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1.
A finite element analysis model for material and geometrical non-linearities due to large plastic deformations of ductile
materials is presented using the continuum damage mechanics approach. To overcome limitations of the conventional plastic
analysis, a fourth-order tensor damage, defined in Part I of this paper to represent the stiffness degradation in the finite
strain regime, is incorporated. General forms of an updated Lagrangian (U.L.) finite element procedure are formulated to solve
the governing equations of the coupled elastic–plastic-damage analysis, and a computer program is developed for two-dimensional
plane stress/strain problems. A numerical algorithm to treat the anisotropic damage is proposed in addition to the non-linear
incremental solution algorithm of the U.L. formulation. Selected examples, compared with published results, show the validity
of the presented finite element approach. Finally, the necking phenomenon of a plate with a hole is studied to explore plastic
damage in large strain deformations.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
2.
M. H. B. M. Shariff 《Journal of Engineering Mathematics》2006,56(4):415-435
The Mullins effect in rubber-like materials is inherently anisotropic. However, most constitutive models developed in the
past are isotropic. These models cannot describe the anisotropic stress-softening effect, often called the Mullins effect.
In this paper a phenomenological three-dimensional anisotropic model for the Mullins effect in incompressible rubber-like
materials is developed. The terms, damage function and damage point, are introduced to facilitate the analysis of anisotropic
stress softening in rubber-like materials. A material parametric energy function which depends on the right stretch tensor
and written explicitly in terms of principal stretches and directions is postulated. The material parameters in the energy
function are symmetric second-order damage and shear-history tensors. A class of energy functions and a specific form for
the constitutive equation are proposed which appear to simplify both the analysis of the three-dimensional model and the calculation
of material constants from experimental data. The behaviour of tensional and compressive ground-state Young’s moduli in uniaxial
deformations is discussed. To further justify our model we show that the proposed model produces a transversely anisotropic
non-virgin material in a stress-free state after a simple tension deformation. The proposed anisotropic theory is applied
to several types of homogenous deformations and the theoretical results obtained are consistent with expected behaviour and
compare well with several experimental data. 相似文献
3.
Alok
Negi Sachin Kumar Leong Hien Poh 《International journal for numerical methods in engineering》2020,121(18):4003-4027
This article presents a localizing gradient damage model with evolving micromorphic stress-based anisotropic nonlocal interactions. The objective is to model mesh independent fracture behavior of quasi-brittle materials, and to avoid the issues associated with the existing gradient-enhanced damage models. In the proposed model, an evolving anisotropic nonlocal interaction domain governs the spatial diffusive behavior, which helps to maintain a localized damage bandwidth during the final stages of loading. The anisotropy in nonlocal interactions is captured through an anisotropic gradient tensor, which defines the orientation of the diffusive interaction domain based on the principal stresses at a given material point. In this article, a smooth micromorphic stress tensor is utilized for the determination of principal stress states, to enforce a properly oriented interaction across the bandwidth of the damage process zone throughout the loading process. The proposed approach also enables the usage of low order finite elements without any oscillatory micromorphic or nonlocal equivalent strain response in the later stages of deformation. The accuracy and performance of the proposed model are demonstrated numerically in plane strain/stress for mode-I, mode-II, and mixed-mode loading conditions. 相似文献
4.
Feng Lu Zhang Guang Zhang Ke-shi J. Q. Xu Yu Hai-dong 《International journal for numerical methods in engineering》2004,61(3):406-432
Based on the concept of continuum damage mechanics, an anisotropic damage model for single crystals under the theory of crystal plasticity is presented. Damage and inelastic deformations are incorporated in the proposed model which is developed within the framework of thermodynamics with internal state variables. The dependence of the plastic anisotropy on the damage evolution has been considered. The anisotropic damage is characterized kinematically here through a second-order damage tensor which is physically based. The proposed model can successfully describe the interaction between the evolution of micro-structure of single crystals such as lattice orientation and the hardness development of each slip system and the process of material degradation. The Newton–Raphson iterative scheme is used to integrate the constitutive equations that work directly with the evolution equations for the elastic deformation gradient. The consistent algorithmic tangent stiffness for the present algorithm is formulated. The prescribed algorithm together with the consistent algorithmic tangent stiffness has been implemented into the ABAQUS finite element code by using user subroutine. Using the loading processes with homogeneous deformations and simulation of the classical tensile test of a notched bar illustrate the basic aspects of the model described. Numerical simulations show the validation and performance of the present model and algorithm. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
5.
A transversely isotropic continuum elasto-viscoplasticity model is formulated to capture the tensile and creep behaviors of a directionally solidified (DS) nickel-base superalloy. A fourth-order tensor is introduced to model material anisotropy. The Kachanov damage evolution equation is coupled with stress tensor to improve capability of modeling creep deformation. This model is implemented as an ABAQUS user material (UMAT) subroutine using a self-adaptive explicit integration scheme. A grouping optimization strategy is employed to identify the material parameters by fitting experimental curves of isothermal tension and creep loading at high temperature. Failure mechanisms are investigated by observing the fracture morphology by means of Scanning Electron Microscope (SEM) with the Energy Dispersive X-ray Spectrometer (EDXS). The results obtained showed that Chaboche constitutive model coupled with anisotropy and creep damage was able to characterize the rate-dependent anisotropic tensile and creep behaviors of DS superalloy and the simulation results agreed well with the experimental data. The tensile fracture surface of DS superalloy mainly contained a mixture of large cleavage planes and small amount of dimples. Meanwhile, the creep fracture mechanism of DS superalloy at 760 and 850 °C was transgranular fracture induced by the dimple accumulation. The morphology of the dimples and non-metallic inclusions at 760 °C was different from that at 850 °C. 相似文献
6.
Flavio V. Souza David H. Allen 《International journal for numerical methods in engineering》2010,82(4):464-504
Multiscale computational techniques play a major role in solving problems related to viscoelastic composites due to the complexities inherent to these materials. In this paper, a numerical procedure for multiscale modeling of impact on heterogeneous viscoelastic solids containing evolving microcracks is proposed in which the (global scale) homogenized viscoelastic incremental constitutive equations have the same form as the local‐scale viscoelastic incremental constitutive equations, but the homogenized tangent constitutive tensor and the homogenized incremental history‐dependent stress tensor at the global scale depend on the amount of damage accumulated at the local scale. Furthermore, the developed technique allows the computation of the full anisotropic incremental constitutive tensor of viscoelastic solids containing evolving cracks (and other kinds of heterogeneities) by solving the micromechanical problem only once at each material point and each time step. The procedure is basically developed by relating the local‐scale displacement field to the global‐scale strain tensor and using first‐order homogenization techniques. The finite element formulation is developed and some example problems are presented in order to verify the approach and demonstrate the model capabilities. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
7.
《Mechanics of materials : an international journal》1988,7(3):231-244
An anisotropic damage model for concrete is developed within the general framework of the internal variable theory of thermodynamics. The rate of change of the compliance tensor is described in terms of kinetic relations involving a damage parameter whose increment is governed by the consistency equation associated with a pressure-dependent damage surface in stress space. The use of the compliance tensor implies that damage is reflected through a fourth-order tensor. Dilatation is obtained as a consequence of damage, and permanent deformation due to damage is addressed via a simple evolution equation. The theory is capable of accommodating the anisotropy induced by microcracking and is very suitable for computer implementation. 相似文献
8.
Two continuous field variables, called as continuity tensor and damage variable tensor, are used to describe the anisotropic responses of an elastic-brittle material under transverse impact load. Based on the continuum damage mechanics, anisotropic damage constitutive equations in both full and incremental forms are proposed here. The expressions of effective elastic module tensor, damage variable tensor and damage propagation force tensor are further derived, and the methods for determining the tensors are explained in detail. An example of strain and damage response of a fiber reinforced composite laminated plate under transverse impact load is employed to demonstrate the application of this theory. In the example, the damage variable coupled with geometric large deformation of laminated plate is also considered. The calculating results illustrate the influence of damage on strain field in the impacted laminated plate. 相似文献
9.
In this work, a meshfree method is used to simulate thermo-mechanical ductile fracture under finite deformation. A Galerkin meshfree formulation incorporating the Johnson-Cook damage model is implemented in numerical computations. We are interested in the simulation of thermo-mechanical effects on ductile fracture under large scale yielding. A rate form adiabatic split is proposed in the constitutive update. Meshfree techniques, such as the visibility criterion, are used to modify the particle connectivity based on evolving crack surface morphology. The numerical results have shown that the proposed meshfree algorithm works well, the meshfree crack adaptivity and re-interpolation procedure is versatile in numerical simulations, and it enables us to predict thermo-mechanical effects on ductile fracture. 相似文献
10.
Summary. Conditions for adaptation (shakedown) of structures of elastic plastic materials with anisotropic damage and strain hardening as subjected to cyclic loading are in question. The nature of damage is assumed ductile, so that the
damage process ceases along with the cessation of plastic deformation process. The consideration is based on a material model
of classical type. The demand of thermodynamical admissibility of deformation processes results in the conclusion: the quadratic
form σ : ˙L : σ has to be positive where L denotes the current value of the elastic compliance tensor. This inequality makes it possible to show that the rate of plastic
deformation tensor tends to zero, and the total plastic dissipation is bounded, if the classical Melan condition of shakedown
holds for the initial state of the material.
Received February 15, 2002; revised January 24, 2003
Published online: June 12, 2003
This research was implemented due to support from the Israeli Ministry of Science and the Hebrew University of Jerusalem. 相似文献
11.
Applications of tensor functions to the formulation of constitutive equations involving damage and initial anisotropy 总被引:3,自引:0,他引:3
Josef Betten 《Engineering Fracture Mechanics》1986,25(5-6):573-584
In this paper some results of the tensor function theory are applied to the formulation of constitutive equations of isotropic and anisotropic materials in the secondary and tertiary creep stage. The creep process, in its tertiary phase, is characterized by a damage tensor. Because of its microscopic nature, damage has, in general, an anisotropic character even in cases where the material was originally isotropic, i.e. isotropic in its virgin state. Fissure orientation and length cause anisotropic macroscopic behaviour. In the first part of the paper some possible ways of representing constitutive equations involving (initial) anisotropy of the material (e.g. from rolling) and involving anisotropic creep-damage are dealt with. The formulations of such equations are based upon theorems concerning tensor-valued functions. Furthermore, some simplified constitutive equations for more practical use are discussed. The main problem of this part is: to find an irreducible set of tensor generators. Besides the problem of finding such tensor generators it is very important to determine the scalar coefficients in constitutive equations as functions of the invariants and experimental data. The second part of the paper is concerned with the determination of the scalar functions. This can be done by using tensorial interpolation methods as pointed out in detail. 相似文献
12.
An incremental form of anisotropic damage constitutive equation is proposed both for brittle and ductile materials. Based on the concept of irreversible thermodynamics that damage processes are history independent coupled with irreversible energy dissipation, two types of definition for damage representation are established, known as damage tensor D and damage strain tensor d, to describe constitutive responses of damaged materials. A state variable coupled with damage and other observable state variables, i.e. d, is formulated separately from other internal variables and defined as an equivalent damage variable. A constitutive relation due to damage is finally formulated by introducing damage flow potential function employing the theory of irreducible integrity bases. A clear physical representation based on theoretical foundations and rigorous mathematical arguments of the conventional damage models defined in terms of damage effect tensor M(D) is also elucidated. Validity of the proposed model is verified by comparing with the formulations of conventional damage effect tensor. A plastic potential function coupled with damage is also introduced by employing the anisotropic plastic flow theory, so that the proposed damage model can be applied to characterize a wide range of damage problems of practical engineering interest. 相似文献
13.
A model for continuous damage combined with viscoelasticity is proposed. The starting point is the formulation connecting the elastic properties to the tensor of damage variables. A hardening law associated with the damage process is identified from available experimental information and the rate-type constitutive equations are derived. This elastic damage formulation is used to formulate an internal variable approximation to viscoelastic damage in the form of a non-linear Kelvin chain. Elastic and viscoelastic equations are implemented into a finite element procedure. The code is verified by comparison with closed-form solutions in simplified configurations, and validated by fitting results of experimental creep tests. 相似文献
14.
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16.
A unified damage factor model for ductile fracture of steels with different void growth and shrinkage rates
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C. Li Z. Zhou Y. Zhu L. Lu 《Fatigue & Fracture of Engineering Materials & Structures》2018,41(5):1132-1145
Micromechanical fracture modelling is an effective method to predict ductile fracture in steel structures. This paper aims to establish a simplified and general fracture model for various loading conditions, which is convenient to calculate the instantaneous damage index. With the concept of the ductile damage factor, a unified ductile damage factor model considering the difference of rates between void growth and shrinkage has been proposed. Based on experiment results and finite element analysis, the model parameters for Q235B Chinese structural steel were calibrated. The ductile damage factor and equivalent plastic strain at fracture initiation were investigated. Comparison among the proposed model, experimental results, and the cyclic void growth model demonstrated the effectiveness and accuracy of the proposed model. A parametric study was conducted to investigate the influence of cyclic constitutive parameters on the accuracy of fracture prediction. The predicted results are acceptable while reducing those calibrated cyclic constitutive parameters by 20%. 相似文献
17.
损伤作为一种缺陷,宏观上通常是在Euclid空间中通过虚拟构形的方式,以连续分布的损伤变量加以描述。但如果描述更复杂的缺陷,处理变形非协调性问题,仅停留在Euclid空间中是不够的。同时,针对工程中不同材料以及同种材料的不同损伤机制,目前尚未建立一个统一的损伤模型。根据Euclid空间中的四阶损伤变量张量,定义了处于自然状态中的损伤变形体在Riemann空间中的三阶拟塑性张量、四阶异物张量,并用其描述损伤缺陷。并给出Riemann空间中异物张量所满足的连续性方程。从而建立了损伤缺陷与Riemann空间的对应关系,以Riemann空间中Bianchi恒等式刻划损伤变形体的非协调性。使得可以在Riemann这样一个弯曲空间中讨论损伤所引起的材料力学性能的劣化。最后给出一个各向异性损伤的算例。 相似文献
18.
A nonlinear cyclic plasticity damage model for ductile metals, which is able to take large deformation effects into consideration, has been developed using a new damage dissipation potential formulation in order to predict the cyclic inelastic behavior of steel bridge piers. The cyclic constitutive equations that employ the combined isotropic–kinematic hardening rule for plastic deformation is incorporated into the damage mechanics in conjunction with the large strain formulation. The damage growth law is based on the experimental observations that the evolution of microvoids results in nonlinear damage accumulation with plastic deformation. The damage model parameters and the procedure for their identification are presented. The proposed model has been validated and successfully applied to thin-walled steel bridge tubular columns subjected to alternating lateral displacements to evaluate the seismic performance. 相似文献
19.
A near-tip plane strain finite element analysis of a crack terminating at and normal to the interface in a laminate consisting
of alternate brittle and ductile layers is conducted under mode-I loading. The studies are carried out for a system representing
steel/alumina composite laminate. The Gurson constitutive model, which accounts for the ductile failure mechanisms of microvoid
nucleation, growth and coalescence, is employed within the framework of small deformation plasticity theory. Evolution of
plastic zone and damage in the ductile layer is monitored with increasing load. High plastic strain localization and microvoid
damage accumulation are found to occur along the brittle/ductile interface at the crack-tip. Fracture initiation in the ductile
phase is predicted and the conditions for crack renucleation in the brittle layer ahead of the crack are established for the
system under consideration. Ductile fracture initiation has been found to occur before plasticity spreads in multiple ductile
layers. Effects of material mismatch and yield strength on the plastic zone evolution are briefly discussed.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
20.
John A. Nairn Chad C. Hammerquist Yamina E. Aimene 《International journal for numerical methods in engineering》2017,112(12):1848-1868
This paper describes implementation of anisotropic damage mechanics in the material point method. The approach was based on previously proposed, fourth‐rank anisotropic damage tenors. For implementation, it was convenient to recast the stress update using a new damage strain partitioning tensor. This new tensor simplifies numerical implementation (a detailed algorithm is provided) and clarifies the connection between cracking strain and an implied physical crack with crack opening displacements. By using 2 softening laws and 3 damage parameters corresponding to 1 normal and 2 shear cracking strains, damage evolution can be directly connected to mixed tensile and shear fracture mechanics. Several examples illustrate interesting properties of robust anisotropic damage mechanics such as modeling of necking, multiple cracking in coatings, and compression failure. Direct comparisons between explicit crack modeling and damage mechanics in the same material point method code show that damage mechanics can quantitatively reproduce many features of explicit crack modeling. A caveat is that strengths and energies assigned to damage mechanics materials must be changed from measured material properties to apparent properties before damage mechanics can agree with fracture mechanics. 相似文献