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+# This file is a part of JuliaFEM.
+# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
+
+"""
+Material model API definitions.
+
+This file defines material-specific abstract types and interfaces.
+Must be included after core api.jl.
+"""
+
+# ============================================================================
+# MATERIAL MODEL ABSTRACTIONS
+# ============================================================================
+
+"""
+    AbstractMaterial
+
+Abstract type for all material models.
+
+# Interface Requirements
+
+All material models must implement:
+```julia
+compute_stress(
+    material::AbstractMaterial,
+    ε::SymmetricTensor{2,3,T},
+    state_old,
+    Δt::Float64
+) -> (σ::SymmetricTensor{2,3,T}, 𝔻::SymmetricTensor{4,3,T}, state_new)
+```
+
+Returns:
+- `σ`: Cauchy stress tensor
+- `𝔻`: Material tangent (4th-order elasticity tensor)
+- `state_new`: Updated material state (for plasticity, damage, etc.)
+
+# Type Hierarchy
+- `AbstractElasticMaterial` - Stateless elastic materials (no history)
+- `AbstractPlasticMaterial` - Stateful plastic materials (history-dependent)
+
+# Design Philosophy
+
+Materials are immutable structs with parameters (E, ν, etc.).
+Material state (plastic strain, damage) stored separately in solution.
+Use Tensors.jl for all tensor operations (no Voigt notation).
+
+# See Also
+- Concrete implementations in src/materials/
+"""
+abstract type AbstractMaterial end
+
+"""
+    AbstractElasticMaterial <: AbstractMaterial
+
+Stateless elastic materials (no history variables).
+
+Elastic materials compute stress directly from strain with no memory of loading history.
+
+# Characteristics
+- No internal state variables
+- Reversible deformation
+- Path-independent response
+- `state_new = state_old` always
+
+# Examples
+- `LinearElastic`: Hooke's law (small strain)
+- `NeoHookean`: Hyperelastic (finite strain)
+- `Mooney-Rivlin`: Hyperelastic with two parameters
+- `Ogden`: Hyperelastic for rubber-like materials
+
+# See Also
+- [`AbstractPlasticMaterial`](@ref) for history-dependent materials
+"""
+abstract type AbstractElasticMaterial <: AbstractMaterial end
+
+"""
+    AbstractPlasticMaterial <: AbstractMaterial
+
+Stateful plastic materials (history-dependent).
+
+Plastic materials have internal state variables that evolve with loading history.
+
+# Characteristics
+- Internal state variables (plastic strain, hardening, etc.)
+- Irreversible deformation
+- Path-dependent response
+- `state_new ≠ state_old` during plastic loading
+
+# Examples
+- `PerfectPlasticity`: J2 plasticity with no hardening
+- `IsotropicHardening`: J2 plasticity with isotropic hardening
+- `KinematicHardening`: Bauschinger effect modeling
+- `FiniteStrainPlasticity`: Large deformation plasticity
+
+# State Variables
+
+Common state variables:
+- `εᵖ`: Plastic strain tensor
+- `α`: Backstress (kinematic hardening)
+- `κ`: Equivalent plastic strain (isotropic hardening)
+- `damage`: Damage parameter (continuum damage mechanics)
+
+# See Also
+- [`AbstractElasticMaterial`](@ref) for stateless materials
+"""
+abstract type AbstractPlasticMaterial <: AbstractMaterial end
+
+# ============================================================================
+# MATERIAL MODEL FUNCTIONS
+# ============================================================================
+
+"""
+    compute_stress(material::AbstractMaterial, ε, state_old, Δt) 
+    -> (σ, 𝔻, state_new)
+
+Compute stress, tangent, and updated state for a material model.
+
+# Arguments
+- `material`: Material model parameters
+- `ε`: Strain tensor (SymmetricTensor{2,3} or similar)
+- `state_old`: Previous state (Dict, NamedTuple, or nothing for elastic)
+- `Δt`: Time step (for rate-dependent materials)
+
+# Returns
+- `σ`: Cauchy stress tensor
+- `𝔻`: Material tangent (∂σ/∂ε)
+- `state_new`: Updated internal state
+
+# Examples
+
+```julia
+# Elastic material (no state)
+σ, 𝔻, _ = compute_stress(LinearElastic(E=210e9, ν=0.3), ε, nothing, 0.0)
+
+# Plastic material (with state)
+state = (εᵖ=zero(SymmetricTensor{2,3}), κ=0.0)
+σ, 𝔻, state_new = compute_stress(PerfectPlasticity(E=210e9, ν=0.3, σ_y=250e6), 
+                                   ε, state, Δt)
+```
+
+# Implementation Notes
+
+Material models implement this function with specific signatures:
+- Elastic: `compute_stress(::LinearElastic, ε, _, _)`
+- Plastic: `compute_stress(::PerfectPlasticity, ε, state, Δt)`
+
+# See Also
+- [`elasticity_tensor`](@ref) for elastic constitutive tensor
+- Material implementations in src/materials/
+"""
+function compute_stress end
+
+"""
+    elasticity_tensor(material::AbstractElasticMaterial) -> Tensor{4,3}
+
+Compute 4th-order elasticity tensor for an elastic material.
+
+For linear elastic material:
+```
+C_ijkl = λ δ_ij δ_kl + μ (δ_ik δ_jl + δ_il δ_jk)
+```
+
+where:
+- λ = Eν/((1+ν)(1-2ν)) (Lamé's first parameter)
+- μ = E/(2(1+ν)) (shear modulus)
+
+# Arguments
+- `material`: Elastic material with parameters (E, ν, etc.)
+
+# Returns
+- `C`: 4th-order elasticity tensor (Tensor{4,3})
+
+# Examples
+
+```julia
+mat = LinearElastic(E=210e9, ν=0.3)
+C = elasticity_tensor(mat)
+
+# Use in stress computation
+σ = C ⊡ ε  # Double-dot product: σ_ij = C_ijkl ε_kl
+```
+
+# See Also
+- [`compute_stress`](@ref) for full stress computation
+"""
+function elasticity_tensor end