复合材料层合板阶梯形挖补胶接修理渐进损伤分析

建立了复合材料层合板阶梯形挖补胶接修理构型的渐进损伤分析三维有限元模型, 同时考虑了复合材料母板、 补片和胶层的损伤扩展以及它们之间的相互影响。层合板采用含正交各向异性损伤的连续介质损伤力学(CDM)本构方程进行描述, 材料积分点处的损伤状态采用二阶张量形式的内部状态变量表征。胶层采用含各向同性损伤的CDM本构方程进行描述, 材料积分点处的损伤状态采用常数形式的损伤变量表示。计算结果与试验数据符合较好, 说明该模型可较好预测挖补胶接修理的复合材料层合板拉伸强度及其失效模式。     

A finite element approach to anisotropic damage of ductile materials in large deformations Part I: an anisotropic ductile elastic-plastic-damage model

During past decades, many material models using the continuum damage mechanics (CDM) approach have been proposed successfully in the small deformation regime to describe inelastic behaviors and fracturing phenomena of a material. For ductile materials, large deformation takes place at the level of damage appearance. Damage is anisotropic in nature. In this paper, the ductile damage at finite deformations is modeled as an anisotropic tensor quantity. Then, a fourth-order symmetric stress correction tensor is proposed for computationally efficient and easy implementation in the finite element formulations. Consequently, an explicit form of the fourth-order constitutive equations of the proposed elastic-plastic-damage model is derived. Both isotropic and kinematic hardening effects are included in the formulation. The new constitutive model can predict not only the elastic-plastic behaviors, but also the sequential variations of ductile materials. An evaluation of the constitutive and damage evolution equations is presented. This revised version was published online in August 2006 with corrections to the Cover Date.     

On the numerical prediction of the ductile fracture in metal forming

In this paper, fully coupled constitutive equations accounting for combined isotropic and kinematic hardening as well as the isotropic ductile damage are implemented into the general purpose finite element code for metal forming simulation. The associated numerical aspects concerning both the local integration of the coupled constitutive equations as well as the global (equilibrium) integration schemes are presented. Various 2D and 3D examples are given in order to show the capability of the proposed numerical methodology to predict the ductile fracture initiation and growth during metal forming processes.     

Applications of tensor functions to the formulation of constitutive equations involving damage and initial anisotropy

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.     

Large strain constitutive modelling and computation for isotropic,creep elastoplastic damage solids

A three-dimensional fully coupled creep elastoplastic damage model at finite strain for isotropic non-linear material is developed. The model is based on the thermodynamics of an irreversible process and the internal state variable theory. A hyperelastic form of stress–strain constitutive relation in conjunction with the multiplicative decomposition of the deformation gradient into elastic and inelastic parts is employed. The pressure-dependent plasticity with strain hardening and the damage model with two damage internal variables are particularly considered. The rounding of stress–strain curves appearing in cycling loading is reproduced by introduction of the creep mechanism into the model. A numerical integration procedure for the coupled constitutive equations with three hierarchical phases is proposed. A consistent tangent matrix with consideration of the fully coupled effects at finite strain is derived. Numerical examples are tested to demonstrate the capability and performance of the present model at large strain.     

Simulation of strain localization with gradient enhanced damage models

The incorporation of higher order strain gradients into the constitutive equations of continuum damage mechanics is presented. Thereby, not only scalar-valued isotropic damage models but also anisotropic damage models allowing for directional dependent stiffness degradation are elaborated. An elegant possibility of describing anisotropic material behavior based on the microplane theory is demonstrated. Its conceptual simplicity originates from the idea of modeling the material behavior through uniaxial stress–strain laws on several individual material planes. For each plane individual damage loading functions are introduced allowing for different failure modes. In order to account for long ranging microstructural mechanisms, second-order gradients of the strains are incorporated in each of these damage loading functions. The overall response can be determined by an integration of the resulting microplane laws over the solid angle. The features of gradient enhanced continuum damage are demonstrated by means of several selected examples.     

Energy Version of the Theory of Creep of Materials with Different Resistance to Tension and Compression

We propose an energy version of the theory of creep for initially isotropic materials containing parallel plane microcracks and deduce constitutive equations of creep and the kinetic equation of accumulation of damage. We consider basic experiments aimed at the determination of material constants according to the proposed theory. The theoretical results are compared with the experimental data obtained for a light alloy with different resistance to tension and compression.     

Computational applications of a coupled plasticity-damage constitutive model for simulating plain concrete fracture

A coupled plasticity-damage model for plain concrete is presented in this paper. Based on continuum damage mechanics (CDM), an isotropic and anisotropic damage model coupled with a plasticity model is proposed in order to effectively predict and simulate plain concrete fracture. Two different damage evolution laws for both tension and compression are formulated for a more accurate prediction of the plain concrete behavior. In order to derive the constitutive equations and for the easiness in the numerical implementation, in the CDM framework the strain equivalence hypothesis is adopted such that the strain in the effective (undamaged) configuration is equivalent to the strain in the nominal (damaged) configuration. The proposed constitutive model has been shown to satisfy the thermodynamics requirements. Detailed numerical algorithms are developed for the finite element implementation of the proposed coupled plasticity-damage model. The numerical algorithm is coded using the user subroutine UMAT and then implemented in the commercial finite element analysis program Abaqus. Special emphasis is placed on identifying the plasticity and damage model material parameters from loading-unloading uniaxial test results. The overall performance of the proposed model is verified by comparing the model predictions to various experimental data, such as monotonic uniaxial tension and compression tests, monotonic biaxial compression test, loading-unloading uniaxial tensile and compressive tests, and mixed-mode fracture tests.     

Numerical integration on the sphere and its effect on the material symmetry of constitutive equations—A comparative study

In the present paper, we consider a class of constitutive models based on numerical integration on the unit sphere. The directional behaviour of the quadrature schemes and its effect on the symmetry properties of these constitutive models are studied by subjecting the set of integration points on the sphere to arbitrary rigid rotations. We investigate a number of recently proposed integration schemes in application to a full network model of rubber elasticity and to an exponential model for soft tissues. In order to assess and compare these schemes, statistical methods are presented and applied. The analysis discloses a number of integration schemes that offer a good compromise between the numerical error and the number of integration points. However, as a general result it turns out that numerical integration is prone to introduce strong anisotropy into originally isotropic constitutive equations, in particular, for highly non‐linear integrand functions. The consequences for application of the investigated class of constitutive models in finite element calculations are highlighted in a benchmark‐like numerical example. Copyright © 2009 John Wiley & Sons, Ltd.     

On simple constitutive restrictions for transversely isotropic nonlinearly elastic materials and isotropic magneto-sensitive elastomers

The aim of this paper is to extend the analysis of constitutive restrictions proposed for isotropic nonlinearly elastic materials to transversely isotropic elastic solids and isotropic magneto-sensitive elastomers. These two models are considered because their more general constitutive equations, which are given as strain-energy functions depending on certain invariants, show a similar formulation. The restrictions imposed on the constitutive relations are based on different physically admissible behaviors and given in terms of inequalities referred to simply as constitutive inequalities. The general considerations studied are used to illustrate the constitutive structure of some examples.     

A nonlinear CDM model for ductile failure analysis of steel bridge columns under cyclic loading

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.     

Finite deformation plasticity and viscoplasticity laws exhibiting nonlinear hardening rules

 This paper deals with plasticity and viscoplasticity laws exhibiting nonlinear kinematic hardening as well as nonlinear isotropic hardening rules. In Tsakmakis (1996a, b) a constitutive theory has been formulated within the framework of finite deformations, which is based on the concept of so-called dual variables and associated time derivatives. Within two families of dual variables, two different formulations have been proposed for kinematic hardening, referred to as Models 1 and 2. In particular, rigid plastic deformations without isotropic hardening have been considered. In the present paper, the constitutive theory of Tsakmakis (1996a, b) is appropriately extended to take into account isotropic hardening as well as elastic deformations. Care is taken that the evolution equations governing the hardening response fulfill the intrinsic dissipation inequality in every admissible process. For the case of small elastic strains combined with a simplification concerning kinematic hardening, to be explained in the paper, an efficient, implicit time-integration algorithm is presented. The algorithm is developed with a view to implementation in the ABAQUS Finite Element code. Also, explicit formulas for the consistent tangent modulus are derived. Received 22 September 1999     

An approach to finite static axially symmetric deformation of a hyperelastic membrane

Summary A simple approach to the problem of finite quasi-static axially symmetric deformation of an isotropic incompressible hyperelastic membrane is presented. Lagrangian type equilibrium equations, expressed in terms of the Biot stresses, are used along with constitutive relations expressing the principal components of Biot stress in terms of the principal stretches. Numerical results, obtained from the application of a finite element method to the governing equilibrium equations and constitutive relations, are presented for two problems, and for two different strain energy functions. It is shown how the proposed equilibrium equations can be obtained from a variational principle, and the variational principle is also used to obtain approximate solutions.     

Multiaxial creep–fatigue under anisothermal conditions

Because creep–fatigue is mainly studied in uniaxial tension, it is shown here how to proceed to perform both experiments and calculations under multiaxial loading and when the temperature varies both in time and space. The constitutive equations used are those of elasto‐visco‐plasticity coupled or not, to damage, with isotropic and kinematic hardening. It is shown that the unified damage law first proposed for ductile failure and then for fatigue may also be applied to multiaxial creep–fatigue interactions with a new expression for the damage threshold. The procedure for the identification of material parameters is described in detail. Finally, it is shown that the uncoupled calculation procedure, where damage is calculated as a post‐processing of an elasto‐visco‐plastic computation, gives satisfactory results in comparison to the fully coupled analysis; the latter being more accurate but very expensive in computer time.     

One damage law for different mechanisms

We consider here a general three-dimensional kinetic damage law. It uses the thermodynamic of irreversible processes formalism and the phenomenological aspects of isotropic damage. It gives the damage rate as a function of its associated variable, the strain energy density release rate and the accumulated plastic strain rate. Associated with different plastic constitutive equations, this damage law takes into account brittle damage, ductile damage, low and high cycle fatigue and creep damage. In this paper we mainly focus on creep-fatigue interaction and high cycle fatigue. Associated to a viscoplastic constitutive equation having kinematic hardening, the damage law gives the non linear creep-fatigue interaction. The agreement with experiments is good. Associated to plastic constitutive equations also having kinematic hardening but introduced in a micromechanical two scale model based on the self-consistent scheme, it models the non linear accumulation of damage induced by a succession of sequences of different amplitudes as well as the effect of the mean stress and the influence of non proportional loading.     

Procedure of Determining Creep and Creep-Rupture Strength Parameters for Isotropic Materials under Nonisothermal Loading

A procedure has been developed for determining the parameters of creep and creep-rupture strength that appear in constitutive equations of thermoviscoplasticity for describing nonisothermal processes of deformation and damage accumulation in isotropic materials due to creep. The procedure is tried out using a high-temperature chromium-nickel alloy ÉI437.     

Simulation of fading path shape memory in the theory of simple materials with elastoplastic behavior and initial loading surface

A mathematical theory is proposed rigorous construction and specialization of constitutive relations for simple (in the Noll’s sense) strain-hardening elastoplastic materials with an initial loading surface and a fading path shape memory at the active deformation segment. Strains and symmetry type of the material are taken to be arbitrary. Physical equations are derived for materials with no path shape memory, with a weak fading memory, and with a fading memory of the nth order. Based on the proposed constitutive relations, physical equations are constructed for isotropic materials. In the context of the fading path shape memory, a definition of an elastic-perfectly plastic material is given. Assuming the condition of smallness of measures of strains throughout the entire “past” history, a theory has been developed for rigorous construction and specialization of constitutive relations for materials with a first-order fading path shape memory for infinitesimal strains. Special emphasis is placed on isotropic materials. __________ Translated from Problemy Prochnosti, No. 4, pp. 5–18, July–August, 2007.     

Numerical damage prediction in dowel connections of wooden structures

The behaviour of timber connections is very complex because of the interaction between brittle and ductile failure modes that develop within the contact areas between the timber and the dowel. Simulating this behaviour numerically requires the use of multidimensional failure criteria as well as the use of coupled constitutive equations accounting for both non-linear isotropic hardening and isotropic ductile damage. Such a formulation is proposed in the present work and implemented within a Vumat user-defined subroutine in Abaqus/Explicit. The model is used to simulate the behaviour of a double shear timber steel connection. Good agreement was found between the FE results and experimental ones, which showed the good capability of the model to predict the onset of ductile damage and growth. It was found that failure results from ductile defects initiation, growth and propagation inside narrow shear bands wherein the plastic strain is highly localised.     

弹性损伤理论的几何-拓扑描述

材料内部微观几何缺陷通常是作为物理非线性问题在本构方程中考虑。针对连续介质弹性损伤理论作几何拓扑,采用非完整标架方法把材料内部微观几何缺陷转化为材料空间的弯曲,并体现在基本几何法则中。首先由连续损伤变量定义拟塑性张量,给出这些基本张量所满足的连续性方程和基本几何法则。由此建立了弹性损伤缺陷与Riemann流形的对应关系,将物理非线性问题转化为物理线性和材料所在空间的弯曲之和。最后讨论了二维情况下,各向同性晶格材料受各向异性损伤的算例。