An improved embedded element method using shell elements with full kinematic constraints for efficient mesoscale simulation of woven laminates

Mesoscale simulation of woven composite laminates offers high-fidelity stress analysis but is limited by the meshing complexity and high computational cost of conformal models. Embedded element methods (EEM) alleviate these challenges by embedding yarn representations within a solid host mesh. Using shell elements for yarns further reduces computational effort, but conventional shell-in-solid EEM couple only translational degrees of freedom (DOFs), leading to kinematic incompatibility and significant stiffness underestimation for laminates under bending and transverse-shear loading. This work develops an improved shell-in-solid EEM with full kinematic constraints that couple both translational and rotational DOFs of the embedded shell elements to solid elements in the host mesh. The method restores bending and transverse-shear fidelity at a fraction of the computational cost of solid-in-solid EEM. Under small deformation assumptions, consistent constraint and overlap-stiffness formulations are derived and implemented within a standard finite element workflow. The method is firstly tested on a cantilever beam model with span-to-thickness ratios from 32 to 4. Results show less than 0.8% deflection error compared with conformal references, while a translational-only scheme produces about 40% error in the most shear-dominated case. In addition, in a quasi-static three-point bending test of plain-woven laminates, the method is validated in comparison to the experimental load–displacement envelope, and the results agree with a solid-in-solid baseline model in global response and local strain distributions. The proposed approach achieves 17.6 times speedup over solid-in-solid EEM, enabling accurate and efficient mesoscale simulation. The method is also readily implemented in commercial finite element packages.