Strain-space Plasticity Research Articles

Elasto-plastic Damage Analysis Based on Strain-space Plasticity

Continuum Damage Mechanics (CDM) is an evolving area of Solid Mechanics. CDM has been found to have great potential. Most of the plastic damage models attempt to bring together the theories of plasticity and CDM. In this paper, the strain-space plasticity theory is implemented for elastic-plastic damage material model in the framework of non-linear finite element analysis. In the stress space plasticity models the yield surface, loading and unloading criteria, flow rule, and often hardening rules are defined in stress space. The research paper presents a set of systematic formulations for the theory of isotropic elasto-plastic ductile damage. Lemaitre's model is considered for the damage evolution growth. The plastic flow and damage flow are coupled within the potential function. In order to verify the formulations presented, numerical results are compared with the results available in literature.

On the constitutive relations for isotropic and transversely isotropic materials

In this work the strain and stress spaces constitutive relations for isotropic and transversely isotropic softening materials are developed. The loading surface is considered in the strain space and the normality rule; the stress relaxation is proportional to the gradient of the loading surface, is adopted. It is found that the strain space plasticity theory allows us to describe the hardening, perfectly plastic and softening materials more accurately. The validity of the strain space constitutive relation for transversely isotropic materials are confirmed by comparing with the experimental data for fiber reinforced composite materials. Some numerical examples in two and three dimensional elasto-plastic problems for various loading–unloading conditions are presented, and give a very good agreement with the existing results.

On postulates of plasticity in classical elastoplasticity

It is commonly known that Drucker’s postulate of plasticity in stress space is applicable to hardening materials only, but not to softening materials, and, on the other hand, that Ilyushin’s postulate of plasticity in strain space is applicable to both softening and hardening materials. Accordingly, it is usually thought that the latter would be less restrictive and hence more general than the former. In this work, we introduce the notions of standard elastoplastic stress and strain cycles, each starting at a point inside the yield surface and incorporating only one infinitesimal plastic strain increment. We show that these standard cycles always exist for a yield function depending continuously on stress and plastic strain history. By means of these standard cycles, we propose respective weakened forms of Drucker’s and Ilyushin’s postulates. These two weakened forms are less restrictive in two respects. One is that, unlike Drucker’s and Ilyushin’s postulates, they are not concerned with stress and strain cycles starting at points on the yield surface. The second is that they are formulated in terms of the rates of change of the net stress work and the stress work when the plastic strain increment incorporated tends to vanish. We demonstrate that either of the proposed weakened forms is adequate to result in the normality rule for the plastic strain rate and the convexity of the yield surface, as does either Drucker’s or Ilyushin’s postulate. These suggest that, in a less restrictive sense and hence in a broader scope, the two proposed weakened forms not only apply to both hardening and softening materials, but also ensure the same consequences.

A strain space nonlinear kinematic hardening/softening plasticity model

Abstract A strain space plasticity theory based on the nonlinear kinematic hardening and softening rule is developed in order to accommodate work-hardening, work-softening, and elastic-perfectly plastic materials with one set of constitutive equations, and to facilitate strain controlled calculations. A generalized hardening/softening parameter is proposed, and the potential of linking the parameter to micro-mechanical material changes is discussed. The theory is used to investigate work-softening materials numerically and highlights a need for additional experimental results in this area.

The equivalence of stress- and strain-based plasticity theories

Strain space plasticity theory has been advocated by a number of researchers as a viable alternative to its stress space counterpart. However, there appears to be a certain level of uncertainty about the equivalence of stress- and strain-based plasticity theories. This paper attempts to clarify some issues raised by Casey and Naghdi [2] concerning the equivalence of these two theories. By providing the alternative conjugate expressions for the loading criteria, it will be shown that the two formulations are indeed equivalent in substance and produce equivalent expressions for the plastic strain rate, provided that the material laws used are identical in both approaches. The use of the strain space formulation in many cases, for example, when dealing with strain-softening materials, is deemed to be convenient and therefore desirable. Nevertheless, it is not essential. The findings in this article exemplify the statement made by Drucker [4]: ‘The use of a strain space or a stress space is equally permissible, but may not be equally convenient for one purpose or the other.’

Strain-space plasticity model for the compressive hardening-softening behaviour of concrete

Concrete exhibits strong strain-softening behaviour in the post-failure range. To simulate the strains-oftening behaviour in concrete structures, numerous stress-space plasticity models have been proposed. Unfortunately, it is found that the application of the stress-space formulation of plasticity to concrete encounters difficulties in modelling the softening behaviour since it cannot explicitly give a clear distinction of loading, unloading and neutral loading. Strain-space formulation is therefore rational for further progress. Although several strain-space plasticity models are proposed, these models can simulate the strain-softening behaviour of concrete only under low confining pressure and they lack experimental verification since the available test data with softening behaviour are very limited. In this paper, a general form of strain-space plasticity formulations applied to strain-hardening-softening materials under both low and high confining pressure is developed. The strain-space formulation is presented by introducing the loading function as well as the plastic potential function, corresponding to those of Drucker-Prager type in the stress space. Two material parameters of the failure surface are determined from the test data on the compressive meridian. Experimental work is carried out to determine the model parameters. The model simulation is performed not only for the current experimental data but also for most of the available test data to demonstrate the capability of the model. It is found that the model can sufficiently predict the hardening as well as the softening behaviour of concrete under both low and high confining pressure.

Strain space plasticity model for cyclic mobility : Iai, S; Matsunaga, Y; Kameoka, T Soils FoundV32, N2, June 1992, P1–15

Strain space plasticity model for cyclic mobility : Iai, S; Matsunaga, Y; Kameoka, T Soils FoundV32, N2, June 1992, P1–15

Liquefaction analyses of sandy ground improved by sand compaction piles

The two-dimensional finite element program NUP2 of dynamic effective stress analysis is developed based on the two-phase mixture theory of Biot and the strain space plasticity theory of soil. The numerical analyses are performed to investigate the liquefaction behavior of sandy ground improved by the sand compaction piles. The good performance of the numerical procedure used here is proved by the comparison of numerical and experimental results. It is also demonstrated that the numerical results provide substantial information which aid in the understanding of the liquefaction mechanisms of improved soil ground. The results of numerical and experimental investigation show that there may exist unstable zones in the compacted area near the unimproved area and an optimum compaction width to resist liquefaction of the ground for design purposes.

Strain Space Plasticity Model for Cyclic Mobility

ABSTRACT The cyclic mobility model proposed in this paper is of a generalized plasticity—multiple mechanism type. The salient feature of the present approach is that the concept of the multiple mechanism, within the framework of plasticity theory defined in strain space, is used as a vehicle for decomposing the complex mechanism into a set of one dimensional mechanisms. The other feature is that the undrained stress path is idealized with the concept of liquefaction front, which is defined in the effective stress space as an envelope of stress points gradually approaching the failure line. Once coded into the finite element program, most of the existing models suffer from serious difficulty in the numerical solution process when effective stress path becomes very close to the failure line. A numerically robust approach is proposed in this paper by introducing a scheme for gradually enlarging scale of shear strain with progress of cyclic mobility.

Application of Strain Space Plasticity Theory to Surface Strain Gage Measurements

Taking strain as the independent variable, the strain space plasticity theory introduced by Naghdi and Trapp is applied to the problem of interpreting strain gage readings for load paths that involve inelastic deformation. Equations developed herein permit the straightforward decomposition of the total measured strain into elastic and plastic components. Further, the strain space formulation leads naturally to the prediction of stress components, both the strain decomposition and the stress calculation requiring information on uniaxial stress-strain behavior obtained from a simple tension test.

塑性理論によるコンクリートの載荷経路依存型圧縮軟化特性のモデル化

塑性理論によるコンクリートの載荷経路依存型圧縮軟化特性のモデル化

塑性理論によるコンクリートの圧縮軟化特性のモデル化

塑性理論によるコンクリートの圧縮軟化特性のモデル化

Strain-space plasticity formulation for hardening-softening materials with elastoplastic coupling : Han, D J; Chen, W F Int J Solids StructV22, N8, Aug 1986, P935–950

Strain-space plasticity formulation for hardening-softening materials with elastoplastic coupling : Han, D J; Chen, W F Int J Solids StructV22, N8, Aug 1986, P935–950

Strain-space plasticity formulation for hardening-softening materials with elastoplastic coupling

Engineering materials such as concretes, rocks and soils exhibit a strong strain-softening behavior in the post-failure range, showing a significant elastoplastic coupling for the degradation of elastic modulus with increasing plastic deformation. Stress-space formulation of plasticity based on Drucker’s stability postulate for these materials encounters difficulties in modeling the softening/elastoplastic coupling behavior; strain-space formulation is therefore necessary for further progress. In this article we first introduce a general form of strain-space plasticity formulation which is somewhat similar to that developed previously by Yoder and Iwan. To account for the elastoplastic coupling effect, the conventional plasticity theory is combined with the fracturing theory of Dougill to give a more general form of strain-space formulation. Attempt is then made to apply the general theory to model the softening behavior of a concrete element failed in a mixed crushing/cracking mode.

Strain-space plasticity analysis of fibrous composites

Abstract A strain-space formulation of plasticity theory for metal matrix fibrous composites is discussed. Specific results are obtained for a composite system in which the fibers are elastic until failure, while the matrix is of the Mises type, with kinematic hardening. The material model of the composite is based on the assumption that the fiber diameter is vanishingly small, and the fiber volume fraction is finite. Explicit expressions are obtained for instantaneous strain concentration factors in the phases, for the instantaneous overall stiffness, and for the overall loading surface and hardening rule during mechanical straining along a prescribed path.

Discussion: “On the Formulation of Strain-Space Plasticity with Multiple Loading Surfaces” (Yoder, P. J., and Iwan, W. D., 1981, ASME J. Appl. Mech., 48, pp. 773–778)

Discussion: “On the Formulation of Strain-Space Plasticity with Multiple Loading Surfaces” (Yoder, P. J., and Iwan, W. D., 1981, ASME J. Appl. Mech., 48, pp. 773–778)

Closure to “Discussion of ‘On the Formulation of Strain-Space Plasticity with Multiple Loading Surfaces’” (1982, ASME J. Appl. Mech., 49, p. 677)

Closure to “Discussion of ‘On the Formulation of Strain-Space Plasticity with Multiple Loading Surfaces’” (1982, ASME J. Appl. Mech., 49, p. 677)

Closure to “Discussion of ‘On the Formulation of Strain-Space Plasticity With Multiple Loading Surfaces’” (1982, ASME J. Appl. Mech., 49, pp. 460–461)

Closure to “Discussion of ‘On the Formulation of Strain-Space Plasticity With Multiple Loading Surfaces’” (1982, ASME J. Appl. Mech., 49, pp. 460–461)

Discussion: “On the Formulation of Strain-Space Plasticity With Multiple Loading Surfaces” (Yoder, P. S., and Iwan, W. D., 1981, ASME J. Appl. Mech., 48, pp. 773–778)

Discussion: “On the Formulation of Strain-Space Plasticity With Multiple Loading Surfaces” (Yoder, P. S., and Iwan, W. D., 1981, ASME J. Appl. Mech., 48, pp. 773–778)

On the Formulation of Strain-Space Plasticity With Multiple Loading Surfaces

An alternative formulation of plasticity is discussed in which strain rather than stress serves as the independent variable. The relationship of the formulation to traditional plasticity is examined for cases of both single and multiple loading surfaces. Conditions are given under which the stress and strain-space formulations are equivalent.