A Generalized Backward Euler algorithm for the numerical integration of an isotropic hardening elastoplastic model for mechanical and chemical degradation of bonded geomaterials

Abstract

SUMMARYAn extended version of the classical Generalized Backward Euler (GBE) algorithm is proposed for the numerical integration of a three-invariant isotropic-hardening elastoplastic model for cemented soils or weak rocks undergoing mechanical and non-mechanical degradation processes. The restriction to isotropy allows to formulate the return mapping algorithm in the space of principal elastic strains. In this way, an efficient and robust integration scheme is developed which can be applied to relatively complex yield surface and plastic potential functions. Moreover, the proposed algorithm can be linearized in closed form, thus allowing for quadratic convergence in the global Newton iteration. A series of numerical experiments are performed to illustrate the accuracy and convergence properties of the algorithm. Selected results from a finite element analysis of a circular footing on a soft rock layer undergoing chemical weathering are then presented to illustrate the algorithm performance at the boundary value problem level.

A 3D Numerical Approach to Assess the Temporal Evolution of Settlement Damage to Buildings on Cavities Subject to Weathering

“…12d) or in ancient temple columns (Fig. 12e) when the intact rock is exposed to long-term chemical degradation (Parise and Lollino 2011;Tamagnini et al 2002).…”

“…In particular, chemo-hydro-mechanical (CHM)-coupled advanced numerical simulations are usually performed for 2D idealized problems to show the robustness of integration schemes or to simulate laboratory-scale boundary value problems (Fernandez-Merodo et al 2007;Tamagnini et al 2002;Tamagnini and Ciantia 2016).…”

Ductile Shear Damage Model for Porous Materials

“…The presence of the third stress invariantJ 3 in the yield function  typically results in a high degree of non-linearity and complex numerical algorithms. Implicit solution strategies for models depending on the third stress invariant have been developed, for associative isotropic elastoplastic and viscoplastic models [20], for associative elastoplastic models with kinematic hardening [21,22] and for models of general isotropic elastoplastic geomaterials [21,23,24]. Generally speaking, regarding elastoplastic material, the incremental-iterative analysis consists in dividing up the applied load into a number of small increments, and within each increment, iterations are performed.…”

Implicit numerical integration of a three-invariant, isotropic/kinematic hardening cap plasticity model for geomaterials

“…Not only would this reduce the size of the matrix to be inverted, but it would also reduce the number of function evaluations, which is expensive given the complexity of the yield function and evolution equations. Tamagnini et al [3] and Borja et al [4] have used spectral decomposition to do this in the case of the isotropic hardening models. However, these algorithms rely on the fact that the trial stress r tr nþ1 has the same spectral directions as og/or (and from this the converged stress also has the same spectral directions).…”

“…For models that also have an isotropic yield function and are isotropically hardening, spectral decomposition can reduce the number of function evaluations and the number of equations to be solved. Tamagnini et al [3] and Borja et al [4] have recently used this approach for three-invariant models for geomaterials. The algorithm is not new, however.…”