Analytical solutions for a three-invariant Cam clay model subjected to drained loading histories

Abstract

SUMMARYAnalytical solutions are derived for a three-invariant Cam clay model subjected to proportional and circular drained loading histories. The solutions are presented for a specific volume, and volumetric and generalized shear strains. In the case of a proportional loading only straight effective stress paths are considered while in the case of a circular loading the maximum possible change in Lode's angle is p/3 due to plastic isotropy. Additionally, a concept of deviatoric stiffness is devised and an analytical expression for the generalized hardening modulus is derived. Qualitative and quantitative analyses are carried out in the form of direct comparisons between analytical solutions for drained and undrained loading histories thus offering an improved understanding of the three-invariant model.

An approach for providing quasi‐convexity to yield functions and a generalized implicit integration scheme for isotropic constitutive models based on 2 unknowns

“…One‐element FE analyses were performed of drained triaxial compression tests in which the effective cell pressure was maintained constant while the deviatoric strain was monotonically increased. The numerical results were then compared with the analytical solution proposed by Perić for the modified Cam‐Clay model. As an hypo‐elastic law is adopted in the original version of that constitutive model, the solution retrieved by Peric was modified to account for linear elasticity.…”

“…Comparison between analytical Perić and numerical integration of the constitutive model for a drained triaxial compression test. FE, finite element…”

An innovative procedure to improve integration algorithm for modified Cam-Clay plasticity model

“…To verify the implementation of GMCC model, we compare the numerical results of our implementation with the analytical solution provided by Perić [18] for infinitesimal strain assumption. The analytical solutions are presented separately for volumetric and deviatoric behavior of the material.…”

“…The MCC model is generally implemented by a numerical integration of two invariant [18]. Inspired by the articles [7,28], to control the plastic surface format, we consider a generalized modified Cam-Clay (GMCC ) model by introducing an additional dependence on the Lode angle β.…”

“…The proposed approach for the MCC model is verified by comparing the numerical results of MCC model with analytical solutions provided by Perić & Ayari [8], Perić [18]. The implementation of the present study is done in the NeoPZ library [19], which is an object-oriented scientific computational environment, providing a framework for developing finite element algorithms [20].…”