Mathematical and numerical modeling of the non-associated plasticity of soils—Part 1: The boundary value problem

The soil is characterized by the influence of the hydrostatic stress, which leads to a yield surface with a shape of a pyramid for Mohr–Coulomb criteria and a shape of a cone for Drucker–Prager one. These materials are also characterized by a non-associated plasticity where the plastic yielding rule does not follow the normality rule. The usual mechanical models use two independent functions to describe this particular collapse. Unfortunately, this manner broke the model formulation. The purpose of this work is to present a consistent formulation of the non-associated plasticity of soil. The frame of the mathematical analysis is the concept of the implicit standard material. The cornerstone of this new idea is the construction of a single function called the bipotential playing in the same time the roles of the yield surface and the plastic potential. The bipotential concept is then intended to involve the constitutive law, cover the normality rule even for the non-associated soil and the proof of the solution existence. The formulation was initially performed for the case of a regular point out of the cone apex and in present, it is extended to the irregular point located at the apex. The paper presents firstly the implicit standard material method. Then, the methodology to build a full model for the boundary value problem is detailed. Particular expressions and relations are sufficiently explained and discussed. Attention is made to the evolution problem and the variational principles related to the elastic–plastic behavior.     

Finite element analysis of the piezocone test in cohesive soils using an elastoplastic–viscoplastic model and updated Lagrangian formulation

In this research, the finite element analysis of piezocone penetration has been conducted using the elastoplastic–viscoplastic bounding surface model in the updated Lagrangian reference frame. A finite element formulation has been performed considering the viscoplastic contribution of the model and the theory of mixtures has been incorporated to explain the behavior of the soil. The formulated model has been implemented into a finite element program, EPVPCS-S (elastoplastic–viscoplastic coupled system-soil), to analyze the mechanism of piezocone penetration. The results of the finite element analysis have been compared and investigated with the experimental results from the piezocone penetration and dissipation tests conducted using LSU/CALCHAS (Louisiana State University Calibration Chamber System).     

HIA: A Hybrid Integral Approach to model incompressible isotropic hyperelastic materials – Part 2: Finite element analysis

The present paper is devoted to the modeling of finite deformations of hyperelastic bodies by using the Hybrid Integral Approach (HIA) model introduced by the Authors. This model combines the affine behavior of chains included in the molecular 8-chains density, the interleaving constraint part and an original phenomenological integral density which allows to balance the mismatch between model and experimental data. A total Lagrangian formulation is adopted to describe the geometrical and material non-linearities and a finite element implementation is performed in the FER software. Four test examples, including homogeneous and non-homogeneous deformations, as well as complex computation involving dynamic contact and impact are proposed to show the applicability of the developed approach and the efficiency of the model.     

Finite elasto-plastic deformation—I: Theory and numerical examples

It is demonstrated that the problem of elasto-plastic finite deformation is governed by a quasi-linear model irrespective of deformation magnitude. This feature follows from the adoption of a rate viewpoint toward finite deformation analysis in an Eulerian reference frame. Objectivity of the formulation is preserved by introduction of a frame-invariant stress rate.Equations for piece-wise linear incremental finite element analysis are developed by application of the Galerkin method to the instantaneously linear governing differential equations of the quasi-linear model. Numerical solution capability has been established for problems of plane strain and plane stress. The accuracy of the numerical analysis is demonstrated by consideration of a number of problems of homogeneous finite deformation admiting comparative analytic solution. It is shown that accurate, objective numerical solutions can be obtained for problems involving dimensional changes of an order of magnitude and rotations of a full radian.     

Finite element analysis of functionally graded plates for coupling effect of extension and bending

In this paper, the coupling effect of extension and bending in functionally graded plate subjected to transverse loading for Kirchhoff-Love plate theory equations is studied. The material properties of the FG plates are assumed to vary continuously throughout the thickness direction of the layer according to sigmoid distribution of the volume fractions of constituents. The two plate functionals are used which are developed by Gateaux differential and potential operator concept. A layer wise, isoparametric, mixed finite element approach was used and results of two different quadrilateral elements, one considering the membrane forces and the other one not, were compared by an analytical study. Finally, for different composition profiles the effect of variations of the Young’s moduli and of variations volume fraction index to dimensionless displacement, strain and stress values are studied.     

On the methodologies of stress analysis of composite structures: Part 1: State of the art—phenomenological and physical methodologies

The rapidly increasing technological importance of composite materials and composite structures is leading to the development of new, more advanced models of their actual response to mechanical and thermal loads. This in turn results in the development of new experimental and analytical methods for determination of the mechanical and thermal responses of such structures and materials to various loads. In this respect the reliability and the predictive power of various methods and techniques of stress analysis become very important since all the analytical, experimental and numerical methods used for the determination, prediction and optimization of the actual mechanical responses of composite structures and materials are based on the concepts of strain and stress. Because of the inherently three-dimensional stress and strain states in composite materials and structures and the wide use of viscoelastic polymers as the matrix and some reinforcing fiber materials, a more rigorous type of modelling than had been common in the past is needed of all the involved physical phenomena which influence the strain and stress states at the local and global levels. Also, a more rigorous analysis of practical consequences of the physical and mathematical simplifications is required to assure reliability and accuracy of various methods of stress analysis. The influence of the above-mentioned factors on the reliability and applicability of analytical and experimental procedures is illustrated by examples of actual material responses.Part 2 of this paper presents theories and techniques of three new methods of strain/stress analysis which have been developed on the basis of comprehensive physical models of involved phenomena: the isodyne, strain gradient and thermoelastic effect methods. Presented examples illustrate the efficacy of these methods.     

Finite element modeling of smart piezo structure: considering dependence of piezoelectric coefficients on electric field

In this work, variation of piezoelectric strain coe?cient and permittivity with change in electric field is included in constitutive equations of piezoelectricity and used for developing finite element model of a plate instrumented with piezoelectric patches. Simulation results show that nodal displacement response and sensor voltage is less controlled if variation of piezoelectric strain coe?cient and permittivity with change in electric field is not included in finite element modelling as compared to the case in which these variations are included in finite element modeling. An experiment is performed so as to validate simulation results.     

Finite volume element method for analysis of unsteady reaction–diffusion problems

A finite volume element method is developed for analyzing unsteady scalar reaction-diffusion problems in two dimensions. The method combines the concepts that are employed in the finite volume and the finite element method together. The finite volume method is used to discretize the unsteady reaction-diffusion equation, while the finite element method is applied to estimate the gradient quantities at cell faces. Robustness and efficiency of the combined method have been evaluated on uniform rectangular grids by using available numerical solutions of the two-dimensional reaction-diffusion problems. The numerical solutions demonstrate that the combined method is stable and can provide accurate solution without spurious oscillation along the high-gradient boundary layers.     

Nonlinear modeling and dynamic analysis of the rotor-bearing system

To overcome the shortcomings of extreme time-consuming in solving the Reynolds equation, two efficient calculation methods, based on the free boundary theory and variational principles for the unsteady nonlinear Reynolds equation in the condition of Reynolds boundary, are presented in the paper. By employing the two mentioned methods, the nonlinear dynamic forces as well as their Jacobians of the journal bearing can be calculated saving time but with the same accuracy. Of these two methods, the one is called a Ritz model which manipulates the cavitation region by simply introducing a parameter to match the free boundary condition and, as a result, a very simple approximate formulae of oil-film pressure is being obtained. The other one is a one-dimensional FEM method which reduces the two-dimensional variational inequality to the one-dimensional algebraic complementary equations, and then a direct method is being used to solve these complementary equations, without the need of iterations, and the free boundary condition can be automatically satisfied. Meanwhile, a new order reduction method is contributed to reduce the degrees of freedom of a complex rotor-bearing system. Thus the nonlinear behavior analysis of the rotor-bearing system can be studied time-sparingly. The results in the paper show the high efficiency of the two methods as well as the abundant nonlinear phenomenon of the system, compared with the results obtained by the usual numerical solution of the Reynolds equation.     

Finite element analysis for the unsteady nearshore circulation due to wave-current interaction (II) — Two-step explicit finite element method

In this paper, the two-step explicit finite element analysis for the numerical model of the unsteady nearshore circulation proposed in·Ref. [1] and its realization of Fortran program are presented. A circulation has been, clearly shown in the calculated wave-current velocity field, and it is in good agreement with observations. First Received March 27, 1987     

Finite element analysis of large contact deformation of an elastic–plastic sinusoidal asperity and a rigid flat

Normal contact deformation of an asperity and a rigid flat is studied within an axisymmetric finite element model. The asperity features a sinusoidal profile and is elastic–plastic with linear strain hardening. Influences of geometrical (asperity height and width) and loading (the maximum interference) parameters on frictionless contact responses are explored for both loading and unloading. Dimensionless expressions for contact size and pressures covering a large range of interference and asperity ratio values are obtained in power-law forms. Results show the mean contact pressure after fully-plastic contact reaches a plateau only for small asperity ratios, while it continues increasing for large asperity ratios. The residual depth is found to be associated with plastically dissipated energy.     

Mathematical modeling and experimental investigation of an embedded vibro-impact system

The subject of this work is the experimental investigation and the mathematical modeling of the impact force behavior in a vibro-impact system, where a hammer is mounted on a cart that imposes a prescribed displacement. By changing the hammer stiffness and the impact gap it is possible to investigate the impact force behavior under different excitation frequencies. The experimental data will be used to validate the mathematical model. The hammer behavior is studied in more detail using a nonlinear analysis, which shows the various responses of the hammer, such as dynamical jumps, bifurcations and chaos.     

Influence of microstructural features on the yield strength of Ti–6Al–4V: a numerical study by using the crystal plasticity finite element method

Meccanica - In this paper, a numerical study was presented on the influence of microstructural features on the yield strength of bimodal α–β Ti–6Al–4V. Tensile tests and...     

A micromechanics-based strain gradient damage model for fracture prediction of brittle materials – Part II: Damage modeling and numerical simulations

In this paper, we established a strain-gradient damage model based on microcrack analysis for brittle materials. In order to construct a damage-evolution law including the strain-gradient effect, we proposed a resistance curve for microcrack growth before damage localization. By introducing this resistance curve into the strain-gradient constitutive law established in the first part of this work (Li, 2011), we obtained an energy potential that is capable to describe the evolution of damage during the loading. This damage model was furthermore implemented into a finite element code. By using this numerical tool, we carried out detailed numerical simulations on different specimens in order to assess the fracture process in brittle materials. The numerical results were compared with previous experimental results. From these studies, we can conclude that the strain gradient plays an important role in predicting fractures due to singular or non-singular stress concentrations and in assessing the size effect observed in experimental studies. Moreover, the self-regularization characteristic of the present damage model makes the numerical simulations insensitive to finite-element meshing. We believe that it can be utilized in fracture predictions for brittle or quasi-brittle materials in engineering applications.     

Mathematical modeling and numerical computation of thee?ective interfacial conditions for Stokes flow onan arbitrarily rough solid surface?

正A. T. TRAN1, H. LE QUANG2,, Q. C. HE2,3, D. H. NGUYEN1