Loading criterion in return-mapping for subloading surface model

While the subloading surface model seems most reasonable among a lot of elastoplastic constitutive models proposed in the past, there exists a mathematical incompleteness in the past formulations of this model. The mathematically exact formulation of this model would be provided in this paper, formulating a reasonable translation rule of the center of similarity of the normal-yield and the subloading surfaces.

The subloading surface model was formulated in the Chaps. 6– 11 within the frameworks of the finite hypoelastic-based plasticity in detail and of the infinitesimal hyperelastic-based plasticity (Sect. 6.9) in brief. Finite deformation and rotation cannot be described in the exact sense by these formulations. The multiplicative elastoplastic constitutive equation will be formulated for the subloading surface model with the translation of the elastic-core, although the multiplicative constitutive equation for the initial subloading surface model, in which the elastic-core is fixed in the back stress point, was formulated in an immature form by Hashiguchi and Yamakawa (2012). One must formulate the constitutive equation possessing the generality and the universality to be inherited eternally, while any unconventional model, i.e. cyclic plasticity model other than the subloading surface model has not been extended to the multiplicative finite strain theory. The exact formulation of the multiplicative finite strain theory based on the extended subloading surface model has been attained by Hashiguchi (2016a, b, c, d), which will be explained in detail in this chapter.

Shear band formation analysis in soils by the subloading surface model with tangential stress rate effect

The subloading surface model fulfills the mechanical requirements for constitutive equations, i.e. the continuity condition, the smoothness condition and the work rate stiffness relaxation and describes pertinently the Masing effect. The constitutive equation of soils is formulated by introducing the subloading surface model and formulating the evolutional rule of rotational hardening for the description of anisotropy. The applicability of the constitutive equation to the prediction of real soil deformation behaviour is verified by predicting monotonic and cyclic loading behaviour of sands under drained and undrained conditions and comparing them with test data. © 1998 John Wiley & Sons, Ltd.

TThe proposal and development of time integration algorithms in hyperelastic-based plasticity or hyperelastoplasticity, are consistently required due to complex issues such as objectivity. Through the multiplicative decomposition of the deformation gradient tensor, a local configuration known as the intermediate or plastic configuration is generated alongside the reference and the current configurations. Utilizing the intermediate configuration for time integrations eliminates the need to analyze the impact of rigid rotations in the current configuration. Moreover, as the Cauchy stress is derived from parameters in the intermediate configuration, there is no necessity to assess its objectivity. By employing the multiplicative decomposition of the gradient tensor of plastic deformation, equations for kinematic hardening can be derived, eliminating the need to verify objectivity. Therefore, in this article, the algorithm for the subloading surface model, based on the intermediate configuration, is derived by adapting the von Mises model. The rationale behind employing the von Mises model lies in its simplicity compared to the subloading surface model, along with its widespread usage. Additionally, in numerical implementation, the subloading surface model is more complex than the von Mises model. Building upon this, the problem of simple shear deformation with small and large elastic strains, incorporating isotropic, kinematic, and combined hardening in plasticity, has been investigated. The obtained results have been compared with the experimental data and findings from various references. The comparison between the results presented in this article and the available data indicates agreement, suggesting the viability of employing this model in practical applications.

The traditional elastoplastic constitutive equation, which is inde- pendent of the stress rate component tangential to the yield surface predicts an unrealistically stiff mechanical response for the nonproportional loading proc- ess in which the stress rate has a component tangential to the yield surface. In this article, the generalized constitutive equation is then formulated by incor- porating the inelastic strain rate due to the stress rate tangential to the subload- ing surface into the subloading surface model exhibiting a smooth elastic- plastic transition.

Prediction of deformation behaviors of sands by the subloading surface model : Proc International Workshop on Constitutive Equations for Granular Non-Cohesive Soils, Cleveland, 22–24 July 1987P293–306. Publ Rotterdam: A A Balkema, 1989

Finite Strain Elastoplastic Constitutive Equation Based on Subloading Surface Model

Constitutive equation of soils is proposed, which is capable of describing the inelastic stretching induced by the stress rate component tangential to the yield or loading surface for materials with an arbitrary smooth yield surface under a general loading process, based on the subloading surface model extended so as to describe the tangential stress rate effect. The basic characteristics are examined by the analysis of instantaneous shear moduli under undrained plane strain condition.

The multiplicative elastoplastic constitutive equation is formulated based on the extended subloading surface model with the translation of the elastic-core. It is to be the only unconventional elastoplasticty model extended to the multiplicative hyperelastic-based plasticity model which is capable of describing finite deformation/rotation exactly.

The deformation behavior of a structure under cyclic loading condition is simulated by using FEM analysis in which a cyclic plasticity model, so-called extended subloading surface model, is incorporated. The adopted cyclic plasticity model is categorized in the framework of the unconventional plasticity model premising that the interior of the yield surface is not a purely elastic domain. The developed FEM program does not include algorithms for both the yielding-judgment and the control of stress so as to lie on the yield surface, since the subloading surface model has the stress controlling function so that a stress approaches the yield surface automatically. In this study, several examples of FEM analysis on the cyclic deformation behaviors are presented to show the potential of the developed FEM program and an incorporated cyclic plasticity model.

The subloading surface model has been formulated and applied to the prediction of cyclic loading behavior of metals. However, the existing formulation of this model is limited to metals exhibiting only the cyclic hardening. In the present paper, the material functions prescribing the elastic-plastic transition are extended so as to describe the inverse and reloading behavior and the strain accumulation in cyclic loading more accurately for metals exhibiting not only the cyclic hardening but also the cyclic softening behavior. The experiments on the uniaxial cyclic loading of the seamless steel pipe P110 which exhibits the cyclic softening are performed for the mechanical ratcheting and the constant strain amplitudes. The simulations to the test data are performed by using the same set of material constants. Then, the validity of the extended model for the description of cyclic loading behavior of the seamless steel pipe is verified by comparisons with the test data.

Several researchers have reported that Bishop’s mean effective stress decreases in unsaturated soils under fully undrained cyclic loading conditions, and unsaturated soils are finally liquefied in a similar manner as saturated soils. This paper presents a series of simulations of such fully undrained cyclic loading on unsaturated soils using an elastoplastic model of the unsaturated soil. This model is formulated using the Bishop’s effective stress tensor incorporating the following concepts: the volumetric movement of the state boundary surface containing the normal consolidation line and the critical state line due to the variation in the degree of saturation, a soil water characteristic curve model considering the effect of specific volume and hysteresis, the subloading surface model, and Boyle’s law. Comparisons between the simulation results and the experimental ones show that the model agreed well with the unsaturated soil behavior under cyclic loading. Finally, the typical cyclic behavior of unsaturated soils under fully undrained conditions, such as the mechanism of liquefaction of unsaturated soils, the compression behavior, and an increase in the degree of saturation, are described through the proposed simulation results.

Ductility in metals includes the material’s capability to tolerate plastic deformations before partial or total degradation of its mechanical properties. Modelling this parameter is important in structure and component design because it can be used to estimate material failure under a generic multi-axial stress state. Previous work has attempted to provide accurate descriptions of the mechanical property degradation resulting from the formation, growth, and coalescence of microvoids in the medium. Experimentally, ductile damage is inherently linked with the accumulation of plastic strain; therefore, coupling damage and elastoplasticity is necessary for describing this phenomenon accurately. In this paper, we combine the approach proposed by Lemaitre with the features of an unconventional plasticity model, the extended subloading surface model, to predict material fatigue even for loading conditions below the yield stress.

Extension of the time-dependent subloading surface model by introducing of the static subloading surface