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 implemented.

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 contrariwise.

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

or

M = 0.06 * 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	77.4194	89.9550	93.2489	93.2489	93.2730	93.2730	93.3092	93.3745
42750	73.9827	88.9944	93.1161	93.1161	93.1467	93.1467	93.1923	93.2748
44100	73.4934	88.8520	93.0963	93.0963	93.1277	93.1277	93.1748	93.2599
45000	73.1707	88.7574	93.0830	93.0830	93.1151	93.1151	93.1632	93.2500
45900	72.8509	88.6630	93.0698	93.0698	93.1025	93.1025	93.1515	93.2400
47250	72.3764	88.5217	93.0499	93.0499	93.0836	93.0836	93.1340	93.2251
54150	70.0444	87.8066	92.9485	92.9485	92.9871	92.9871	93.0447	93.1489
55860	69.4895	87.6312	92.9235	92.9235	92.9632	92.9632	93.0226	93.1301
56250	69.3642	87.5912	92.9177	92.9177	92.9577	92.9577	93.0176	93.1258
57000	69.1244	87.5146	92.9067	92.9067	92.9473	92.9473	93.0079	93.1175
57624	68.9262	87.4509	92.8976	92.8976	92.9386	92.9386	92.9999	93.1107
58140	68.7632	87.3983	92.8900	92.8900	92.9314	92.9314	92.9932	93.1050
58800	68.5558	87.3312	92.8804	92.8804	92.9221	92.9221	92.9847	93.0977
59850	68.2283	87.2245	92.8650	92.8650	92.9075	92.9075	92.9711	93.0861
59976	68.1893	87.2117	92.8631	92.8631	92.9057	92.9057	92.9695	93.0847
60000	68.1818	87.2093	92.8628	92.8628	92.9054	92.9054	92.9692	93.0845
61200	67.8119	87.0878	92.8452	92.8452	92.8887	92.8887	92.9537	93.0713
61740	67.6468	87.0332	92.8373	92.8373	92.8811	92.8811	92.9467	93.0653
62424	67.4388	86.9642	92.8273	92.8273	92.8716	92.8716	92.9379	93.0578
63000	67.2646	86.9061	92.8189	92.8189	92.8636	92.8636	92.9305	93.0514
64260	66.8866	86.7794	92.8004	92.8004	92.8460	92.8460	92.9142	93.0376
66150	66.3277	86.5901	92.7728	92.7728	92.8197	92.8197	92.8899	93.0168
71250	64.8649	86.0832	92.6983	92.6983	92.7487	92.7487	92.8242	92.9607
73500	64.2398	85.8615	92.6655	92.6655	92.7175	92.7175	92.7953	92.9360
75000	63.8298	85.7143	92.6436	92.6436	92.6966	92.6966	92.7760	92.9196
76500	63.4249	85.5676	92.6217	92.6217	92.6758	92.6758	92.7567	92.9031
78750	62.8272	85.3485	92.5890	92.5890	92.6446	92.6446	92.7278	92.8784
93750	59.1133	83.9161	92.3711	92.3711	92.4370	92.4370	92.5357	92.7143

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

Penetration depth affect how deep stabs go. Unlike contact area, penetration depth is the maximum shear distance the weapon can go before an edged force stops and converts into a blunt force. If the penetration depth is greater than the size of the struck body part, the body part may be sliced off entirely. Interestingly, for a blunt hit, while the value isn't used, having penetration depth means that it can push fragments of bone into other parts, such as other bone or the brain. If the hit has no fragments, it will break rigid layers (materials with very low strain at yield) and keep going as bruising blunt force, not tearing the body parts underneath. This means that weapons like morningstars mainly deal surface damage but can still damage arteries, nerves, tendons, toes, and the like.^[Verify]

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, a platinum war hammer in dwarven hands only gets about 12% more momentum over a steel one, despite being thrice as heavy. (An 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 100000; 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.