Composite Constitutive Model Research Articles

Numerical studies of one-way Lamb and SH mixing method in composite laminates with transverse-isotropic quadratic nonlinearity

Abstract The resonant behavior of one-way Lamb and SH (shear horizontal) mixing method in composite laminates with transverse-isotropic quadratic nonlinearity is investigated through numerical simulations in this paper. Different from previous studies, the composite constitutive model is combined from orthotropic elasticity and transverse-isotropic quadratic nonlinearity, which is implemented by ABAQUS/VUMAT subroutine. When two fundamental waves (S 0-mode Lamb waves and SH 0 waves) mix in composite laminates with quadratic nonlinearity, the resonant SH 0 waves can be generated with the resonance condition ω S 0 /ω SH 0 = 2 κ/(κ + 1). Meanwhile, the relationships between the acoustic nonlinear parameter (ANP) and damage degree, fundamental frequency, frequency deviation, propagation distance are also investigated. Moreover, the method of locating the damage region in composite laminates is proposed and verified by using the resonant wave time-domain signal.

Mechanical-permeability characteristics of composite coal rock under different gas pressures and damage prediction model

Determining the influence of gas pressure on the mechanics, permeability, and energy evolution of gas-bearing composite coal is helpful to better understand the formation process and prevention measures of gasdynamic disasters. In this paper, true triaxial mechanical-permeability tests are carried out on the gas-bearing composite coal rock under different gas pressures, focusing on the influence of gas pressure on the mechanics, permeability, and energy response characteristics of the composite coal rock, and a damage constitutive model based on energy dissipation is established. The results show that increasing the gas pressure decreases the load bearing capacity, strain, pre-peak relative permeability, and deformation capacity of the sample. The greater the gas pressure is, the greater the relative permeability decreases and the greater the post-peak relative permeability increases. The gas pressure has a great influence on the energy of the sample. The elastic strain energy ratio (Ue/U) increases with the increase in gas pressure, and the dissipative energy ratio (Ud/U) decreases with the increase in gas pressure. The coal-rock composite constitutive model based on energy dissipation is in good agreement with the experimental curves.

Effective magnetoelastic responses of hybrid fiber composites with viscoelastic matrices

This study examines the overall magnetoelastic responses of unidirectional fiber composites constructed by magnetostrictive fibers embedded in viscoelastic polymer matrices that had been reinforced by stiff fillers. In some polymer-based fiber composites, modifying polymer’s property by infiltrating particulate fillers is necessary. To design such hybrid composite systems with magnetoelastic coupling, it requires a detailed understanding of aggregate responses. In this study, we formulate a composite constitutive model based on a two-scale homogenization scheme for effective coupled viscoelastic and magnetoelastic responses for hybrid fiber composites. We first verify the validity of the model by comparing the predictions with experimental results available in literatures. We next investigate the performance of a hybrid composite in light of blocked stress and free strain which are two common factors of characterizing sensors and actuators. We finally elucidate how viscoelastic polymer matrices affect the overall magnetoelastic responses and ΔE-effect phenomenon in terms of some critical parameters such as phase concentrations, loading rates, prestresses and temperatures. The findings of this study serve as a preliminary guidance for the rational design of hybrid magnetostrictive composite materials. The proposed mathematics model can further integrate into a finite element framework for composite structure analysis.

A new woven composite constitutive model validated by shock wave experiments

In this paper, we present results of plate impact simulations of shock compressed woven glass fiber-reinforced plastic (GRP) performed using the Arbitrary Lagrangian–Eulerian three-dimensional finite element code. A hyperelastic large-strain-based empirical Continuum Damage Mechanics (CDM) formulation is employed to describe damage initiation and growth in the shock-compressed GRP. The model parameters calibration scheme utilizes the Velocity Interferometer System for Any Reflector normal particle velocity measurements at the free surface of the GRP target plates. The impact velocity in the experiments ranged from 8.5 to 418 m/s. The finite element model considered planar 0°/90° bidirectional plies with an individual ply thickness of 0.68 mm, stacked to reach a total laminate thickness of 6.8 mm. The anisotropic elastic strains were estimated from the experimentally determined tetragonal symmetry stiffness matrix for the GRP. The strain-based damage model captures several salient features observed in the measured free surface particle wave profiles, including the shock rise time, onset of Elastic—Elastic Cracking, and the shape of the nonlinear portion of the experimental particle velocity profiles. The CDM model predicts the dominant damage mode to be matrix microcracking due to shear and the associated bulk expansion (bulking) under the global compressive loading in the plate impact configuration.

Thermo-mechanical analysis of laminated composites shells exposed to fire

This paper describes the research performed within the scope of H2020 project FIBRESHIP in the development and validation of a thermo-mechanical model to assess the fire performance of composite structures. A one-dimensional thermal model with pyrolysis is used to obtain the temperature profile across the thickness, and later, introduced in the thermo-mechanical model with a quadrilateral shell element approach. The composite constitutive model employed is the so-called Serial/Parallel Rule of Mixtures (SPROM) which has been modified to introduce the effect of the thermal deformation. A set of experimental tests are then used to validate the correctness of the numerical method proposed. The experimental data used to validate the thermal model is the classic Henderson experimental test. The thermo-mechanical coupling is validated against an original vertical furnace test of an FRP ship’s bulkhead, following on the 2010 FTP Code standards. These validations demonstrate the correctness and accuracy of the proposed decoupled thermo-mechanical formulation.

Contact characteristics of steel-rubber rollers based on modified contact theory considering viscoelasticity

This paper mainly studied the contact characteristics of steel-rubber rollers. First, according to the dynamic mechanical experimental data of rubber, the hyperelastic-viscoelastic composite constitutive model was constructed to accurately describe the properties of rubber. Then, for the contact problem of steel-rubber rollers, the elastic modulus of rubber presents an instantaneous change due to the influence of rubber's viscoelasticity, so the Hertz contact theory was modified through the instantaneous elastic modulus. Next, a dimensionless parameter [Formula: see text] was constructed to judge the viscoelastic influence degree of rubber. Finally, based on modified contact theory and the dimensionless parameter [Formula: see text], the influence of compressive force and rolling speed on the contact characteristics of steel-rubber rollers was analyzed. The research in this paper is helpful to the analysis of dynamic contact problem of rollers structure and the development of contact theory.

Designing and modeling new generation of advanced hybrid composite sandwich structure armors for ballistic threats in defense applications

Composite sandwich structures under ballistic impact loading can be a key point in the design for defense applications. This paper presents new armor designs consist of two composite plates with honeycomb core subjected to ballistic impact via 0.3-caliber Armor-Piercing projectile APM2. The numerical modeling of composite materials poses high challenges in simulating their anisotropic behavior under impact loading. Optimizing the failure criteria and examining the influence of changing the materials on ballistic response and energy absorption are considered. An enhanced composite constitutive model for composite plates and Johnson–Cook constitutive model for metallic honeycomb core are employed to permit the simulation of dynamic plastic deformations with the failure mechanisms during impact loading in LS-DYNA. A three-dimensional simulation is employed as highly efficient through the back-analysis of laboratory tests. The results of the numerical simulations are found to be in good agreement with the experimental results. Numerical studies are performed to assess the effects of different composite materials and various aluminum alloys for honeycomb core with different impact velocities on the behavior of hybrid composite sandwich armor. The proposed armor design can introduce a significant influence on enhancing the new armors generations and achieving good sturdiness and lightweight armors for defense applications.

The Effect of Steel Reinforcement on Seismic Damage to Concrete Gravity Dams Based on Distributed-Steel Model

Tensile cracking at the position where geometry changes is a typical failure mode of gravity dams under strong earthquakes. Steel reinforcement has been proposed to reduce the degree of dam cracking. In this paper, a nonlinear model is presented to consider the interaction effect between the steel reinforcement and the dam concrete in a combined concrete damage model and distributed-steel model. In the model, a composite constitutive model of a steel reinforcement-concrete element is proposed. The approach can model the process of gradual degradation of the concrete loading capacity and load transfer to the steel reinforcement by establishing the concrete and steel models separately. Taking a typical gravity dam with positions where geometry changes upstream and downstream as a case study, the influence of steel reinforcement on seismic damage of the gravity dam is investigated. The analytical results show that the steel reinforcement strengthening prevents cracks thoroughly around the elevation of the downstream slope change. However, the cracking around the elevation of the upstream slope change extends to the downstream direction. This reflects the transfer of fracture energy release during the cracking process.

Analysis of rolling on steel and rubber-covered rollers using viscoelasticity

In this article, a series of analysis were performed on a two-dimensional structure of steel and rubber-covered rollers. First, a hyperelastic–viscoelastic composite constitutive model based on a dynamic mechanical experiment of rubber was formulated to accurately describe rubber properties. Meanwhile, a hyperelastic constitutive model not considering viscoelasticity was set as the control group. The material used in this article was the nitrile rubber with the Shore hardness of 40. Then, the effects of viscoelasticity on the von Mises stress were analyzed by comparing results of two models. The influences of working conditions (roller speeds/compression displacement) on the von Mises stress and the area of hysteresis loop were also studied. Next, the contact characteristics under different working conditions and constitutive models were analyzed combining viscoelasticity. A verification experiment of contact width was carried out, and the theoretical and simulated values were calculated and compared. Finally, the relation of “low peak” phenomenon with viscoelasticity was studied, and the effects of working conditions and rubber viscoelasticity on contact feature of rollers were summarized. The conclusions of the article can help engineers to better optimize dynamic working conditions and judge the working state of the structure.

Implementation of a tabulated failure model into a generalized composite material model

The need for accurate material models to simulate the deformation, damage, and failure of polymer matrix composites under impact conditions is becoming critical as these materials are gaining increased use in the aerospace and automotive communities. To attempt to improve the predictive capability of composite impact simulations, a next generation material model is being developed for incorporation within the commercial transient dynamic finite element code LS-DYNA. The material model, which incorporates plasticity, damage, and failure, utilizes experimentally based tabulated input to define the evolution of plasticity and damage and the initiation of failure as opposed to specifying discrete input parameters such as modulus and strength. The plasticity portion of the composite constitutive model is based on an extension of the Tsai-Wu composite failure model into a generalized yield function. For the damage model, a strain equivalent formulation is used to allow for the uncoupling of the deformation and damage analyses. For the failure model, a tabulated approach is utilized in which a stress- or strain-based invariant is defined as a function of the location of the current stress state in stress space to define the initiation of failure. Failure surfaces can be defined with any arbitrary shape, unlike traditional failure models where the mathematical functions used to define the failure surface impose a specific shape on the failure surface. In the current paper, the complete development of the failure model is described and the generation of a tabulated failure surface for a representative composite material is discussed.

Grain size effect on mechanical behavior of thin pure titanium foils at elevated temperatures

To contribute to process design of microforming at elevated temperatures, the effect of grain size on mechanical behavior of pure titanium foils was studied. Uniaxial tensile tests and microbending tests were performed at different temperatures of 298, 433, 573, and 723 K and at different strain rates of 10−3, 10−2, and 10−1 s−1. Pure titanium (Ti) foils with various grain sizes of 2.7–42.4 µm were used. As results, flow stress of Ti foils with a larger grain size showed stronger dependency on the temperature and strain rate conditions. In particular, both the reduction rate of the yield stress and that of the ultimate tensile strength relative to that at 298 K increased with increasing grain size at higher strain rates of 10−2 and 10−1 s−1. However, only at a higher temperature and at a lower strain rate of 10−3 s−1, the flow stress increased for the foils with larger grain sizes. This is attributed to the dynamic strain aging, which is known as hardening behavior due to the diffusion of additional inclusion under higher temperatures. Furthermore, in microbending tests, the reduction rate of springback angle by increasing temperature also increased with increasing grain size. This is attributed to the increased reduction of strain gradient of the foils with a larger grain size. To clarify the mechanism of grain size effect on the mechanical behavior of pure Ti foils deformed at high strain rates, a composite constitutive model involving statistically stored dislocations (SSDs) and geometrically necessary dislocations (GNDs) was built with the capability of being employed at elevated temperatures. The effect of strain gradient on the material behavior was discussed in terms of its relationship with the density of GNDs.

A composite approach for modeling deformation behaviors of thermoplastic polyurethane considering soft-hard domains transformation

Thermoplastic polyurethane elastomers (TPUs) are the most used engineering thermoplastics combining the properties for both elastomers and glassy materials. TPUs have good physical and mechanical properties, excellent chemical and abrasion resistances. Compared with typical thermoset rubbers, TPUs are easier to be processed and recycled. However, the deformation behaviors of TPUs are very complex due to their nonlinear, hysteresis, rate and temperature dependences, and softening properties. Therefore, development of a constitutive model with microstructure considerations is important for predicting the deformation behavior of TPUs under mechanical loading as well as during forming processes such as rolling and stretching. In this work, TPUs were taken as a two-phase material consisting of both hard and soft phases corresponding to their hard and soft domains. A new composite constitutive model for stress-strain response of TPUs was proposed taking into account the microstructure of TPUs as well as its evolution (hard to soft phase transformation) induced by deformation. Excellent agreement between model predictions and experimental results for the loading-unloading behaviors of two TPUs with different hard and soft segment contents confirmed the efficacy of our proposed composite constitutive model.

Tensile Stability of Medial Arterial Tissues

Tensile stability of healthy medial arterial tissue and its constituents, subject to initial geometrical and/or material imperfections, is investigated based on the long wavelength approximation. The study employs existing constitutive models for elastin, collagen, and vascular smooth muscle which comprise the medial layer of large elastic (conducting) arteries. A composite constitutive model is presented based on the concept of the musculoelastic fascicle (MEF) which is taken to be the essential building block of medial arterial tissue. Nonlinear equations governing axial stretch and areal stretch imperfection growth quantities are obtained and solved numerically. Exact, closed-form results are presented for both initial and terminal rates of imperfection growth with nominal load. The results reveal that geometrical imperfections, in the form of area nonuniformities, and material imperfections, in the form of constitutive parameter nonuniformities, either decrease or increase only slightly with increasing nominal load; a result which is to be expected for healthy tissue. By way of contrast, an examination of a simple model for elastin with a degrading stiffness gives rise to unbounded imperfection growth rates at finite values of nominal load. The latter result indicates how initial geometrical and material imperfections in diseased tissues might behave, a topic of future study by the authors.

Evaluation of a strain based failure criterion for the multi-constituent composite model under shock loading

This study details and demonstrates a strain-based criterion for the prediction of polymer matrix composite material damage and failure under shock loading conditions. Shock loading conditions are characterized by high-speed impacts or explosive events that result in very high pressures in the materials involved. These material pressures can reach hundreds of kbar and often exceed the material strengths by several orders of magnitude. Researchers have shown that under these high pressures, composites exhibit significant increases in stiffness and strength. In this work we summarize modifications to a previous stress based interactive failure criterion based on the model initially proposed by Hashin, to include strain dependence. The failure criterion is combined with the multi-constituent composite constitutive model (MCM) within a shock physics hydrocode. The constitutive model allows for decomposition of the composite stress and strain fields into the individual phase averaged constituent level stress and strain fields, which are then applied to the failure criterion. Numerical simulations of a metallic sphere impacting carbon/epoxy composite plates at velocities up to 1000 m/s are performed using both the stress and strain based criterion. These simulation results are compared to experimental tests to illustrate the advantages of a strain-based criterion in the shock environment.

Comparison of a composite model and an individually fiber and matrix discretized model for kink band formation

Failure by kink band instability in a unidirectional fiber composite is analyzed. A micromechanical discretized finite element model is used and compared to an existing composite constitutive model. The comparison is made in a fiber angle vs. applied compressive stress space. An investigation on the relation between the kink band angle and the fiber angle is conducted in the postbuckling regime. The critical kink band angle is examined for different initial fiber misalignment angles.

Orthotropic composite constitutive model of mineral–asphalt mix reinforced with grid and its approximation with an isotropic model

A theoretical model for an elastic anisotropic composite of road mixtures reinforced with grids together with its isotropic approximation is proposed. In the considered models, some elements of the mechanics of fibrous composite materials and optimisation theory are used. A composite model is an energy model; that is, constitutive relationships result from the differentiation of the stored energy function arising from two summed parts corresponding to the matrix and reinforcement grid energy via mixture theory. The obtained model is incorporated into the commercial finite element program ABAQUS via a user subroutine written in Fortran. The correctness of the proposed composite constitutive model has been tested by a numerical solution (with the application of a finite element program) of the structure, in which the matrix is modelled as a three-dimensional continuum region and the reinforcement as working in one dimension a set of truss elements. In addition, in the paper the proposition of approximation of the composite orthotropic model with an isotropic one is presented. The interpretation and application of this approximation are analysed. The energetically equivalent isotropic model for the layer with grid reinforcement can be directly used in standard programs used for designing road pavements with mechanistic methods.

A strain-gradient plasticity theory of bimodal nanocrystalline materials with composite structure

For the purpose of evaluating the mechanical property of bimodal nanocrystalline (nc) materials, a new composite constitutive model comprised of coarse grains evenly distributed in the nc matrix with respect to strain gradient has been developed. Due to their dissimilar properties and mismatch between the two phases, dislocation-controlling mechanism based on the statistically stored dislocations (SSDs) and geometrically necessary dislocations (GNDs) was analyzed and extended to consider the different influences of two parts in the composite model. We firstly built a stress–strain relation for strain gradient plasticity to predict the effect of grain size distribution on the flow stress. To describe the strain strength quantitatively, a strain-hardened law determined from strain gradient and a nanostructure characteristic length parameter were developed. The strain-hardened law and nanostructure characteristic length parameter were not the same as described in classical strain gradient theory.

Effects of strain gradient on the mechanical behaviors of nanocrystalline materials

For the purpose of evaluating the effects of strain gradient on the mechanical behavior of nanocrystalline (NC) materials, a new composite constitutive model comprised of grain interior (GI) regarded as an ordered crystal phase and plastically softer grain boundary affected zone (GBAZ) phase with respect to strain gradient has been developed. Due to their dissimilar properties and mismatch between the two phases, dislocation-controlling mechanism based on the statistically stored dislocations (SSDs) and geometrically necessary dislocations (GNDs) was analyzed and extended to NC regime to consider the different influences of two parts in the composite model, respectively. A stress–strain relation for strain gradient plasticity was firstly built to predict the effect of grain size on the flow stress. To describe the strain strength quantitatively, a strain-hardened law determined from strain gradient and a nanostructure characteristic length parameter which differed from that of classical strain gradient theory were introduced in detail. It was shown that the strain gradient in NC materials contributes directly to the mechanical behaviors of this sort of materials and cannot be neglected.

Evaluation of a composite damage constitutive model for PP composites

Glass mat or chopped fiber reinforced polypropylene (PP) composites are interesting alternatives to steel for vehicle closure applications. The current work evaluates the application of the CODAM model, a damage mechanics based composite constitutive model, for impact simulation of PP composites. As the first step, the damage parameters in the CODAM model were determined for a PP composite. This paper presents the process for determining tensile, compression and shear damage parameters through correlation of finite element (FE) simulations with standard material test results, including tensile, compression, compact tension and Iosipescu shear tests; also a preliminary validation of the model is presented with driven dart impact experiments.

A Constitutive Model for Glass Fibre Fabric Composites under Impact

A new composite constitutive failure model for woven glass fibre fabric reinforced with epoxy/polyester was developed, and implemented into an explicit dynamic non-linear finite element code for both the shell and solid element implementation. The approach uses a novel damage mechanics formulation to predict both matrix cracks and fibre fracture in the warp and weft directions with the woven fabric composite, subject to an impact or other dynamic event. Strain-rate effects are implicitly incorporated into the model using a damage lag methodology. Results are compared with laboratory composite beam and plate impact experiments. The comparisons indicate that the damage model can predict with reasonable accuracy the damage modes observed in the laboratory experiments. Conclusions are presented also on the logical extensions to the damage formulation necessary to improve both the accuracy and the scope of composite materials that may be analysed.