doc_id: DOC-028-WP10-FORMULATION-001 revision: 0.1 status: controlled_candidate applicable_version: 0.2.8-development reviewer: "" approver: ""
WP10 HEX8 selective reduced integration formulation¶
WP10 studies a separate research element. The qualified HEX8 implementation and all existing analysis routes remain unchanged.
Selected formulation¶
The reference interpolation is the existing trilinear HEX8 interpolation and the existing Jacobian/strain-displacement operator. For isotropic linear elasticity, the constitutive matrix is split as
[ C = C_{dev} + C_{vol},\qquad C_{vol}=K\,m m^T,\qquad m=(1,1,1,0,0,0)^T, ]
where K = E/(3(1-2ν)) and C_dev = C-C_vol in the engineering-Voigt
convention used by QF Solver. The SRI stiffness is
[ K_{SRI}=\sum_{2\times2\times2} w_q\det J_q B_q^T C_{dev}B_q +w_0\det J_0 B_0^T C_{vol}B_0. ]
The deviatoric contribution uses the eight standard Gauss points. The volumetric contribution uses the element centre only. This choice targets volumetric locking while retaining full deviatoric/shear integration; no hourglass control or production reduced-integration HEX8 variant is added.
Risks and boundaries¶
The centre-only volumetric term can alter stiffness and must not be treated as a general accuracy improvement. The gate therefore checks symmetry, six rigid body modes, numerical rank, affine and constant-strain reproduction, energy, distortion and invalid geometry. A rank loss, zero-energy mode, or materially unstable distorted response rejects the candidate.
The candidate is internal and isotropic linear-static only. It is not added to the public element registry, compatibility descriptor, standard HEX8 class, modal/dynamic routes, nonlinear routes or release maturity records.