Anisotropic subloading surface Cam‐clay plasticity model with rotational hardening: Deformation gradient‐based formulation for finite strain

Abstract

This study is aimed at developing an anisotropic elastoplastic constitutive model for geomaterials at finite strain and its stress calculation algorithm based on the fully implicit return-mapping scheme. The Cam-clay plasticity model is adopted as a specific prototype model of geomaterials. As a pertinent representation of deformation-induced anisotropy in geomaterials, nonlinear rotational hardening is incorporated into the model in a theoretically reasonable manner by introducing the dual multiplicative decompositions of the deformation gradient tensor. In addition to the usual decomposition into elastic and plastic parts, the plastic part is decomposed further into a part contributing to the rotational hardening and a remainder part. The former part leads to a back stress ratio tensor related to the rotational hardening via a hyperelastic-type hardening rule. The constitutive theory is thereby formulated on proper intermediate configurations entirely in terms of deformation-like tensorial variables possessing invariance property, without resort to any objective rates of stress or stress-like variables. Combining the Cam-clay plasticity with the concept of subloading surface, a class of unconventional plasticity, enables the model to be capable of reproducing complex hardening/softening accompanied by volumetric contractive/dilative responses.Basic characteristics and predictive capability of the proposed model, as well as the accuracy of the developed numerical scheme, are verified through several numerical examples including monotonic and cyclic loadings. K E Y W O R D Sanisotropy, cam-clay plasticity, finite strain, return-mapping algorithm, rotational hardening, subloading surface conceptThis is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Re-Interpretation of the Homogenized Constrained Mixture Theory within the Plasticity Framework and Application to Soft Tissue Growth and Remodeling

“…( 23) might not be isotropic. To that end, we use the widely assumed spinless & isoclinic configuration Γ [25,32,[36][37][38][39]. By also defining the flow vector to be of the associative type, it follows that…”

Modified unified critical state model for soils considering over-consolidation and cyclic loading behaviours

“…Asaoka et al 28 and Zhang et al 29 described the mechanical properties of structured soils through the combination of superloading and subloading surfaces. Since the concept of rotational hardening mechanism has been widely adopted in the constitutive modeling to capture the induced anisotropic properties of soils 30 – 32 , Hashiguchi and Chen 33 , Yamakawa et al 34 and Hashiguchi et al 35 combined the subloading surface concept with rotational hardening theory to characterize the cyclic mobility mechanism of anisotropic soils.…”

A hybrid strength criterion for a soil medium based on tension strength and its implementation in numerical analysis

“…The second limit is the continuous numerical calculation of the yield surface on the deviatoric planes owing to the six sharp corners in the Mohr-Coulomb strength criterion (De Borst et al 1991). These singularities lead to convergence difficulties in the iterative process that can abort the calculation (De Borst et al 1991;Booker 1986, 1992;Crisfield 1987;Zhang and Chen 1987;Pankaj and Bicanic 1997;Peric and De Souza 1999;Borja et al 2003Borja et al , 2020Clausen et al 2006;Jiang and Xie 2011;Bennett et al 2019;Yamakawa et al 2021).…”