feat(physics): Add backend-agnostic physics API with BC types

New file src/physics_api.jl defining user-facing elasticity API:
- ElasticityPhysicsType (alias Elasticity) for problem configuration
- DirichletBC struct for prescribed displacements
- NeumannBC struct for surface tractions/pressures
- Physics{P} container for problem with elements and BCs
- Works with both CPU and GPU backends
- 183 lines with comprehensive examples

src/physics_api.jl

@@ -0,0 +1,183 @@
+# This file is a part of JuliaFEM.
+# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
+
+"""
+Backend-agnostic elasticity API
+
+This file defines the user-facing API that works regardless of backend (CPU or GPU).
+"""
+
+"""
+    Elasticity <: FieldProblem
+
+Elasticity physics problem type.
+
+Properties:
+- `formulation`: `:continuum` (3D solid) or `:plane_stress`, `:plane_strain`
+- `finite_strain`: Enable geometric nonlinearity
+- `geometric_stiffness`: Include stress-dependent stiffness
+"""
+mutable struct ElasticityPhysicsType <: FieldProblem
+    formulation::Symbol         # :continuum (3D)
+    finite_strain::Bool         # Geometric nonlinearity
+    geometric_stiffness::Bool   # Stress-dependent stiffness
+end
+
+const Elasticity = ElasticityPhysicsType
+ElasticityPhysicsType() = ElasticityPhysicsType(:continuum, false, false)
+
+"""
+    DirichletBC
+
+Dirichlet boundary condition (prescribed displacement).
+
+Fields:
+- `node_ids`: Constrained node IDs
+- `components`: Which components per node ([1,2,3] for all)
+- `values`: Prescribed values per node
+"""
+struct DirichletBC
+    node_ids::Vector{Int}           # Constrained nodes
+    components::Vector{Vector{Int}} # Which components per node ([1,2,3] for all)
+    values::Vector{Vector{Float64}} # Prescribed values per node
+end
+
+DirichletBC() = DirichletBC(Int[], Vector{Int}[], Vector{Float64}[])
+
+"""
+    NeumannBC
+
+Neumann boundary condition (surface traction/pressure).
+
+Fields:
+- `surface_elements`: Surface elements (Tri3, Quad4, etc.) with geometry
+- `traction`: Traction vector [t_x, t_y, t_z] per element [N/m²]
+"""
+struct NeumannBC
+    surface_elements::Vector{Element}  # Surface elements with geometry
+    traction::Vector{Vec{3,Float64}}   # Traction per element [N/m²]
+end
+
+NeumannBC() = NeumannBC(Element[], Vec{3,Float64}[])
+
+"""
+    Physics{P}
+
+Container for physics problem with elements and boundary conditions.
+
+Type parameter `P` is the physics type (e.g., Elasticity, HeatTransfer).
+
+Fields:
+- `name`: Problem name
+- `dimension`: Spatial dimension (1, 2, or 3)
+- `properties`: Physics-specific properties (e.g., Elasticity struct)
+- `body_elements`: Volume elements with geometry and material
+- `bc_dirichlet`: Dirichlet boundary conditions
+- `bc_neumann`: Neumann boundary conditions (surface loads)
+
+# Example
+
+```julia
+physics = Physics(Elasticity, "beam", 3)
+add_elements!(physics, elements)
+add_dirichlet!(physics, [1,2,3], [1,2,3], 0.0)
+sol = solve!(physics)
+```
+"""
+mutable struct Physics{P}
+    name::String
+    dimension::Int
+    properties::P
+    body_elements::Vector{Element}
+    bc_dirichlet::DirichletBC
+    bc_neumann::NeumannBC
+end
+
+"""
+    Physics(::Type{P}, name::String, dimension::Int) where P
+
+Create a physics problem of type P.
+
+# Example
+
+```julia
+physics = Physics(Elasticity, "cantilever", 3)
+```
+"""
+function Physics(::Type{P}, name::String, dimension::Int) where P
+    properties = P()
+    body_elements = Element[]
+    bc_dirichlet = DirichletBC()
+    bc_neumann = NeumannBC()
+    return Physics{P}(name, dimension, properties, body_elements, bc_dirichlet, bc_neumann)
+end
+
+"""
+    add_elements!(physics::Physics, elements::Vector{Element})
+
+Add volume elements to the physics problem.
+
+# Example
+
+```julia
+add_elements!(physics, [el1, el2, el3])
+```
+"""
+function add_elements!(physics::Physics, elements::Vector{Element})
+    append!(physics.body_elements, elements)
+    return nothing
+end
+
+"""
+    add_dirichlet!(physics::Physics, node_ids::Vector{Int}, components::Vector{Int}, value::Float64)
+
+Add Dirichlet boundary condition (prescribed displacement).
+
+# Arguments
+- `node_ids`: Node IDs to constrain
+- `components`: Which DOF components to constrain (1=x, 2=y, 3=z)
+- `value`: Prescribed value
+
+# Example
+
+```julia
+# Fix nodes 1,2,3 in all directions
+add_dirichlet!(physics, [1,2,3], [1,2,3], 0.0)
+
+# Fix nodes 4,5 in x-direction only
+add_dirichlet!(physics, [4,5], [1], 0.0)
+```
+"""
+function add_dirichlet!(physics::Physics, node_ids::Vector{Int}, components::Vector{Int}, value::Float64)
+    # Expand: for each node, store which components are fixed
+    for node in node_ids
+        push!(physics.bc_dirichlet.node_ids, node)
+        push!(physics.bc_dirichlet.components, components)
+        push!(physics.bc_dirichlet.values, fill(value, length(components)))
+    end
+    return nothing
+end
+
+"""
+    add_neumann!(physics::Physics, surface_element::Element, traction::Vec{3,Float64})
+
+Add Neumann boundary condition (surface traction/pressure).
+
+# Arguments
+- `surface_element`: Surface element (Tri3, Quad4, etc.) with geometry
+- `traction`: Traction vector [t_x, t_y, t_z] [N/m²]
+
+# Example
+
+```julia
+# Apply pressure load
+pressure = -1e6  # -1 MPa
+traction = Vec{3}((0.0, 0.0, pressure))
+add_neumann!(physics, surface_element, traction)
+```
+"""
+function add_neumann!(physics::Physics, surface_element::Element, traction::Vec{3,Float64})
+    push!(physics.bc_neumann.surface_elements, surface_element)
+    push!(physics.bc_neumann.traction, traction)
+    return nothing
+end