Macro-mechanical Model Research Articles

Macromechanical modelling of woven fabrics

PurposeThe purpose of this paper is to focus on the development of a thorough method for the macromechanical analysis of fabrics.Design/methodology/approachThe homogenization method was implemented for the generation of continuum equivalent model for the plain woven structure. Keystone of the method is the mesomechanical analysis of the textile unit cell for the evaluation of the apparent properties and the generation of an equivalent macromechanical model supporting the mechanical performance of the structure. The finite element method (FEM) using beam elements was applied for the mechanical analysis of the discrete model of the unit cell and the FEM using shell elements was applied for the analysis of the continuum macromechanical model.FindingsThe tensile, shear and bending test of the unit cell were simulated. The constitutive equations of the continuum model were formed considering equivalent performance with the discrete model.Originality/valueThe reliability of the equivalent model in tensile, shear (in‐plane) and bending (out‐of‐plane) deformation was achieved even for asymmetric woven structures. The low computational power demanded for the meso‐ and macro‐mechanical modelling and analysis is a beneficial feature of the proposed method.

Characterization and finite element modeling of montmorillonite/polypropylene nanocomposites

Finite element modeling can be a useful tool for predicting the behavior of composite materials and arriving at desirable filler contents for maximizing mechanical performance. In the present study, to corroborate finite element analysis results, quantitative information on the effect of reinforcing polypropylene (PP) with various proportions of nanoclay (in the range of 3–9% by weight) is obtained through experiments; in particular, attention is paid to the Young’s modulus, tensile strength and failure strain. Micromechanical finite element analysis combined with Monte Carlo simulation have been carried out to establish the validity of the modeling procedure and accuracy of prediction by comparing against experimentally determined stiffness moduli of nanocomposites. In the same context, predictions of Young’s modulus yielded by theoretical micromechanics-based models are compared with experimental results. Macromechanical modeling was done to capture the non-linear stress–strain behavior including failure observed in experiments as this is deemed to be a more viable tool for analyzing products made of nanocomposites including applications of dynamics.

Drilling of woven glass fiber-reinforced plastic—an experimental and finite element study

Drilling in woven fiber-reinforced plastics is a well-known practice in modern-day manufacturing. The high fracture toughness of woven fiber-based composites over unidirectional counterparts is increasing demand in aviation and electronics industries. Hence, failure of these materials at harsh environments is a matter of concern. Very few numerical studies on drilling of these composites have been carried out; hence, the present scope may be considered as a trial de novo. Delamination was studied in the present work at different feed–speed combinations. Drilling responses were estimated using finite element as a numerical simulation tool. An equivalent elastic macromechanical model was assumed for the woven composite workpiece. A 3D drill bit was modeled using commercial CAD package Pro-Engineer and Ansys Autodyn was used as the solver environment. The simulation and validation experiments were carried out at planned feed–speed combinations. The effect of process parameters on exit and entry delamination is also documented. The thrust determined by finite element techniques showed good prediction with the experimental results.

Three-Dimensional Modeling and Analyses of Orthotropic Bridge Decks Using Representative Volume Element

A representative volume element (RVE)–based modeling procedure, macromechanical modeling, is presented for the homogenization of orthotropic bridge superstructures. The purpose of the models is the simplification of the complex deck structures for three-dimensional (3D) load-response analyses. A numerical example for the application of the model to a prototype bridge superstructure analysis is presented. The macromechanical model was validated by performing static patch load analysis and comparing results with 3D finite element (FE) analysis results. Continuation of this work will include the development of RVEs and associated stiffness matrices of commonly used orthotropic bridge superstructures. By using these stiffness matrices in conjunction with ordinary structural analysis programs, 3D simplified models can be developed for calculating load demands.

Size Dependent Strength of Fiber Eutectics and Transformation Particles Composite Ceramic

Fiber eutectics and transformation particles composite ceramic possessed good strengths and creep resistance. It is mainly composed of fiber eutectics with random orientation and transformation particles. First, on basis of the strong constraining effect of the microstructure in fiber eutectics, the micromechanical stress field in fiber eutectics is determined by shear stress that develop between the fiber- inclusion and matrix is obtained. Then, the stress concentration duo to the dislocation pileup on the fiber- matrix interphase is analysised, and the maximum stress in matrix is obtained. Letting maximum stress in matrix equaled to theoretical strength of matrix, the micro strength formation of fiber eutectics is gotten. Finally, considering random orientation and length of fiber eutectics, the macro mechanical strength model of fiber eutectics and transformation particles composite ceramic is built. Result indicates that the fracture strength of composite ceramic has obvious size dependence: the fracture strength of composite ceramic will increase as the diameter of the fiber inclusion in fiber eutectics decrease.

A macro-mechanical constitutive model for shape memory polymer

It is of theoretical and engineering interest to establish a macro-mechanical constitutive model of the shape memory polymer (SMP), which includes the mechanical constitutive equation and the material parameter function, from the viewpoint of practical application. In this paper, a new three-dimensional macro-mechanical constitutive equation, which describes the mechanical behaviors associated with the shape memory effect of SMP, is developed based on solid mechanics and the viscoelasticity theorem. According to the results of the DMA test, a new material parameter function is established to express the relationship of the material parameters and temperature during the glass transition of SMP. The new macro-mechanical constitutive equation and material parameter function are used to numerically simulate the process producing the shape memory effect of SMP, which includes deforming at high temperature, stress freezing, unloading at low temperature and shape recovery. They are also used to investigate and analyze the influences of loading rate and temperature change rate on the thermo-mechanical behaviors of SMP. The numerical results and the comparisons with Zhou’s material parameter function and Tobushi’s mechanical constitutive equation illustrate that the proposed three-dimensional macro-mechanical constitutive model can effectively predict the thermo-mechanical behaviors of SMP under the state of complex stress.

A macro-mechanical constitutive model of shape memory alloys

It is of practical interest to establish a precise constitutive model which includes the equations describing the phase transformation behaviors and thermo-mechanical processes of shape memory alloy (SMA). The microscopic mechanism of super elasticity and shape memory effect of SMA is explained based on the concept of shape memory factor defined by the author of this paper. The conventional super elasticity and shape memory effect of SMA are further unified as shape memory effect. Shape memory factor is redefined in order to make clear its physical meaning. A new shape memory evolution equation is developed to predict the phase transformation behaviors of SMA based on the differential relationship between martensitic volume fraction and phase transformation free energy and the results of DSC test. It overcomes the limitations that the previous shape memory evolution equations or phase transformation equations fail to express the influences of the phase transformation peak temperatures on the phase transformation behaviors and the transformation from twinned martensite to detwinned martensite occurring in SMA. A new macro-mechanical constitutive equation is established to predict the thermo-mechanical processes realizing the shape memory effect of SMA from the expression of Gibbs free energy. It is expanded from one-dimension to three-dimension with assuming SMA as isotropic material. All material constants in the new constitutive equation can be determined from macroscopic experiments, which makes it more easily used in practical applications.

Outer hair cell electromechanical properties in a nonlinear piezoelectric model

A nonlinear piezoelectric circuit is proposed to model electromechanical properties of the outer hair cell (OHC) in mammalian cochleae. The circuit model predicts (a) that the nonlinear capacitance decreases as the stiffness of the load increases, and (b) that the axial compliance of the cell reaches a maximum at the same membrane potential for peak capacitance. The model was also designed to be integrated into macro-mechanical models to simulate cochlear wave propagation. Analytic expressions of the cochlear-partition shunt admittance and the wave propagation function are derived in terms of OHC electro-mechanical parameters. Small-signal analyses indicate that, to achieve cochlear amplification, (1) nonlinear capacitance must be sufficiently high and (2) the OHC receptor current must be sensitive to the velocity of the reticular lamina.

Macromechanical modelling of cosserat elastic and visco-elastic media

В 2009 году исполняется 100 лет со времени опубликования работы Э. и Ф. Коссера [1]. Появление модели континуума Коссера ознаменовало собой начало перехода в теории сплошных сред от механики Ньютона, исходным объектом которой является материальная точка, к механике Эйлера, имеющей в качестве исходного объекта твердое тело. Именно как континуальное обобщение уравнений механики Эйлера модель среды Коссера интересует исследователей. Недостаточная на сегодняшний день практическая применимость модели Коссера обусловлена, главным образом, отсутствием двух факторов: методик надежного определения материальных констант и концепции учета вязкости такой среды. В данной работе предпринимается попытка найти подсказку, как вводить вязкоупругие операторы в уравнение Коссера с помощью модели составного (слоистого) вязкоупругого стержня, идентичного по своим дисперсионным свойствам модели среды Коссера. Деформированное состояние среды Коссера описывается несимметричным тензором деформаций ji γ и тензором изгиба-кручения ji κ [2]:

Macroscopic mechanical properties of metal foam in dependence on the inhomogenities of the mesoscale

AbstractIn this contribution, a way of simulating the influence of the mesoscopic irregular structure of metal foams on the macroscale is shown. To this end, mesoscopic periodic volume elements of a foam are derived in order to compute the mechanical properties including the effects of inhomogenities like imperfections, irregular structure and varying cell wall thicknesses. With the help of these volume elements, which are analysed via the finite element method, and their varying mechanical properties, a local varying stiffness can be computed and inserted into the macromechanical model. In this way the propagation of uncertainities from the mesoscale to the macroscale can be assessed. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Three-dimensional macro-mechanical finite element model for machining of unidirectional-fiber reinforced polymer composites

A three-dimensional macro-mechanical finite element (FE) model is developed to study the machining response of unidirectional (UD) carbon fiber reinforced polymer composites. This study is conducted for a range of fiber orientations, depths of cut and rake angles both experimentally as well as numerically. In the FE model the material properties are assumed as degraded based on the three-dimensional Tsai-Hill failure criterion. Cutting/thrust forces obtained from the FE simulation matches well with the experimental observations. Cutting force increases with fiber orientation and depth of cut but is less influenced by rake angle. Chip formation mechanism is observed under an optical microscope and is compared with FE simulation results. The chip formation mechanism predicted by FE simulations has a good agreement with experimental observations.

Postbuckling analysis of 3D braided composite cylindrical shells under torsion in thermal environments

A postbuckling analysis is presented for a 3D braided composite cylindrical shell of finite length subjected to torsion in thermal environments . Based on a micro–macro-mechanical model, a 3D braided composite may be as a cell system and the geometry of each cell is deeply dependent on its position in the cross section of the cylindrical shell . The material properties of epoxy are expressed as a linear function of temperature. The governing equations are based on a higher-order shear deformation shell theory with a von Kármán–Donnell-type of kinematic nonlinearity and including thermal effects. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, braided composite cylindrical shells with different values of geometric parameter and of fiber volume fraction in different cases of thermal environmental conditions. The results show that the shell has lower buckling loads and postbuckling paths when the temperature-dependent properties are taken into account. The results reveal that the temperature changes, the fiber volume fraction, and the shell geometric parameter have a significant effect on the buckling load and postbuckling behavior of braided composite cylindrical shells. They also confirm that the torsional postbuckling equilibrium path of a moderately thick shell is stable and the shell structure is virtually imperfection–insensitive.

Rate-Dependence of Off-Axis Tensile Behavior of Cross-Ply: CFRP Laminates at Elevated Temperature and Its Simulation

The present paper focuses on experimental verification of the ply-by-ply basis inelastic analysis of multidirectional laminates. First of all, rate dependence of the tensile behavior of balanced symmetric cross-ply T800H/epoxy laminates with a [0/90]3S lay-up under off-axis loading conditions at 100°C is examined. Uniaxial tension tests are performed on plain coupon specimens with various fiber orientations [/(90 – )]3S ( = 0, 5, 15, 45 and 90°) at two different strain rates (1.0 and 0.01%/min). The off-axis stress–strain curves exhibit marked nonlinearity for all the off-axis fiber orientations except for the on-axis fiber orientations = 0 and 90°, regardless of the strain rates. Strain rate has significant influences not only on the off-axis flow stress in the regime of nonlinear response but also on the apparent off-axis elastic modulus in the regime of initial linear response. A macromechanical constitutive model based on a ply viscoplasticity model and the classical laminated plate theory is applied to predictions of the rate-dependent off-axis nonlinear behavior of the cross-ply CFRP laminate. The material constants involved by the ply viscoplasticity model are identified on the basis of the experimental results on the unidirectional laminate of the same carbon/epoxy system. It is demonstrated that good agreements between the predicted and observed results are obtained by taking account of the fiber rotation induced by deformation as well as the rate dependence of the initial Young's moduli.

Postbuckling of 3D braided composite cylindrical shells under combined external pressure and axial compression in thermal environments

A postbuckling analysis is presented for a three-dimensional (3D) braided composite cylindrical shell of finite length subjected to combined loading of external pressure and axial compression in thermal environments. Based on a micro–macro-mechanical model, a 3D braided composite may be a cell system and the geometry of each cell is highly dependent on its position in the cross-section of the cylindrical shell. The material properties of epoxy are expressed as a linear function of temperature. The governing equations are based on a higher order shear deformation shell theory with a von Kármán–Donnell-type kinematic nonlinearity and includes thermal effects. A singular perturbation technique is employed to determine interactive buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, braided composite cylindrical shells with different values of shell geometric parameter and of fiber volume fraction under combined loading conditions. The results show that the shell has lower buckling loads and postbuckling paths when the temperature-dependent properties are taken into account. The effects of temperature rise, fiber volume fraction, shell geometric parameter, load-proportional parameter, as well as initial geometric imperfections are studied.

Postbuckling analysis of three-dimensional textile composite cylindrical shells under axial compression in thermal environments

A postbuckling analysis is presented for a three-dimensional textile composite cylindrical shell of finite length subjected to axial compression in thermal environments. Based on a micro–macro-mechanical model, a three-dimensional textile composite may be as a cell system and the geometry of each cell is deeply dependent on its position in the cross-section of the cylindrical shell. The material properties of epoxy are expressed as a linear function of temperature. The governing equations are based on a higher order shear deformation shell theory with a von Kármán–Donnell-type of kinematic nonlinearity and including thermal effects. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, braided composite cylindrical shells with different values of geometric parameter and of fiber volume fraction in different cases of thermal environmental conditions. The results show that the shell has lower buckling load and postbuckling path when the temperature-dependent properties are taken into account. The results reveal that the temperature changes, the fiber volume fraction, and the shell geometric parameter have a significant effect on the buckling load and postbuckling behavior of textile composite cylindrical shells.

Mechanical properties of ABS resin reinforced with recycled CFRP

This paper presents the mechanical properties of a composite consisting of acrylonitrile-butadiene-styrene (ABS) resin mixed with carbon fiber reinforced plastics (CFRP) pieces (CFRP/ABS). CFRP pieces made by crushing CFRP wastes were utilized in this material. Nine kinds of CFRP/ABS compounds with different weight fraction and size of CFRP pieces were prepared. Firstly, tensile and flexural tests were performed for the specimens with various CFRP content. Next, fracture surfaces of the specimens were microscopically observed to investigate fracture behavior and fiber/resin interface. Finally, the tensile modulus and strength were discussed based on the macromechanical model. It is found that the elastic modulus increases linearly with increasing CFRP content while the strength changes nonlinearly. Microscopic observation revealed that most carbon fibers are separated individually and dispersed homogeneously in ABS resin. Epoxy resin particles originally from CFRP are dispersed in ABS resin and seem to be in good contact with surrounding resin. The modulus and strength can be expressed using a macromechanical model taking account of fiber orientation, length and interfacial bonding in short fiber composites.

High density polyethylene (HDPE): Experiments and modeling

The uniaxial tension (loading and unloading), creep and relaxation experiments on high density polyethylene (HDPE) have been carried out at room temperature. The stress–strain behavior of HDPE under different strain rates, creep (relaxation) behavior at different stress (strain) levels have been investigated. These experimental results are used to compare the simulation results of a unified state variable theory, viscoplasticity theory based on overstress (VBO) and a macro-mechanical constitutive model for elasto-viscoplastic deformation of polymeric materials developed by Boyce et al. (Polymer 41:2183–2201, 2000). It is observed that elasto-viscoplasticity model by Boyce et al. (Polymer 41:2183–2201, 2000) is not good enough to simulate stress–strain, creep and relaxation behaviors of HDPE. However, the aforementioned behaviors can be modeled quantitatively by using VBO model.

A micromechanical model for predicting the fracture toughness of functionally graded foams

In this paper, finite element method based micromechanical analysis is used to understand the fracture behavior of functionally graded foams. The finite element analysis uses a micro-mechanical model in conjunction with a macro-mechanical model in order to relate the stress intensity factor to the stresses in the struts of the foam. The stress intensity factor at the crack tip of the macro-mechanical model can be evaluated using either the J-contour integral or the stresses in the singularity-dominated zone. The fracture toughness is evaluated for various crack positions and length within the functionally graded foam. Then the relationship between the fracture toughness of the graded foam and the local density at the crack tip is studied. Convergence tests for both macro-mechanical and micro-mechanical model analysis were conducted in order to maintain adequate accuracy with reasonable computational time. Fracture toughness of homogenous foams and functionally graded foams for various cases are presented as a function of relative density. This study indicates that the fracture toughness of functionally graded foams mainly depends on the relative density at the crack-tip.

Constitutive model of shape memory alloys: Theoretical formulation and experimental validation

The technological application of nickel–titanium shape memory alloys (SMA) requires a constitutive model that can be easily implemented into numerical methods. It should also be possible for the parameters of this model to be obtained experimentally. For these reasons, macroscopic constitutive models have gained ground in SMA designs. To develop a new macroscopic model that encompasses all the characteristics of these materials over the whole range of transformation temperatures, several macromechanical models have been analysed, evaluated and experimentally validated. From the discrepancies observed in these experimental validations, a model is proposed based on a specific critical stress–temperature diagram. In this model, various laws of evolution are formulated for the martensite fraction. Expressions for the elastic modulus and constitutive transformation tensor are also proposed. Experimental validation showed that this model predicts the behaviour of the material better than the previous models.

Rapid simulation of impacts on composite sandwich panels inducing barely visible damage

The finite element based design tool, CODAC, has been developed for efficiently simulating the impact behavior of sandwich structures consisting of two composite face sheets and a compliant core. To achieve a rapid and accurate stress analysis, three-layered finite shell elements are used. A number of macromechanical damage models are implemented to model damage onset and damage growth. The transient impact analysis is assessed via an experimental impact test program on honeycomb sandwich panels. Force–time histories and damage sizes are examined. The influence of distinct damage and degradation models on the impact response is analyzed. Results show that the presented time-efficient methodology is capable of accurately modeling core failure behavior and rapidly simulating low-velocity impacts which induce barely visible damage.