contact area: generally concentrated strikes (area of 50 or less) are considered stabbing while wider areas correspond to slashing attacks. This distinction shall be emphasized later.

Every other attack is considered blunt. [IMPACT_*] tokens affect blunt combat. Most specialised blunt weapons have small contact area; edged weapons generally also have blunt attacks with larger area values; items or creatures without defined attacks get default blunt attack with area = (size)^2/3. Under certain circumstances edged attack can be converted to blunt, but not otherwise.

Wrestling moves are special: breaking bones uses [BENDING_*] values, pinching utilizes [COMPRESSIVE_*] properties, and biting can deal [TENSILE] or [TORSION] damage depending on whether the attack is edged. Those attacks generally ignore armor.

Contact Area

Attack contact area is the minimum of weapon contact area and armor/layer contact area. Body parts have areas dependent on their size, as with non-weapon items; part size is creature size times relative size of the part in proportion to whole body.

Body part	Relative size (human)	Kobold	Elf	Human	Troll
Total	100%	20000	60000	70000	250000
Upper body	18%	3599	10818	12621	43133
Lower body	18%	3599	10818	12621	43133
Neck	1.8%	359	1081	1262	4313
Head	5.4%	1079	3245	3786	12939
Upper arm	3.6%	719	2163	2524	8626
Lower arm	3.6%	719	2163	2524	8626
Hand	1.4%	287	865	1009	3450
Upper leg	9.0%	1799	5409	6310	21566
Lower leg	7.2%	1439	4327	5048	17253
Foot	2.2%	431	1298	1514	5175

Armor size is calculated as underlying body part size times coverage/100% times size/100 times 1+(UPSTEP+UBSTEP+LBSTEP)/4; MAX count as 3 in the last sum.

Item	Size multiplier	Body part	Dwarf	Human	Extra body parts covered (humanoid)	Notes
Cap	0.05	Head	162	189	none	Cloth
Mask	0.1	Head	324	378	none	Cloth
Helm	0.3	Head	973	1135	none
Leather armor	0.3	Upper body	3245	3786	Lower body, neck, upper arms, upper legs	leather
Mail shirt	0.225	Upper body	2434	2839	Lower body, neck, upper arms, upper legs	Chain
Breastplate	0.2	Upper body	2163	2524	Lower body
Gauntlets	0.25	Hands	216	252	Lower arms, fingers
Leggings	0.2625	Lower body	2839	3313	Upper legs, lower legs, toes	Chain
Greaves	0.2625	Lower body	2839	3313	Upper legs, lower legs, toes
Low boots	0.25	Feet	324	378	Toes
High boots	0.3125	Feet	405	473	Lower legs, toes

Attack Momentum

DF uses momentum-based combat physics, so the momentum plays central role in calculations. Since momentum equals velocity times mass, and lighter items can be swung faster, attack momentum is largely independent from weapon weight. The simplified formula is as follows:

M = Str * Vel / ( 10⁶/Size + 10*F/W ),

or

M = Size * Str * Vel / (10 * ( 10⁵ + i_Size/W )),

or

M = Size * Str * Vel / (10⁶ * (1 + i_Size/(w_density*w_size) )

where:

M is the momentum.
Str is the creature's strength (e.g. 1250 for the average dwarf)
Vel is the weapon's velocity modifier if present (e.g. 1.25x, 2x)
Size is the average creature size (e.g. 60000 for dwarves)
i_Size is the specific creature's size
F is "fatness modifier" (also includes muscle) = i_Size/Size; dwarf with size of 66150 will have F=66150/60000=1.1025
W is weapon mass in kilograms (Γ)
w_density is the weapon's material's density
w_size is the weapon's size.

Or, to sum up:

A stronger, smaller creature from a larger species wielding a more massive weapon hits with more momentum. A stronger, smaller creature from a larger species wielding a larger, denser weapon hits with more momentum.

For dwarves, the formula becomes

M = 6*10⁵ * Str * Vel / (10 * ( 10⁵ + i_Size/W )) = 6*10⁴ * Str * Vel / ( 10⁵ + i_Size/W )

or

M = 0.6 * Str * Vel / (1 + i_Size/(w_density*w_size) )

There are 28 possible sizes for your dwarves from 33750 to 93750; strength can vary from 0 to 5000 with an average of 1250; velocity can vary from 1 (pommel strikes) to 5 (whip lashes); weapon size can vary from 100 (whips) to 1300 (great axes, which are unwieldable by dwarves; the largest wieldable weapon is size 800, in the form of battle axes and maces).

Momenta for dwarves of strength 1250 hacking (velocity 1.25) with battle axes (size 800), rounded to 3 decimal places
Dwarf Size	Adamantine	Divine metal	Steel	Iron	Bismuth bronze	Bronze	Copper	Silver
33750	774.194	899.55	932.489	932.489	932.73	932.73	933.092	933.745
42750	739.827	889.944	931.161	931.161	931.467	931.467	931.923	932.748
44100	734.934	888.52	930.963	930.963	931.277	931.277	931.748	932.599
45000	731.707	887.574	930.83	930.83	931.151	931.151	931.632	932.5
45900	728.509	886.63	930.698	930.698	931.025	931.025	931.515	932.4
47250	723.764	885.217	930.499	930.499	930.836	930.836	931.34	932.251
54150	700.444	878.066	929.485	929.485	929.871	929.871	930.447	931.489
55860	694.895	876.312	929.235	929.235	929.632	929.632	930.226	931.301
56250	693.642	875.912	929.177	929.177	929.577	929.577	930.176	931.258
57000	691.244	875.146	929.067	929.067	929.473	929.473	930.079	931.175
57624	689.262	874.509	928.976	928.976	929.386	929.386	929.999	931.107
58140	687.632	873.983	928.9	928.9	929.314	929.314	929.932	931.05
58800	685.558	873.312	928.804	928.804	929.221	929.221	929.847	930.977
59850	682.283	872.245	928.65	928.65	929.075	929.075	929.711	930.861
59976	681.893	872.117	928.631	928.631	929.057	929.057	929.695	930.847
60000	681.818	872.093	928.628	928.628	929.054	929.054	929.692	930.845
61200	678.119	870.878	928.452	928.452	928.887	928.887	929.537	930.713
61740	676.468	870.332	928.373	928.373	928.811	928.811	929.467	930.653
62424	674.388	869.642	928.273	928.273	928.716	928.716	929.379	930.578
63000	672.646	869.061	928.189	928.189	928.636	928.636	929.305	930.514
64260	668.866	867.794	928.004	928.004	928.46	928.46	929.142	930.376
66150	663.277	865.901	927.728	927.728	928.197	928.197	928.899	930.168
71250	648.649	860.832	926.983	926.983	927.487	927.487	928.242	929.607
73500	642.398	858.615	926.655	926.655	927.175	927.175	927.953	929.36
75000	638.298	857.143	926.436	926.436	926.966	926.966	927.76	929.196
76500	634.249	855.676	926.217	926.217	926.758	926.758	927.567	929.031
78750	628.272	853.485	925.89	925.89	926.446	926.446	927.278	928.784
93750	591.133	839.161	923.711	923.711	924.37	924.37	925.357	927.143

There is also a hard velocity limit (10000) that might skew these calculations, but it's actually impossible to reach in unmodded game. (Well, okay, if you're a zombie adventurer with maxed out strength you might reach the limit using an adamantine whip -- but why?)

Situational Modifiers

Momentum can be further increased with weapon skill, status effects, attack modifiers etc. For example:

Skill adds gradual multiplier, up to 2x at Grand Master.
Quick attacks halve momentum, wild and heavy attacks add 50%.
Attacking a prone opponent doubles momentum value.

Ranged Attacks

Attacks from missile launchers are entirely dependent on the launcher's [SHOOT_FORCE] and [SHOOT_MAXVEL] tags:

	SHOOT_FORCE	SHOOT_MAXVEL	Maximum Velocity	Magic Density / Constant Momentum
Bows and Crossbows	1000	200	20	1666 / 50
Blowguns	100	1000	100	250 / 5

Specifically, as long as projectile is heavy enough, it is fired with a momentum of SHOOT_FORCE/20; if this would make its speed exceed SHOOT_MAXVEL/10, it is capped at this value instead. (As usual, momentum = velocity times weight.) This gives the launcher a magic density above which momentum becomes a constant and velocity decays, shown in the table; below this density, velocity is constant (SHOOT_MAXVEL/10), and momentum decays.

Vanilla bolts and arrows end up with a momentum of 50 (velocity nearly 20, at density 1667), as long as their density exceeds 1666. Divine ammo (1.5kg) has momentum 30 (velocity 20), bone and most wood (0.75kg) get 15 (velocity 20), and adamantine bolts (0.3kg) have only 6 (velocity 20). Wooden darts (0.1kg) usually have 5 (velocity 50).

Weapon Traps

Traps always have a fixed attack velocity of 200, no matter the weapon weight; the momentum thus is 200 times weight. This includes shot ammunition.

Attack Momentum Costs

The attack generally needs some momentum threshold to break through each armor/tissue layer. If the attack is edged, it also can cut through it instead. For latter it has to have momentum no less than:

M >= (rSY + (A+1)*rSF) * (10 + 2*Qa) / (S * Qw),

where:

rSY is the ratio of layer's to weapon's SHEAR_YIELD
rSF is ditto with SHEAR_FRACTURE
A is attack contact area
S is weapon material sharpness multiplier (1x for most metals, 1.2x for divine metal, 1.5x for glass, 2x for obsidian, 10x for adamantine and 0.1x for all other materials)
Qw is quality sharpness multiplier (1x for normal quality, 1.4x for fine, 2x for masterwork (or artifact) etc.)
Qa is armor quality multiplier (same but x3 for artifacts)

Should it exceed this value, attack momentum is decreased by some 5% and the layer is considered punctured/severed. Calculations then repeat for the underlying layer. Otherwise damage is converted to blunt just for this layer and proceeds as following.

Blunt attacks can be entirely deflected by armor if weapon's IMPACT_YIELD is especially low relative to armor's density:

2 * Sw * IYw < A * Da,

where Da is armor material's density (in g/cm³), A is attack contact area, Sw is weapon size and IYw is its impact yield in MPa (i.e. raw value divided by 10⁶).

Otherwise, attack must have minimum momentum of:

M >= (2*IF - IY) * (2 + 0.4*Qa) * A,

where IF and IY are layer's impact fracture and impact yield in MPa, Qa is armor quality multiplier and A is contact area as above. Again, on success layer is considered thrashed, momentum is reduced by about 5% and next layer is tested.

If both edged and blunt momenta thresholds haven't been met, attack is permanently converted to blunt and its momentum may be greatly reduced. Specifically, it is multiplied by SHEAR_STRAIN_AT_YIELD/50000 for edged attacks or IMPACT_STRAIN_AT_YIELD/50000 otherwise. I.e., most metals reduce blocked attacks by 98%-99%, but see below. Note that elastic armor, such as a mail shirt, has both strain at yield values raised to 50000, so it multiplies by 1 at this step (i.e. does nothing to the momentum, but does still convert it to blunt) regardless of material.

Elastic Material Modifiers

Clothing with [STRUCTURAL_ELASTICITY_*] tokens has its stress properties modified.

Items with [STRUCTURAL_ELASTICITY_CHAIN_ALL] or metallic items with [STRUCTURAL_ELASTICITY_CHAIN_METAL] have their [*_STRAIN_AT_YIELD] increased to 50000, which means that blocked attack will not be dampened; it still may be converted to blunt, however. Metal leggings and chainmail shirts have this property in vanilla.

Items made of cloth (including adamantine!) with [STRUCTURAL_ELASTICITY_WOVEN_THREAD] additionally have their SHEAR values reduced to negligible 20-30 kPa. This makes candy clothing especially useless in combat. Caps and all clothing have this tag in vanilla.

Penetration Depth

This is also very important parameter. Please write something about it.

Pulping

Pulping appears to work by evaluating the layers in a body part. If each layer meets any one of the following criteria then the body part is pulped:

100% bruised/burned/frostbite/melt/necrosis/blister/boil/freeze/condense (i.e. 10000+ in layer_effect_fraction)
250% dented (i.e. 25000+ in layer_dent_fraction)
100% cut (i.e. 10000+ in layer_cut_fraction) (cut in this case is synonymous with fracture)

Spines, skulls, and perhaps other body parts have the [PREVENTS_PARENT_COLLAPSE] token which prevents the parent body part (such as the head, upper body, or lower body) from being pulped until the sub-part is broken. It appears that only external body parts can be pulped, not internal organs. You will find that boneless body parts that don't contain a spine/skull part will pulp VERY easily (i.e. eyes/ears).

There does not appear to be any distinctions between the combat text descriptions of the pulping, beyond the messages being appropriate to the weapon used (edged, blunt, or creature body part).

Material and item properties

As can be seen from above, importance of different material/item properties greatly varies in different scenarios. Below are some guidelines to estimating weapon/armor merit.

When dealing with dwarf-sized targets, layer contact areas usually lay in 200~10000 range. The majority of vanilla weapons, however, has contact areas either below or above that (dagger is the lone exception); it therefore can be said, as a rule of thumb, that weapons with area of five or six digits assume their target's contact area, whereas the others use their own.
Weapon weight matters very little past a certain threshold: for example, platinum war hammer in dwarven hands only gets about 12% more momentum over a steel one, despite being thrice as heavy. (Adamantine hammer, however, only has 1/7th as much.) Thus, since all common weapon metals have about the same density, it can be safely ignored.
- The only exception are weapon traps, which are much more effective with heavy weapons loaded.
Shear yield doesn't actually matter. Even with dagger/bolt's contact area of 5 it contributes only ~15% to piercing cost, and since it equals about half of shear fracture for most metals, it can be approximated as such without much error.
Blunt weapons only use impact yield value. Impact fracture protects from blunt attacks instead. Curiously, layer impact yield actually decreases blunt fracturing cost, so lower yield is better for armor.
- Most dedicated blunt weapons cannot be deflected by anything but slade, so their impact yield can in fact be ignored.
Chain mail cannot block attacks via momentum cost thresholds; it still can blunt slashing attacks and then deflect them. Thus, the best defence can be reached by wearing dense (like copper) mail shirt under a rigid (like candy) one.
Strain at yield values are used in comparison to 50000. Since all metals have much less strain values than this, they all can be considered to have zero elasticity.
Adamantine clothing is absolutely useless as armor.
Armor quality doesn't matter much: masterwork armor provides only about 15% more protection than low-quality one.
Blunt weapon quality appears to not affect damage at all.

With that in mind, here are some numbers for vanilla weapon/armor materials:

Material	Density	Impact Yield	2*(Impact Fracture) - Impact Yield	Shear Fracture	Elasticity	Sharpness	Bolt	adj.	Sword	adj.	Mace	min M
Adamantine	0.20	5.00	5.00	5.00	0	10	6	300	9	450	31	200
Bone/shell	0.50	0.20	0.20	0.13	<1%	0.1	15	0.20	19	0.25	60	8
Bronze	8.25	0.60	1.08	0.24	<=1%	1	49	12	75	18	138	43
Copper	8.93	0.25	1.30	0.22	<1%	1	49	11	77	17	138	52
Divine metal	1.00	1.00	3.00	2.00	0	1.2	30	72	31	74	86	120
Glass	2.6	1.00	1.00	0.04	4%/<1%	1.5	--	--	53	3.2	116	40
Iron	7.85	0.54	1.62	0.31	<1%	1	49	15	75	23	137	65
Leather	0.50	0.01	0.01	0.03	100%	--	--	--	--	--	--	0.4
Obsidian	2.67	1.00	1.00	0.04	4%/<1%	2	--	--	54	4.3	117	40
Platinum	21.4	0.35	1.05	0.20	<1%	1	--	--	86	17	145	42
Silver	10.49	0.35	0.84	0.17	<1%	1	49	8.3	79	13	140	34
Slade	200	4.00	6.00	5.00	<1%	0.1	--	--	93	46	149	240
Steel	7.85	1.51	3.54	0.72	2%/<1%	1	49	35	75	54	137	142
Wood	0.50	0.01	0.01	0.04	2%	0.1	15	0.06	19	0.076	60	0.4

Clarifications:

On the left side of the table there are some raw values. Density and impact yield are important for a blunt weapon; 4th column is adjusted impact fracture that appears in the formula for blunt defense. Shear fracture is important for edged attacks and defense. Elasticity is in %s of 50000; as you can see, it is universally low.

On the right side there are some typical weapon momenta. From left to right: bolt momentum; ditto multiplied by SF and sharpness (signifies piercing ability); short sword momentum in dwarven hands; ditto multiplied by sharpness and SF; dwarf swinging a mace; and minimum momentum some mace needs to break through armor of this material.