Implementation of an Associative Flow Rule Including Hydrostatic Stress Effects into the High Strain Rate Deformation Analysis of Polymer Matrix Composites

A previously developed analytical formulation has been modified in order to more accurately account for the effects of hydrostatic stresses on the nonlinear, strain rate dependent deformation of polymer matrix composites. State variable constitutive equations originally developed for metals have been modified in order to model the nonlinear, strain rate dependent deformation of polymeric materials. To account for the effects of hydrostatic stresses, which are significant in polymers, the classical J2 plasticity theory definitions of effective stress and effective inelastic strain, along with the equations used to compute the components of the inelastic strain rate tensor, are appropriately modified. To verify the revised formulation, the shear and tensile deformation of a representative polymer are computed across a wide range of strain rates. Results computed using the developed constitutive equations correlate well with experimental data. The polymer constitutive equations are implemented within a strength of materials based micromechanics method to predict the nonlinear, strain rate dependent deformation of polymer matrix composites. The composite mechanics are verified by analyzing the deformation of a representative polymer matrix composite for several fiber orientation angles across a variety of strain rates. The computed values compare well to experimentally obtained results.     

Axisymmetric Stress Analysis of a Thick Conical Shell with Varying Thickness under Nonuniform Internal Pressure

A mathematical approach based on the perturbation theory has been used for axisymmetric stress analysis of a thick conical shell with varying thickness under nonuniform internal pressure. The equilibrium equations have been derived using the energy principle and considering the second-order shear deformation theory (SSDT), which includes shear deformation effects. This system of ordinary differential equations with variable coefficients has been solved analytically using the matched asymptotic expansion method of the perturbation theory. A comparison of the results with the finite-element method and the first-order shear deformation theory shows that the SSDT can predict the displacements and stresses of the shell for a wide range of thicknesses as well with less calculations than other analytical methods such as the Frobenius series method.     

Axial transformation method in the analysis of the axisymmetric plastic flow

A new method for the analysis of mechanics of plastic flow is presented in this paper. The basis of the method is nonlinear transformation of the deformation zone. After transformation, the deformation zone is divided into several rectangular elements. It is a characteristic feature of the presented method which enables to determine a continuous strain and stress field. The exact fulfillment of equations concerning equilibrium and incompressibility conditions was accomplished. The method was verified by experiments. An example of the strain and stress fields in a material deformed between concave anvils was presented.     

基于Marzars损伤模型的胶结充填体合理强度确定

为了研究金山金矿不同灰砂比的尾砂胶结充填体破坏规律,运用损伤力学理论,建立了不同灰砂比的尾砂胶结充填体压缩损伤本构模型。采用采场采矿后的岩体释放能量逼近胶结充填体峰值变形能原则,结合金山金矿条带式充填采矿法试验采场的具体位置、地应力、采场结构参数,确定了尾砂胶结充填体的强度,为尾砂胶结充填参数的确定提供理论依据。     

镁合金变形的晶体塑性有限元分析

晶体塑性理论已被广泛应用于现有的有限元分析中,从微观角度来模拟和预测晶体材料的宏观各向异性力学行为及塑性变形过程中织构的演化与发展。现有的晶体塑性理论框架核心主要基于由滑移引起的塑性变形机制,在预测由滑移和孪晶引起塑性变形的材料力学响应方面还不够完善。本文以具有密排六方(HCP)结构的变形镁合金塑性变形过程为例,综述了以滑移和孪晶为核心的晶体塑性理论的理论研究和应用现状,重点评述了现有孪晶的数值实现方法,并预测了相应理论的发展方向。     

Unsaturated Soil Mechanics in Engineering Practice

Unsaturated soil mechanics has rapidly become a part of geotechnical engineering practice as a result of solutions that have emerged to a number of key problems (or challenges). The solutions have emerged from numerous research studies focusing on issues that have a hindrance to the usage of unsaturated soil mechanics. The primary challenges to the implementation of unsaturated soil mechanics can be stated as follows: (1) The need to understand the fundamental, theoretical behavior of an unsaturated soil; (2) the formulation of suitable constitutive equations and the testing for uniqueness of proposed constitutive relationships; (3) the ability to formulate and solve one or more nonlinear partial differential equations using numerical methods; (4) the determination of indirect techniques for the estimation of unsaturated soil property functions, and (5) in situ and laboratory devices for the measurement of a wide range of soil suctions. This paper explains the nature of each of the previous challenges and describes the solutions that have emerged from research studies. Computer technology has played a major role in achieving practical geotechnical engineering solutions. Computer technology has played an important role with regard to the estimation of unsaturated soil property functions and the solution of nonlinear partial differential equations. Breakthroughs in the in situ and laboratory measurement of soil suction are allowing unsaturated soil theories and formulations to be verified through use of the “observational method.”     

Damage-Coupled Progressive Failure and Yield Line Analyses of Metal Plates

Continuum damage mechanics based progressive failure analysis of an aluminum alloy AL2024-T3 plate has been carried out. Isotropic continuum damage mechanics model proposed by Chandrakanth and Pandey in 1995 has been implemented in a nonlinear finite element computational scheme based on damage-coupled and damage-uncoupled elastoplastic constitutive relationship. In order to model the progressive growth of damage and plasticity from extreme fibers toward the neutral axis, discrete layered approach has been adopted in the formulation using Ahmed’s degenerate isoparametric shell element, which accounts for shear deformation. A critical damage criteria is used for determining the onset and propagation of failure in the plate. Damage-coupled and damage-uncoupled analyses have been carried out on rectangular and triangular plates of aluminum alloy Al2024-T3. Yield line patterns have been generated using extensive nonlinear progressive failure analysis and comparison with conventional yield line analysis has been made. It is envisioned that employing the methodology presented herein, yield line pattern generation for structural components with complex shapes can be obtained, which would significantly assist engineers in analysis and design of structures.     

Moving Least-Squares Differential Quadrature Method for Free Vibration of Antisymmetric Laminates

In this paper, the moving least-squares differential quadrature (MLSDQ) method is employed for free vibration of thick antisymmetric laminates based on the first-order shear deformation theory. The generalized displacements of the laminates are independently approximated with the centered moving least-squares (MLS) technique within each domain of influence. The MLS nodal shape functions and their partial derivatives are computed quickly through back-substitutions after only one LU decomposition. Subsequently, the weighting coefficients in the MLSDQ discretization are determined with the nodal partial derivatives of the MLS shape functions. The MLSDQ method combines the merits of both the differential quadrature and meshless methods which can be conveniently applied to complex domains and irregular discretizations without loss of implementation efficiency and numerical accuracy. The natural frequencies of the laminates with various edge conditions, ply angles, and shapes are calculated and compared with the existing solutions to study the numerical accuracy and stability of the MLSDQ method. Effects of support size, order of completeness of basis functions, and node irregularity on the numerical accuracy are investigated in detail.     

Analysis of Gravity Dam on a Complicated Rock Foundation Using an Adaptive Block Element Method

In this Technical Note, the adaptive block element method of rock masses is formulated, in which the elastoplastic characteristics of both rock blocks and discontinuities are taken into account. The concept of an overlay element is illustrated first; then the displacement fields of rock blocks are expressed as functions of so-called general degree of freedoms using the shape functions of the hierarchical finite element method; the governing equations of the rock block system are deduced on the basis of the virtual work principle; and the p-version adaptive algorithm based on the energy norm error estimation of each block element is proposed. The method is applied to the deformation and stability study of a gravity dam, and the parallel laboratory physical test is used to check the validity and ability of the method.     

Creep of Polymer Matrix Composites. I: Norton/Bailey Creep Law for Transverse Isotropy

This research concerns polymer matrix composite (PMC) materials having long or continuous reinforcement fibers embedded in a polymer matrix. The objective is to develop comparatively simple, designer friendly constitutive equations intended to serve as the basis of a structural design methodology for this class of PMC. Here (Part I), the focus is on extending the deformation model of an anisotropic deformation/damage theory presented earlier. The resulting model is a generalization of the simple Norton/Bailey creep law to transverse isotropy. A companion paper (Part II) by the writers deals with damage and failure of the same class of PMC. An important feature of the proposed deformation model is its dependence on hydrostatic stress. Characterization tests on thin-walled tubular specimens are defined and conducted on a model PMC material. Additional exploratory tests are identified and carried out for assessing the fundamental forms of the multiaxial creep law.