ACosine Bounded-Decay Model for Tangent Modulus: Eliminating the Singularity in Soil Constitutive Relations
Year: 2026
Type: preprint
Abstract: 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.
Author: Chen, Zhiyuan
Institution: Central South University of Forestry and Technology
Language: English
Subfield: Civil and Structural Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7171160930
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