An abstract inf-sup problem inspired by limit analysis in perfect plasticity and related applications

This paper is concerned with an abstract inf-sup problem generated by a bilinear Lagrangian and convex constraints. We study the conditions that guarantee no gap between the inf-sup and related sup-inf problems. The key assumption introduced in the paper generalizes the well-known Babuška–Brezzi condition. It is based on an inf-sup condition defined for convex cones in function spaces. We also apply a regularization method convenient for solving the inf-sup problem and derive a computable majorant of the critical (inf-sup) value, which can be used in a posteriori error analysis of numerical results. Results obtained for the abstract problem are applied to continuum mechanics. In particular, examples of limit load problems and similar ones arising in classical plasticity, gradient plasticity and delamination are introduced.

A constitutive model for hydromechanically coupled behavior of unsaturated soils with hydraulic hysteresis

There are several constitutive models developed for understanding coupled hydromechanical behavior of three phase medium of unsaturated soils as well as models for explaining hydraulic hysteresis in water retention. However, very few attempts that merge the two aspects of behavior are available. This study develops a one-way coupled model for understanding the hydromechanical behavior of unsaturated soils. In addition to the hysteresis between main drying and wetting retention curves, the model considers non-uniqueness of retention behavior resulting from void ratio changes due to compression under the stress application. As for the elastoplastic stress strain relationship of soil skeleton, the model is based on the formulation of classical plasticity relying on the critical state concept. Consequently, volumetric deformation due to wetting-drying cycles and its effect on elastoplastic behavior through simultaneously changing matric suction is modeled. Model results are calibrated with the results of isotropic compression stages of triaxial tests at both constant suction and constant water content conditions.

Assessment of Pohang Earthquake-Induced Liquefaction at Youngil-Man Port Using the UBCSAND2 Model

The practical constitutive model UBCSAND2, which combines two-mobilized planes—a maximum shear stress plane and a horizontal plane within a framework of classical plasticity approach—is used to incorporate shear-induced effects in both loading and unloading as well as principal stress rotation effects. UBCSAND2 was calibrated by capturing cyclic direct simple shear (CDSS) test results of Pohang sand, which was collected from liquefied paddy fields due to the 2017 Pohang earthquake (Mw = 5.4) in South Korea. The model procedure focuses on simple shear condition because it best simulates field conditions under earthquake loading. The calibrated UBCSAND2 model is then used to assess the liquefaction-induced damages that occurred at the quay wall and backfill layer in Youngil-man port near the epicenter of the Pohang earthquake. The numerical results show that liquefaction mostly occurred in silty sand layers, in which the excess pore pressure ratio reached almost one. The estimated displacements of the quay wall and the predicted settlement of reclaimed area obtained from the analysis were in good agreement with those obtained from field measurements.

Plastic Dissipation of the Fractional Plasticity using Modified Cam-Clay Yielding Function

ABSTRACTSoils usually exhibit state-dependent frictional behaviour that undergoes plastic volumetric deformation. To correctly capture such response under the framework of classical plasticity, a non-associated flow rule using additional plastic potential is inevitably needed. Recently, a novel fractional plasticity (FP) without using plastic potential has been developed, and successfully applied in modelling the state-dependent nonassociated behaviour of soils. However, the energy dissipation characteristics of FP has not been probed in depth. This note examines the plastic dissipation behaviour of FP, when modelling the constitutive behaviour of soils. It is found that the plastic dissipation of FP increases continuously with the shear strain. However, the rate of plastic dissipation depends on the initial material state in relation to the critical state line.

Prediction of Wrinkling of a Beverage Can Subjected to the Redrawing Process by J2 Deformation Theory

Wrinkling of beverage cans is one of the problems faced by can manufacturers and aluminum suppliers. The bottom of an aluminum can is wrinkled by compression during the forming process. In this study, to predict the occurrence of wrinkles during the redrawing process of AA3104 (t = 0.265 mm), which is the material used to fabricate aluminum cans, the classical plasticity J2 deformation theory (J2D) and flow theory (J2F) were considered. J2F considers only the deformation perpendicular to the yield locus, whereas J2D considers the deformation perpendicular to the yield locus and that tangential to the yield locus. Wrinkles are predicted using finite element (FE) analyses based on J2D and J2F, and the results are compared. J2F could not predict the number and amplitude of wrinkles. By contrast, the wrinkles predicted using J2D exhibited good agreement with sample data obtained for a real can. To find the difference between the results obtained using J2F and J2D, evolutions of stress path in a wrinkled element are compared. It was confirmed that compressive stress is more dominant in the J2D case than in the J2F case. Moreover, the measured effective strain of the element is small, under 0.04. In conclusion, J2D is more suitable for predicting the wrinkling behavior of aluminum cans than J2F. In addition, ANOVA and ANOM analysis are performed to evaluate the influence of the design parameters, namely friction coefficient, thickness, and outer profile angle, and the parameters are optimized to reduce wrinkles by combining the Taguchi method with FE simulation based on the J2D theory.

Return Mapping Algorithms (RMAs) for Two-Yield Surface Thermoviscoplastic Models Using the Consistent Tangent Operator

The return mapping algorithms (RMAs) presented here are designed for use with pressure-dependent thermoviscoplastic constitutive models involving irreversible effects associated with solid–solid phase transformations. During the volume solid–solid phase transformations occurring under mechanical loads, an “anomalous” plasticity, the so-called “TRansformation Induced Plasticity” (TRIP), is generated at much lower stress levels than those related to the yield stress of the material in the context of the classical plasticity. TRIP mechanisms are superimposed on the classical plasticity which is liable to occur in the case of metallic materials. Based on a non-standard generalized material framework, two different models are presented in which an “associative” plastic flow is introduced in the context of classical plasticity and a “non-associative” flow rule in the context of TRIP-like plasticity. In this paper, a complete algorithmic treatment of these two rate-dependent constitutive models is therefore proposed with the associated consistent tangent operator for dealing the quasi-surface irreversible solid–solid transformations which can appear in metal alloys during specific thermomechanical solicitations. The predictive abilities of the presented numerical procedure for modelling this kind of the irreversible solid–solid transformations involving two plasticity processes are tested and assessed by performing a two-dimensional finite-element analysis on some numerical examples.