From ec8efd52ddf3d75d81df1595148d54d0a693b030 Mon Sep 17 00:00:00 2001
From: Jukka Aho <ahojukka5@gmail.com>
Date: Sat, 9 May 2026 18:32:29 +0300
Subject: [PATCH] feat(materials): add symmetric fourth-order identity helper
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Provide the Lamé-style symmetric identity tensor builder shared by elastoplastic
material implementations.

- Add `symmetric_identity_tensor()` returning `SymmetricTensor{4,3}` with SPDX header.
---
 src/materials/symmetric_fourth_identity.jl | 10 ++++++++++
 1 file changed, 10 insertions(+)
 create mode 100644 src/materials/symmetric_fourth_identity.jl

diff --git a/src/materials/symmetric_fourth_identity.jl b/src/materials/symmetric_fourth_identity.jl
new file mode 100644
index 0000000..7f2af76
--- /dev/null
+++ b/src/materials/symmetric_fourth_identity.jl
@@ -0,0 +1,10 @@
+# SPDX-FileCopyrightText: 2015-2026 Jukka Aho
+# SPDX-License-Identifier: MIT
+
+using Tensors
+
+"""Fourth-order symmetric identity 𝕀ˢʸᵐ for Lamé-style stiffness `λ I⊗I + 2μ 𝕀ˢʸᵐ`."""
+@inline function symmetric_identity_tensor()
+    return SymmetricTensor{4,3}((i, j, k, l) ->
+        (i == k && j == l ? 0.5 : 0.0) + (i == l && j == k ? 0.5 : 0.0))
+end