Material science

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v50.14 · v0.47.05 This article is about the current version of DF. Note that some content may still need to be updated. More Info · V

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.

Note: Strain at yield is the inverse of the 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 dependant 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 ),

where:

• Str is creature strength (e.g. 1250 for average dwarf)
• Vel is weapon's velocity modifier if present (e.g. 1.25x, 2x)
• Size is normal creature size (e.g. 60000 for dwarves)
• F is "fatness modifier" (also includes muscle); dwarf with weight of 66000 will have F=66000/60000=1.1
• W is weapon weight in kilograms (Γ).

There is also a hard velocity limit 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?)

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

Ranged Attacks

Attacks from missile launchers are entirely dependent on launcher's [SHOOT_FORCE] and [SHOOT_MAXVEL] tags. Specifically, as long as projectile is heavy enough, it is fired with momentum of SHOOT_FORCE/20; if this would make its speed exceed SHOOT_MAXVEL, it is capped at this value instead. (As usual, momentum = velocity times weight.)

Vanilla bolts and arrows end up with momenta of 49, as long as their density exceeds 1670. Divine ammo has momentum of 30, bone and most wood get 15, and adamantine bolts have only 6. Wooden darts usually have 5.

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 / (S * Q),

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 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)
• Q is quality sharpness multiplier (1x for normal quality, 1.4x for fine, 2x for masterwork (or artifact) etc.)

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 yeild in MPa (i.e. raw value divided by 10⁶).

Otherwise, attack must have minimum momentum of:

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

where IF and IY are layer's impact fracture and impact yield in MPa, 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.

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:
a) 100% bruised/burned/frostbite/melt/necrosis/blister/boil/freeze/condense (i.e. 10000+ in layer_effect_fraction)
b) 250% dented (i.e. 25000+ in layer_dent_fraction)
c) 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. (Adamantime hammer, however, only has 1/7th as much.) Thus, since all common weapon metals have about the same density, it can be safely ignored.
• On the contrary, velocity multiplier influences momentum linearly and as such is very important.
• 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 yeild value. Impact fracture protects from blunt attacks instead. Curiously, layer impact yeild actually decreases blunt fracturing cost, so lower yeild is better for armor.
• Chain mail cannot block attacks via momentum cost thresholds; they 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 yeild values are used in comparsion 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.