Generalized Cyclic Plasticity Constitutive Model for Sands within a Hyperplasticity Framework

Abstract

This study presents a novel generalized cyclic plasticity model within the hyperplasticity framework for modeling the cyclic behavior of sands. The formulation adopts a multisurface plasticity approach that accommodates multiple yield criteria, namely Tresca, von~Mises, Drucker–Prager, Mohr–Coulomb , Matsuoka–Nakai, and Lade–Duncan. Following the generalized principle of maximum dissipation, the proposed Generalized Cyclic Plasticity (GCP) model introduces a third potential into Ziegler’s classical two-potential thermodynamics framework, enabling a rigorous treatment of non-associative plasticity. The framework further incorporates critical state soil mechanics (CSSM) through a state-parameter-linked dilatancy angle and employs a phase transformation condition that governs the transition between contraction and dilation. This combination reproduces the monotonic and cyclic response of loose and dense states. The model parameters are physically interpretable and can be calibrated using standard soil laboratory tests. These features allow the GCP model to reproduce a wide spectrum of behaviors, including excess pore pressure generation, cyclic mobility, stiffness and damping evolution with cycling, Lode angle dependency, shakedown through pressure-dependent combined hardening, and dilation and contraction responses within the CSSM framework. The numerical implementation is based on robust return mapping algorithms that avoid numerical instabilities near the apex of the yield surface. The modular structure of the formulation enables exact recovery of classical constitutive models such as associative and non-associative Mohr–Coulomb and Prevost, while systematically extending them through optional features including enhanced dilatancy and hardening laws, thereby providing a unified framework for benchmarking and model development. The model performance is evaluated through triaxial and direct simple shear tests.