A linearized integration technique for incremental constitutive equations

Abstract

SUMMARYA numerical technique is proposed to obtain stress-strain response curves from rate-type and incremental constitutive equations during generalized loadings. The proposed method linearizes the loading constraints of laboratory experiments, links them to the constitutive relations, and forms a linear system of ordinary differential equations. It circumvents the difficulties associated with the non-uniqueness and bifurcation of boundary value problems. The method is illustrated for the elastoplastic von Mises and Roscoe and Burland models subjected to torsion, circular stress path, and undrained triaxial compression. The approach pertains to most stress-strain relationships and laboratory experiments of geomechanics. It is useful for research on material modelling, engineering practice and computational mechanics.

A constitutive model for granular materials with grain crushing and its application to a pyroclastic soil

“…4-7 along the different loading paths considered in sections 3 and 4, an adaptive, embedded Runge-Kutta-Fehlberg method of order 2 and 3 [36] has been employed in connection with an algorithm to simulate generalized loading paths first proposed by Bardet & Choucair [5].…”

“…The procedure adopted for the numerical integration of the constitutive equations along the prescribed loading paths is a modified version of an algorithm initially proposed by Bardet & Choucair [5], and is detailed in the Appendix.…”

“…By an appropriate choice of the coefficients of matrices E and S, eq. (49) can describe the loading conditions imposed in practically all currently available testing equipments, from stress-path controlled triaxial cells to true triaxial apparati or hollow cylinders (see [5] for details). ¿From eqs.…”

Application of an Anisotropic Constitutive Model for Structured Clay to Seismic Slope Stability

“…This constitutive driver is prepared based on a linearized integration algorithm for incremental constitutive equations, a technique proposed by Bardet and Choucair (1991). The implementation is conducted using a refined explicit integration of the constitutive model.…”

“…Some additional equations pertinent to the numerical implementation are derived and presented in detail in the "Numerical Implementation of the Model" section. The numerical implementation of the model in the framework of FLAC 3D is subsequently verified with a stand-alone constitutive driver prepared based on earlier works of Bardet and Choucair (1991). The section on "Numerical Simulations" is devoted to application of the resulting numerical framework for modeling a boundary value problem.…”