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1.
Deformation and rate theories of nonlocal plasticity are formulated. Constitutive equations are obtained for elasto-plastic solids extending Lévy-von Mises and Prandtl-Reuss theories to include nonlocal effects. Combined elastic-plastic constitutive equations are given. A nonlocal deformation theory is also presented. Thermodynamical restrictions are studied.  相似文献   

2.
The purpose of this article is to explore in details the theoretical and numerical aspects of the behavior of spatial trusses, undergoing large elastic and/or elastoplastic strains. Two nonlocal formulations are proposed in order to regularize the problem, avoiding the mesh dependence of the numerical response. The classical example of a simple bar in tension is chosen to explore the various features of the proposed models and to highlight the interplay between material and geometrical nonlinearity in the localization.Aknowledgement The financial support of FAPESP, a Brazilian research funding agency and of the italian miur, project prin 2003082105, are greatly appreciated.  相似文献   

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In virtue of their intrinsic integro-differential formulation of underlying physical behavior of materials, discontinuous computational methods are more beneficial over continuum-mechanics-based approaches for materials failure modeling and simulation. However, application of most discontinuous methods is limited to elastic/brittle materials, which is partially due to their formulations are based on force and displacement rather than stress and strain measures as are the cases for continuous approaches. In this article, we formulate a nonlocal maximum distortion energy criterion in the framework of a lattice particle model for modeling of elastoplastic materials. Similar to the maximum distortion energy criterion in continuum mechanics, the basic idea is to decompose the energy of a discrete material point into dilatational and distortional components, and plastic yielding of bonds associated with this material point is assumed to occur only when the distortional component reaches a critical value. However, the formulated yield criterion is nonlocal since the energy of a material point depends on the deformation of all the bonds associated with this material point. Formulation of equivalent strain hardening rules for the nonlocal yield model was also developed. Compared to theoretical and numerical solutions of several benchmark problems, the proposed formulation can accurately predict both the stress-strain curves and the deformation fields under monotonic loading and cyclic loading with different strain hardening cases.  相似文献   

5.
The paper addresses a certain nonlocal plasticity model, where the consistency condition may be rewritten from a Fredholm equation of the second kind into a second order differential equation. Hereby, a case of equivalence between a nonlocal model and a gradient model will be found.  相似文献   

6.
The simple microfluid theory of Eringen [1] is generalized to include nonlocal effects. The balance laws, jump conditions, and constitutive equations are obtained. The nonlocal intermolecular forces, energy and entropy are accounted for by nonlocal field residuals and functional constitutive equations of space type. The second law of thermodynamics is used to obtain specific forms of these residuals, constitutive equations and restrictions to be imposed. The linear theory is developed fully for the micromorphic and micropolar nonlocal fluids. The nonlocal effects are shown to include surface tension and surface stresses. Passage is made to material gradient theories.  相似文献   

7.
梯度依赖的混凝土弹塑性非局部损伤的本构模型   总被引:1,自引:0,他引:1  
以连续介质力学和不可逆热力学为基础,提出了新的混凝土弹塑性损伤本构模型.在该模型中采用了塑性应变εp、各向同性损伤标量D以及应变梯度(△)ε作为内变量,其中应变梯度反应了损伤的非局部性质,本模型是梯度依赖的非局部损伤模型,严格满足热力学的基本方程.应用梯度依赖弹塑性非局部损伤本构模型得出的结果比已有的混凝土损伤塑性模型更为合理.  相似文献   

8.
The nonlocal residual is a novel physical quantity introduced in the nonlocal field theory of mechanics. In this paper, the nonlocal residual and some related problems are discussed. Firstly, a representative theorem of nonlocal residual is proved, in which the relation between the nonlocal residual and the spatial distributed fluctuation of the interaction among microstructures in materials is established. The existence of nonlocal residuals of body force, body moment and energy is investigated in detail based on the objectivity of the balance equations. To meet the requirements in physics, an eigen-scale parameter is introduced into the nonlocal kernel. And the properties of nonlocal kernel are then discussed. Finally, the nonlocal hyperelastic constitutive equation is deduced through the representation of the nonlocal residual of energy. Results show that the nonlocality of hyperelastic constitutive equation comes directly from the interaction potential among microstructures within materials.  相似文献   

9.
A new solution approach, based on Tikhonov regularization on the Fredholm integral equations of the first kind, is proposed to find the approximate solutions of the strain softening problems. In this approach, the consistency condition is regularized with the Tikhonov stabilizers along with a regularization parameter, and the internal variable increments are solved from the resulting Euler's equations. It is shown that, as the regularization parameter is increased, the solutions converge to a unique one. A nonlocal yield condition and a nonlocal return mapping algorithm are proposed to carry out the integration of constitutive equations in the time and spatial domains. A global plastic dissipation principle is proposed to relax the classical local plastic dissipation postulate. Numerical examples show that the proposed approach leads to objective, mesh‐independent solutions of the softening‐induced localization problems. A comparison of the results from the proposed approach with those from the gradient‐dependent plasticity model shows that the two models give close solutions.  相似文献   

10.
The positive definiteness of strain energy in nonlocal elasticity is studied. It is shown that the strain energy of nonlocal elasticity with a continuous positive valued and monotone decreasing interaction kernel is not necessarily positive definite.  相似文献   

11.
On the kinematics of finite-deformation plasticity   总被引:1,自引:0,他引:1  
Summary A theory of finite deformation plasticity is developed which involves a multiplicative decomposition of the deformation gradient through the assumption that there exists a stress-free configuration which can be used to separate the elastic and plastic components of the response. By using the polar decomposition on the usual indeterminate elastic and plastic deformation tensors, two uniquely defined stress-free configurations can be identified. The structure of this theory is compared with that of a spatial theory involving the polar decomposition of the total deformation gradient. It is shown that for the special case of linear response between the stress and the elastic strain, the two theories are indistinguishable in terms of their stress responses.With 1 Figure  相似文献   

12.
Summary Making use of the Eringen-Kroener form of the nonlocal constitutive equations and the exponential Fourier transformation, a system of two coupled differential equations of the second order describing the equilibrium of the body is derived. By appeal to the Helmholtz representation, the system is reduced to a single differential equation of the fourth order for the Love function, reminding a Bessel type transform of the biharmonic equation. A solution of this equation is found, and inverse transforms of the stress components using the convolution theorem established. A recourse to the formula of de la Vallée Poussin shows that, in contrast to the classical result, the stress singularity at the point of application of a concentrated force fails to appear, though the stress concentration at that point is extremely high.  相似文献   

13.
After determining the nonlocal elastic moduli and the constitutive equations used, a brief review of the Kelvin problem in nonlocal setting is given. The Westergaard procedure of transition from the classical Kelvin problem to the classical Boussinesq problem is discussed, and applied to the nonlocal case using Fourier's exponential transformation. An example illustrating the application of the method to calculate the stress system in a nonlocal half-space is given.  相似文献   

14.
Propagation of Love waves in an isotropic homogeneous elastic medium is analyzed in the context of the linear theory of nonlocal continuum mechanics. The dispersion equation, obtained for the plane transverse horizontally polarized waves in an infinite space, is compared with the corresponding equation given by the atomic lattice dynamics in order to determine a nonlocal modulus. It is found that the lower bound for the speed of Love waves predicted by the nonlocal theory agrees better with the seismological observations of such waves than its counterpart furnished by the conventional theory.  相似文献   

15.
Summary. It is commonly known that Druckers postulate of plasticity in stress space is applicable to hardening materials only, but not to softening materials, and, on the other hand, that Ilyushins 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 Druckers and Ilyushins postulates. These two weakened forms are less restrictive in two respects. One is that, unlike Druckers and Ilyushins 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 Druckers or Ilyushins 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.  相似文献   

16.
Summary It is well-known that twisting of cylindrical specimens has shown that axial stress or strain are induced in constrained or unconstrained torsion respectively. During monotonic loading in torsion, the axial stress or axial strain do not change monotonically, but tensile/compressive or lengthening/shortening phenomena are observed. In this study, a two-component model to account phenomenologically for coexisting different textures of rate-independent and rate-dependent finite deformation plasticity is proposed to predict axial shortening/lengthening and tensile/compressive phenomena in torsion. Such predictions are compared with available experimental data as well as recent simulations based on crystal plasticity models. In most cases, the results are in reasonable agreement with both experiments and simulations.  相似文献   

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Summary In some cases the plastic stress-strain relations based on the so-called normality rule lead to an unsatisfactory agreement with experimental results. This is particularly true in bifurcation problems or more generally in problems with non-proportional loading paths. Within the frame of a phenomenological theory of non-isothermic large deformations it is shown how plastic stress-strain relations can be modified in order to improve the agreement with the real material behaviour.With 6 Figures  相似文献   

20.
The coupling of elasto-plasticity and damage is still the subject of many papers, namely in the construction of evolution laws for internal parameters. In this paper we propose to partly overcome some difficulties by using the only basic fact that a plastic-damaged body is made up of two physical constituents, namely the matrix material and the micro-defects. The elasto-plastic matrix material is the resisting skeleton connecting the elements of the body and the micro-defects bring their own contributions to reversible and irreversible strains. Naturally strong couplings exist between the stress states of the body and the matrix material. These considerations will lead to generalisations and new formulations of the so-called equivalence principles and a new equivalence principle will be proposed. Finally, concerning the irreversible strains due to both plasticity of the matrix and growing of micro-defects, we will prove that yield conditions must be used simultaneously on the body as well as on the matrix, leading to some non-smooth resultant yield-damage surface. The modified Gurson model for porous material is then analysed in order to illustrate this last point. In this paper, large strains are considered, but time-dependant plasticity and thermal effects are excluded.  相似文献   

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