Multiplicative Elastoplasticity: Subloading Finite Strain Theory

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 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 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.

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.

Views on multiplicative elastoplasticity and the continuum theory of dislocations

On theory and numerics of large viscoplastic deformation

Finite Strain Elastoplastic Constitutive Equation Based on Subloading Surface Model

Cyclic mean stress relaxation behaviour of P91 steel: Experiments and constitutive modeling

The aim of the present paper is to propose a phenomenological thermodynamically consistent 3D model for shape memory alloys (SMA) in the finite strain range. In particular, a model able to predict the main features of SMA materials, such as the superelastic and the shape‐memory effects, is proposed. The model is based on the assumption of the local multiplicative split of the deformation gradient into an elastic and a phase transformation part. The governing state and evolutive equations are written in the undeformed configuration. The material parameters of the model are characterized by a clear physical meaning so that they can be determined by simple experimental tests. The finite deformation SMA model is also reformulated in the framework of small strain, linearizing the strain and stress measures in order to obtain a consistent constitutive model preserving the nonlinear material response. A robust algorithm is adopted in order to integrate the nonlinear evolutive equations; 2D and 3D finite elements are implemented in a numerical code considering finite and small deformations. Some numerical applications are carried out showing the performances of the proposed model and the developed numerical procedure to describe the superelastic and the shape‐memory effects of SMA devices. Comparisons of different results obtained by the small and finite strain formulations are reported. Copyright © 2009 John Wiley & Sons, Ltd.

This paper deals with the development of a cyclic plasticity model suitable for predicting the strain range-dependent behavior of austenitic steels. The proposed cyclic plasticity model uses the virtual back-stress variable corresponding to a cyclically-stable material under strain control. This new internal variable is defined by means of a memory surface introduced in the stress space. The linear isotropic hardening rule is also superposed. First, the proposed model was validated on experimental data published for the SS304 material (Kang et al., Constitutive modeling of strain range dependent cyclic hardening. Int J Plast 19 (2003) 1801–1819). Subsequently, the proposed cyclic plasticity model was applied to our own experimental data from uniaxial tests realized on 08Ch18N10T at room temperature. The new cyclic plasticity model can be calibrated by the relatively simple fitting procedure that is described in the paper. A comparison between the results of a numerical simulation and the results of real experiments demonstrates the robustness of the proposed approach.

The ability of the constitutive model to simulate the ratcheting behavior of metastable austenitic stainless steel S30408 is significant to ensure the safety of the liquefied natural gas (LNG) semi-trailer tanks in the lightweight process of the inner containers. This is because the lightweight inner vessels often encounter cyclic stresses due to the road inertia loads together with high mean stresses due to internal pressures. In this study, we performed cryogenic uniaxial tension experiments and a series of ratcheting experiments to investigate the cyclic plasticity behavior of the metastable austenitic stainless steel S30408. Based on the Ohno-Wang II model, we proposed a new cyclic plasticity constitutive model with martensitic transformation, which relates the content of deformation-induced martensite with isotropic hardening and kinematic hardening. The ratcheting behaviors of S30408 were first simulated by the proposed model with the incremental loading method using MATLAB. The results showed that the model could reasonably predict the ratcheting behavior of S30408, and the evolution law of martensite content could well predict the content of deformation-induced martensite. Under the assumption of the von Mises yield criterion and normal plasticity flow rule, we developed a numerical algorithm of plastic strain with the proposed model to implement the finite element calculation of the model. Internal iteration in the numerical algorithm was implemented with the Euler backward method, which calculated the trial strain for each equilibrium iteration using the consistent tangent matrix. With a user subroutine, the proposed model was programmed into ANSYS for a user - executable version. By simulating the uniaxial ratcheting of a S30408 round bar, we found that the calculated results were in good agreement with the experimental results, which promises further applications in the design of structures, such as LNG semi-trailer tanks.

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

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

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.

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.