A novel parameter-free and locking-free enriched Galerkin method for linear elasticity
Shuai Su, Xiurong Yan, Qian Zhang
TL;DR
The paper tackles volumetric locking in nearly incompressible linear elasticity by introducing a parameter-free, locking-free enriched Galerkin method. It enriches the first-order continuous Galerkin space with edge/face-based piecewise constants, enabling a commutative weak gradient/divergence and a stabilized, parameter-free formulation. The authors prove well-posedness and derive error estimates that are independent of the Lamé parameter $λ$, and they show through 2D/3D numerical experiments that the method achieves optimal convergence and oscillation-free stress without post-processing. Compared with other approaches, the method maintains a continuous displacement field with reduced degrees of freedom and demonstrates robustness across compressible and nearly incompressible regimes, with potential for higher-order extensions.
Abstract
We propose a novel parameter-free and locking-free enriched Galerkin (EG) method for solving the linear elasticity problem in both two and three dimensions. Unlike existing locking-free EG methods, our method enriches the first-order continuous Galerkin (CG) space with piecewise constants along edges in two dimensions or faces in three dimensions. This enrichment acts as a correction to the normal component of the CG space, ensuring the locking-free property and delivering an oscillation-free stress approximation without requiring post-processing. Our theoretical analysis establishes the well-posedness of the method and derives optimal error estimates. Numerical experiments further demonstrate the accuracy, efficiency, and robustness of the proposed method.