Stress-driven integration strategies and m-AGC tangent operator for Perzyna viscoplasticity and viscoplastic relaxation: application to geomechanical interfaces

This is the peer reviewed version of the following article: [Aliguer, I., Carol, I., and Sture, S. (2017) Stress-driven integration strategies and m-AGC tangent operator for Perzyna viscoplasticity and viscoplastic relaxation: application to geomechanical interfaces. Int. J. Numer. Anal. Meth. Geomech., 41: 918–939. doi: 10.1002/nag.2654.], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nag.2654/abstract. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.The paper proposes a stress-driven integration strategy for Perzyna-type viscoplastic constitutive models, which leads also to a convenient algorithm for viscoplastic relaxation schemes. A generalized trapezoidal rule for the strain increment, combined with a linearized form of the yield function and flow rules, leads to a plasticity-like compliance operator that can be explicitly inverted to give an algorithmic tangent stiffness tensor also denoted as the m-AGC tangent operator. This operator is combined with the stress-prescribed integration scheme, to obtain a natural error indicator that can be used as a convergence criterion of the intra-step iterations (in physical viscoplasticity), or to a variable time-step size in viscoplastic relaxation schemes based on a single linear calculation per time step. The proposed schemes have been implemented for an existing zero-thickness interface constitutive model. Some numerical application examples are presented to illustrate the advantages of the new schemes proposed.Peer ReviewedPostprint (author's final draft

Wall Adhesion and Constitutive Modelling of Strong Colloidal Gels

Wall adhesion effects during batch sedimentation of strongly flocculated colloidal gels are commonly assumed to be negligible. In this study in-situ measurements of colloidal gel rheology and solids volume fraction distribution suggest the contrary, where significant wall adhesion effects are observed in a 110mm diameter settling column. We develop and validate a mathematical model for the equilibrium stress state in the presence of wall adhesion under both viscoplastic and viscoelastic constitutive models. These formulations highlight fundamental issues regarding the constitutive modeling of colloidal gels, specifically the relative utility and validity of viscoplastic and viscoelastic rheological models under arbitrary tensorial loadings. The developed model is validated against experimental data, which points toward a novel method to estimate the shear and compressive yield strength of strongly flocculated colloidal gels from a series of equilibrium solids volume fraction profiles over various column widths.Comment: 37 pages, 12 figures, submitted to Journal of Rheolog

Some numerical verification examples for plane stress elasto-viscoplasticity

This paper presents analytical, semi-analytical and numerical reference examples which can be employed for code verification of elasto-viscoplastic models under plane stress conditions. Mainly because of the overstress function the algorithms traditionally employed in elasto-plastic implementations must be rewritten to correctly impose the plane stress state along with the viscoplastic flow. The viscoplastic formulation presented here considers the strain-rate hardening effects by means of a hardening law that are assumed to have terms depending on the strain rate, which removed can represent a Voce type hardening. The proposed verification tests were employed for the numerical verification of an in-house implementation of the so-called stress-projected procedure inside the finite element method context. Although the focus of this paper is on the stressprojected algorithms the examples presented here can be employed for the verification of other algorithms intended to impose the plane stress state in viscoplasticit

Comparison of ALE finite element method and adaptive smoothed finite element method for the numerical simulation of friction stir welding

In this paper, the material flow around the pin during friction stir welding (FSW) is simulated using a 2D plane\ud strain model. A pin rotates without translation in a disc with elasto-viscoplastic material properties and the outer boundary of\ud the disc is clamped. Two numerical methods are used to solve this problem and an analytical solution is derived. The analytical\ud model is complementary to validate the two numerical methods, i.e. the arbitrary Lagrangian-Eulerian (ALE) method and the\ud adaptive smoothed finite elements method (ASFEM)

Viscoplastic constitutive models for zero-thickness interface elements, formulation and applications

An energy-based work-softening visco-plastic model for zero-thickness interface elements has been developed as an extension of an existing elastic-perfectly-viscoplastic formulation. In the inviscid limit the model also collapses into a well-established fracture mechanics-based elasto-plastic model. The new model is verified satisfactorily for common loading cases at interfaces such as pure tension (mode I) opening, and shear-compression (mixed-mode) sliding, with results that in the long term match the predictions of the fracture mechanics inviscid model.Postprint (published version

Numerical modeling of strain rate hardening effects on viscoplastic behavior of metallic materials

The main goal of the present work is to provide a finite strain elasticviscoplastic framework to numerically account for strain, strain rate hardening, and viscous effects in cold deformation of metallic materials. The aim is to provide a simple and robust numerical framework capable of modeling the main macroscopic behavior associated with high strain rate plastic deformation of metals. In order to account for strain rate hardening effects at finite strains, the hardening rule involves a rate dependent saturation hardening, and it accounts for linear hardening prevailing at latter deformation stages. The numerical formulation, finite element implementation, and constitutive modeling capabilities are assessed by means of decremental strain rate testing and constant strain rate loading followed by stress relaxation. The numerical results have demonstrated the overall framework can be an efficient numerical tool for simulation of plastic deformation processes where strain rate history effects have to be accounted for

Viscoplastic constitutive models for zero-thickness interface elements, formulation and applications

An energy-based work-softening visco-plastic model for zero-thickness interface elements has been developed as an extension of an existing elastic-perfectly-viscoplastic formulation. In the inviscid limit the model also collapses into a well-established fracture mechanics-based elasto-plastic model. The new model is verified satisfactorily for common loading cases at interfaces such as pure tension (mode I) opening, and shear-compression (mixed-mode) sliding, with results that in the long term match the predictions of the fracture mechanics inviscid model

Experimental and mechanical characterizations of a lead free solder alloy for electronic devices

Electronic power modules devices are paramount components in the aeronautical,automotive and military applications. The solder layers are the most critical parts of the module and are usually subjected in their whole life to complex loading conditions. To improve the design task, realistic thermoelastoviscoplastic and lifetime prediction models which can describe efficiently the deformation-damage of the electrical device must be chosen carefully. Some of the most common behavior models are based on the separation between creep and plasticity deformations such as power law, Garofalo, Darveaux… So, to take into account the creep-plasticity interaction, the thermal cycling as well as the hardening-softening effects, unified viscoplastic models are increasingly being used to describe more efficiently the physical state of the material. We propose in this framework a survey of some unified viscoplastic models used in the electronic applications for the viscoplastic modeling of the solder as well as creep-fatigue life prediction rules. The models are used for the characterization of a SnAgCu solder and are briefly compared within tensile, creep data and stabilized responses

Implicit integration scheme for porous viscoplastic potential-based constitutive equations

This paper deals with a viscoplastic potential-based model allowing thermomechanical damage behavior modeling of porous materials. The model describes rate dependent effects, hardening, creep as well as defects coalescence and propagation. Kinematic and isotropic hardening effects are taken into account by a set of internal state variables. The integration and implementation of the model into the FE code using a fully implicit integration scheme is exposed. Finally, it 19s used to predict mechanical behaviour degradation of solder layers used in power electronic packaging. Stress-strain behaviour and the evolution of volumic fraction of voids for the material under cyclic loading are presented