梯度依赖的混凝土弹塑性非局部损伤的本构模型

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.     

New crystal plasticity constitutive model for large strain deformation in single crystals of magnesium

A new rate-dependent elastic–viscoplastic crystal plasticity constitutive model (CPCM) to simulate the large strain deformation in magnesium alloys is presented. The observed intragranular plastic deformation mechanisms of primary extension, primary contraction, and secondary extension (double) twinning are accounted for. The basal and non-basal slip systems in the parent grain, primary and double twins were also incorporated in the model. The crystallographic planes and directions of various slip and twinning systems are calculated. The slip-induced shear in the parent grain, as well as primary and secondary twinned regions are simulated. The twinning-induced shear from the primary and secondary twinned regions are also computed. In the model the texture evolution in the parent, as well as primary and secondary twinned regions are tracked. Separate resistance evolution functions for all the slip and twinning systems were considered. The interactions between various slip and twinning systems are accounted for in a comprehensive manner. Using the proposed CPCM, the plastic deformation in a magnesium single crystal in simple shear strain path is simulated. The contributions of various plastic deformation mechanisms to the macroscopic plastic deformation of the magnesium single crystal in this strain path are presented. The importance of identifying the active plastic deformation in a given strain path on a magnesium single crystal for a reliable model prediction was shown with an example.     

A simple orthotropic finite elasto–plasticity model based on generalized stress–strain measures

 In this paper we present a formulation of orthotropic elasto-plasticity at finite strains based on generalized stress–strain measures, which reduces for one special case to the so-called Green–Naghdi theory. The main goal is the representation of the governing constitutive equations within the invariant theory. Introducing additional argument tensors, the so-called structural tensors, the anisotropic constitutive equations, especially the free energy function, the yield criterion, the stress-response and the flow rule, are represented by scalar-valued and tensor-valued isotropic tensor functions. The proposed model is formulated in terms of generalized stress–strain measures in order to maintain the simple additive structure of the infinitesimal elasto-plasticity theory. The tensor generators for the stresses and moduli are derived in detail and some representative numerical examples are discussed. Received: 2 April 2002 / Accepted: 11 September 2002     

A large strain plasticity model for implicit finite element analyses

The theoretical basis and numerical implementation of a plasticity model suitable for finite strains and rotations are described. The constitutive equations governing J ₂ flow theory are formulated using strains-stresses and their rates defined on the unrotated frame of reference. Unlike models based on the classical Jaumann (or corotational) stress rate, the present model predicts physically acceptable responses for homogeneous deformations of exceedingly large magnitude. The associated numerical algorithms accommodate the large strain increments that arise in finite-element formulations employing an implicit solution of the global equilibrium equations. The resulting computational framework divorces the finite rotation effects on strain-stress rates from integration of the rates to update the material response over a load (time) step. Consequently, all of the numerical refinements developed previously for small-strain plasticity (radial return with subincrementation, plane stress modifications, kinematic hardening, consistent tangent operators) are utilized without modification. Details of the numerical algorithms are provided including the necessary transformation matrices and additional techniques required for finite deformations in plane stress. Several numerical examples are presented to illustrate the realistic responses predicted by the model and the robustness of the numerical procedures.     

A constitutive equation for nonlinear stress–strain curves of crystalline polymers

We present a new method for the analysis of stress–strain curves for crystalline polymers such as polypropylene and polyethylene. A nonlinear constitutive equation that includes terms that cover the plastic deformation and anharmonicity of the spring is developed. In order to quantitatively characterize the nonlinear viscoelasticity using this equation, data on the transient moduli during elongation at a constant rate of strain are required. Hence, the simultaneous measurements of linear oscillatory viscoelastic moduli during a constant rate of elongation were investigated. It was found that the present method makes possible the evaluation of the plastic deformation fraction and the Gruneisen constant for crystalline polymers. © 1998 Chapman & Hall     

A constitutive equation for concrete

A more rational approach to strength criterion development for concrete is proposed to cover the composite nature and complex failure mechanism of concrete materials. The use of scalar valued function theory as applied to concrete failure prediction is demonstrated. The results are applicable to general brittle materials     

A practical constitutive equation covering a wide range of strain rates

A practical constitutive equation of a single form combining stress, strain, strain rate and temperature effect is proposed with which the various material behaviors can be described covering a wide range of strain rates, especially the high strain rates. It is illustrated that the proposed form of the equation is useful when compared to some experimental results obtained under a dynamical uniaxial stress and an incremental torsional impact.     

An approximated computational method for fast stress reconstruction in large strain plasticity

This article describes a numerical method to reconstruct the stress field starting from strain data in elastoplasticity. Usually, this reconstruction is performed using the radial return algorithm, commonly implemented also in finite element codes. However, that method requires iterations to converge and can bring to errors if applied to experimental strain data affected by noise. A different solution is proposed here, where an approximated numerical method is used to derive the stress from the strain data with no iterations. The method is general and can be applied to any plasticity model with a convex surface of the yield locus in nonproportional loading. The theoretical basis of the method is described and then it is implemented on two constitutive models of anisotropic plasticity, namely, Hill48 and Yld2000-2D. The accuracy of the proposed method and the advantage in terms of computational time with respect to the classical radial-return algorithm are discussed. The possibility of using such method to reconstruct the stress field in case of few temporal data and noisy strain fields is also investigated.     

Numerical integration of a pressure‐dependent,non‐linear kinematic hardening constitutive model for large strain cyclic plasticity of metals

A Gurson‐based constitutive model is presented, which includes non‐linear mixed isotropic–kinematic hardening and creep, and allows the analysis of problems involving arbitrarily large plastic strains. This model was developed with the main objective of allowing, on the basis of a single set of material parameters, the numerical simulation of all the main features of cold metal forming processes, which usually imply severe loading–unloading cycles with very large plastic strains, difficult to be correctly reproduced numerically. A suitable integration scheme of the rate equations is described and implemented into a finite element code. The results obtained are compared with some reference experimental ones; an application of the model for the simulation of wire drawing processes is also presented. Copyright © 2011 John Wiley & Sons, Ltd.     

A variational constitutive model for porous metal plasticity

This paper presents a variational formulation of viscoplastic constitutive updates for porous elastoplastic materials. The material model combines von Mises plasticity with volumetric plastic expansion as induced, e.g., by the growth of voids and defects in metals. The finite deformation theory is based on the multiplicative decomposition of the deformation gradient and an internal variable formulation of continuum thermodynamics. By the use of logarithmic and exponential mappings the stress update algorithms are extended from small strains to finite deformations. Thus the time-discretized version of the porous-viscoplastic constitutive updates is described in a fully variational manner. The range of behavior predicted by the model and the performance of the variational update are demonstrated by its application to the forced expansion and fragmentation of U-6%Nb rings.     

Phenomenological formulation of viscoplastic constitutive equation for polyethylene by taking into account strain recovery during unloading

A viscoplastic constitutive equation for polyethylene that properly describes significant strain recovery during unloading was proposed. The constitutive equation was formulated by combining the kinematic hardening creep theory of Malinin and Khadjinsky with the nonlinear kinematic hardening rule of Armstrong and Frederick. In order to describe the strain recovery, the nonlinear kinematic hardening rule was modified. First, a loading surface was defined in a viscoplastic strain space. A loading–unloading criterion was then introduced using the loading surface. Moreover, a new parameter was defined by the relationship between the loading surface and the current state of the viscoplastic strain, and the evolution equation of back stress was modified using this parameter, which has some value only during unloading. Experimental results for polyethylene were simulated by using the modified constitutive equations, and cyclic inelastic deformation in both uniaxial and biaxial states of stress was predicted. Finally, the validity of the above-described modification was verified, and the features of the constitutive equation and the deformation were discussed.     

A constitutive equation for non-linear electro-active solids

Summary Electro-active solids are solids that are either infused with electrorheological fluids or embedded with electrically conducting particles, the body as a whole however conducting negligible current. In this paper, we provide a mathematical framework, within the context of continuum mechanics, for the study of electro-active solids. The theory assumes that the body can be considered as a continuum, in the sense of homogenization, which is isotropic, incompressible, elastic and is capable of responding to an electric field. Appealing to standard techniques in continuum mechanics, we obtain a constitutive relation for the stresses in terms of the deformation and electric field. This is used in a study of triaxial extension, simple shear and anisotropy induced by the electric field.     

A simple novel constitutive equation for concrete

A simple novel constitutive equation, three parameter strength criterion for concrete is proposed to represent the composite nature and complex failure mechanism of material of concrete. In this paper, the study is to demonstrate the use of scalar valued function, invariant theory, as applied to concrete failure prediction. Without the loss of accuracy of prediction, a three parameter strength criterion is developed.     

Evaluation of low strain rate constitutive equation of 7075 aluminium alloy at high temperature

Abstract

The 7075 aluminium alloy is one of the most important engineering alloys utilised extensively in aircraft and transportation industries due to its high specific strength. In the present research, the flow behaviour of this alloy has been investigated using hot compression test at strain rates of 0·001, 0·01, 0·1 and 1 s^?1 and temperatures of 350, 400 and 450°C. The results reveal that dynamic softening occurred in these temperatures and strain rates. The activation energy, strain rate sensitivity and two constitutive equations (hyperbolic sine law and the power law) are derived from the results. It is shown that the hyperbolic sine law has a better agreement with the experimental results.     

A thermomechanical crystal plasticity constitutive model for ultrasonic consolidation

We present a micromechanics-based thermomechanical constitutive model to simulate the ultrasonic consolidation process. Model parameters are calibrated using an inverse modeling approach. A comparison of the simulated response and experimental results for uniaxial tests validate and verify the appropriateness of the proposed model. Moreover, simulation results of polycrystalline aluminum using the identified crystal plasticity based material parameters are compared qualitatively with the electron back scattering diffraction (EBSD) results reported in the literature. The validated constitutive model is then used to simulate the ultrasonic consolidation process at sub-micron scale where an effort is exerted to quantify the underlying micromechanisms involved during the ultrasonic consolidation process.     

Incremental constitutive formulation for time dependent materials: creep integral approach

This paper deals with the development of a mathematical approach for the solution of linear, non-ageing viscoelastic materials undergoing mechanical deformation. The formulation is derived from integral approach based on a discrete spectrum representation for the creep tensor. Finite difference integration is used to discretize the integral operators. The resulting constitutive model contains an internal state variable which represents the influence of the whole past history of stress and strain. Thus the difficulty of retaining the strain history in computer solutions is avoided. A complete general formulation of linear viscoelastic stress-strain analysis is developed in terms of increments of stresses and strains. Numerical simulations are included in order to validate the incremental constitutive equations.     

A rate-dependent constitutive equation for 5052 aluminum diaphragms

In this article, both experimental and numerical approaches are conducted to present a constitutive equation for 5052 aluminum diaphragms under quasi-static strain rate loadings. For this purpose the stress–strain curves at different strain rates are obtained using tensile tests. Brittle behavior during tensile tests is observed due to samples thin thicknesses. Employing Johnson–Cook constitutive equation no yields in reasonable agreement with these tensile tests results. Therefore, developing a more suitable constitutive equation for aluminum diaphragms is taken into consideration. This equation is then implemented into the commercial finite element software, ABAQUS, via a developed user material (UMAT) subroutine utilizing von Mises plasticity theory and an own solution algorithm. A single-element pathological test method is adopted to show the well-development of the UMAT subroutine. In order to verify the proposed constitutive equation for precision predicting of mechanical behavior, a bulge test is performed in which demonstrates a good agreement between experimental and numerical results.     

A constitutive model for metals over a large range of strain rates Identification for mild-steel and aluminium sheets

A phenomenological model is presented to describe the mechanical behaviour for metals and alloys over a large range of strain rates. It is an elasto-plastic model with a strain rate and temperature-sensitive yield stress. This model partially relies on physical considerations and is specially developed for an easy application in explicit finite element method (FEM) codes. The process for identifying the constants from experimental data is presented, taking into account the exact testing conditions such as temperature increase and strain rate variations during the loading. Applying the model to data obtained for mild steel and commercial aluminium sheets yields satisfactory results.     

Proposal for a constitutive equation of temperate firn

From deformation measurements at a 20 m deep firn pit, a constitutive equation for temperate firn under natural stress has been derived. The analytical and numerical formulation passes over into Glen's flow law for ice at the transition of firm to ice. Basis of the analysis is the determination of the shear strain rate from the tilt rate of the pit axis, under consideration of the longitudinal and vertical strain rates, the compressibility of the firn, as well as the triaxial pit deformation.