feat(physics): add helper utilities for multi-field microkernel assembly

New 88-line formulation utilities:
- field_type_for_dispatch(): extract field type from Element's S parameter
- Helper functions for multi-field Element{K,P,S} system
- Works with NamedTuple-based field specifications
- Supports thermoelasticity and other multi-physics couplings
- Already integrated in JuliaFEM.jl (line 500)

Provides utilities for multi-field microkernel assembly with Element{K,P,S} system.

src/physics/formulations.jl

@@ -0,0 +1,87 @@
+# This file is a part of JuliaFEM.
+# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
+
+"""
+Helper utilities for multi-field microkernel assembly.
+
+Works with existing Element{K,P,S} system where S is a NamedTuple specifying fields.
+
+# Philosophy
+
+Element{K,P,S} encodes everything:
+- K: Topology (Triangle, Tetrahedron, etc.)
+- P: Basis (Lagrange{1}, Lagrange{2}, etc.)
+- S: NamedTuple of fields with types and entity locations
+
+# Example
+
+```julia
+# Thermoelasticity using Element{K,P,S} directly:
+S = @DOFSet{T::DOF{Temperature,Vertex}, u::DOF{Displacement{3},Vertex}}
+elem = Element{Tet4, Lagrange{1}, S}(id, dof_indices)
+
+# Extract field info (compile-time!):
+field_names = fieldnames(S)  # (:T, :u)
+range_T = field_dof_range(elem, :T)  # Compile-time range
+```
+"""
+
+using ..JuliaFEM: AbstractField, Displacement, Temperature
+
+# ============================================================================
+# FIELD TYPE EXTRACTION FROM S (Element{K,P,S})
+# ============================================================================
+
+"""
+    field_type_for_dispatch(S, field_name::Symbol)
+
+Extract field type from Element's S parameter for dispatch.
+
+Works at runtime with NamedTuple-based field specifications.
+
+# Example
+```julia
+S = @DOFSet{T::DOF{Temperature,Vertex}, u::DOF{Displacement{3},Vertex}}
+field_type_for_dispatch(S, :T)  # Temperature()
+field_type_for_dispatch(S, :u)  # Displacement{3}()
+```
+"""
+function field_type_for_dispatch(::Type{S}, field_name::Symbol) where S<:DOFSet
+    # Get field names at runtime
+    names = fieldnames(S)
+    idx = findfirst(==(field_name), names)
+    isnothing(idx) && error("Field $field_name not found in $S")
+    
+    # Get the type of that field
+    field_tuple_type = fieldtype(S, idx)
+    
+    # field_tuple_type should be DOF{FieldType, EntityType}
+    # Extract the FieldType (first element)
+    FieldType = field_tuple_type.parameters[1]
+    
+    # FieldType must be a field type (AbstractField)
+    if FieldType <: AbstractField
+        # Create an instance of the field type
+        return FieldType()
+    else
+        error("Expected field type (AbstractField) in DOF, got $FieldType. Use format: DOF{FieldType, EntityType} where FieldType <: AbstractField")
+    end
+end
+
+# ============================================================================
+# CONVENIENCE TYPE ALIASES (for documentation/examples)
+# ============================================================================
+
+"""
+    ThermoelasticityFields
+
+Type alias for common thermoelasticity field specification.
+Use as Element{K, P, ThermoelasticityFields} type parameter.
+
+# Example
+```julia
+const ThermoelasticityFields = @DOFSet{T::DOF{Temperature,Vertex}, u::DOF{Displacement{3},Vertex}}
+elem = Element{Tet4, Lagrange{1}, ThermoelasticityFields}(id, dofs)
+```
+"""
+const ThermoelasticityFields = @DOFSet{T::DOF{Temperature,Vertex}, u::DOF{Displacement{3},Vertex}}