ACosine Bounded-Decay Model for Tangent Modulus: Eliminating the Singularity in Soil Constitutive Relations

The classical Duncan--Chang hyperbolic model leads to an unbounded tangent modulus near peak strength, giving rise to ill-conditioned stiffness matrices and numerical divergence in implicit finite-element simulations. This paper proposes a cosine-based bounded evolution function for tangent modulus. Within a finite strain range, the modulus decays smoothly from its initial value to a bounded residual value, thereby eliminating the denominator-induced singularity. A dimensionless shape parameter controls the decay rate. Closed-form stress solutions are derived for the symmetric case, and Gauss--Legendre quadrature is adopted for general cases. A companion bounded evolution law for Poisson's ratio ensures a consistent volumetric response. The model is validated using triaxial test data for Toyoura sand and Jinping marble. The results demonstrate accurate predictions over the full strain range together with a bounded condition number. The proposed model is well-suited for large-deformation implicit analyses where numerical stability is paramount. This is the original submission version for Computers & Geotechnics. Manuscript source files, finite element UMAT code and test calculation materials are uploaded for reproducibility. No duplicate submission exists, and the work is licensed under CC-BY 4.0.