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

Tamagnini, Claudio; Castellanza, Riccardo; Nova, Roberto

doi:10.1002/nag.231

Cited by 88 publications

(98 citation statements)

References 44 publications

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“…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).…”

Section: Bvp#2: Std and Ltd Processes Inducing Model Pillar Failurementioning

confidence: 99%

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

2018

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The goal of this paper is to show how a recently developed advanced chemo-hydro-mechanical (CHM)-coupled constitutive and numerical model for soft rocks can be applied to predict the temporal evolution of settlement damage to buildings on cavities subject to weathering. In particular, a Building Damage Index (BDI) and its evolution with time is proposed. The definition of the BDI is inspired by the work of Boscardin and Cording (J Geotech Eng 115:1-21, 1989) and uses the surface differential settlements obtained by finite element (FE) analyses to assess how far a building is from a non-acceptable service condition. By modelling the reactive transport of chemical species in 3D and using a coupled CHM constitutive and numerical model, it is possible to simulate weathering scenarios and monitor the temporal evolution of surface settlements making the BDI time dependent. This approach is applied to evaluate the damage evolution of two buildings lying on two anthropic caves in a calcarenite deposit belonging to the Calcarenite di Gravina Formation. Standard and advanced experimental tests are performed on the in situ material, and the results are used to calibrate the constitutive model. The soundness of both constitutive relationship and reactive transport solver is subsequently tested by simulating two laboratory-scale boundary value experiments. The first is a model footing test on dry and wet calcarenite, while the second is a small-scale pillar that, after the saturation-induced short-term water weakening, fails due to a long-term dissolution weathering process. Finally, both 2D and 3D coupled FE analyses simulating different weathering scenarios and corresponding settlements affecting the buildings above the considered cavities are presented. Particular attention is placed on assessing the BDI and its temporal evolution. Keywords

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“…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).…”

Section: Bvp#2: Std and Ltd Processes Inducing Model Pillar Failurementioning

confidence: 99%

“…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).…”

Section: Introductionmentioning

confidence: 99%

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

2018

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“…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.…”

Section: 3numerical Integration Of the Present Constitutive Modelmentioning

confidence: 99%

Ductile Shear Damage Model for Porous Materials

Siad¹,

Gangloff²,

Bohr³

2014

JMSE-B

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Based on a pre-existing yield function, an extended version of the well-known Gurson-Tvergaad-Needleman (GTN)isotropic hardening model is presented in this investigation. The yield function of the proposed constitutive model possesses the distinctiveness to be more accurate for arbitrary void volume fraction and especially to explicitly depend upon the third stress invariant. As a numerical example, the presented constitutive model and, for the purpose of comparison, the GTN model, are used to analyse the necking of a round tensile bar and the two-dimensional simple dynamic shearing problem. The numerical results highlight similarities, good agreement as long as softening initiation of specimen is not reached, and discrepancy as soon as failure of specimen starts, between the proposed model and the GTN model.

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“…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).…”

Section: Return Mapping Algorithm For Implicit Integrationmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Foster

Regueiro

Fossum

et al. 2005

Computer Methods in Applied Mechanics and Engineering

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The mechanical constitutive behavior of geomaterials is quite complex, involving pressure-sensitive yielding, differences in strength in triaxial extension vs. compression, the Bauschinger effect, dependence on porosity, and other factors. Capturing these behaviors necessitates the use of fairly complicated and expensive non-linear material models. For elastically isotropic materials, such models usually involve three-invariant plasticity formulations. Spectral decomposition has been used to increase the efficiency of numerical simulation for such models for the isotropically hardening case. We modify the spectral decomposition technique to models that include kinematic hardening. Finally, we perform some numerical simulations to demonstrate quadratic convergence.

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

Cited by 88 publications

References 44 publications

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

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

Ductile Shear Damage Model for Porous Materials

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

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