feat(materials): Add material model API with elastic and plastic abstractions

Create src/materials/api.jl defining material-specific abstractions:
- AbstractMaterial base type for all material models
- AbstractElasticMaterial for stateless materials (no history)
- AbstractPlasticMaterial for stateful materials (history-dependent)
- compute_stress() interface (strain → stress + tangent + updated state)
- elasticity_tensor() for elastic constitutive relations

Material models use Tensors.jl (no Voigt notation). Elastic materials
are stateless (LinearElastic, NeoHookean). Plastic materials have internal
state (plastic strain εᵖ, backstress α, hardening κ, damage).

Interface returns (σ, 𝔻, state_new) where 𝔻 is the material tangent ∂σ/∂ε.

Part of systematic modular API architecture.

src/materials/api.jl

@@ -0,0 +1,186 @@
+# 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