A new generation of advanced composite materials has recently emerged through the use of Carbon Nanotubes (CNTS) as the reinforcing constituent in polymer matrix. In this paper, the dynamic response of polymer sandwich beams with functionally graded face sheets subject to two successive harmonic moving loads has been studied. Three different patterns of CNTs distributions for the face sheets have been investigated: Uniform Distribution (UD), Symmetrically Functionally Graded (SFG) distribution, and Unsymmetrically Functionally Graded (USFG) distribution. A thorough study on the effects of velocity, position, excitation frequency, and the phase angles of loads has been carried out using the Radial Point Interpolation Meshfree (RPIM) method based on the 2D theory of elasticity. The SFG is found to result in the highest stiffness of all three distribution patterns. Increasing the volume fraction of the reinforcement is seen to have resulted in an increase of around 33% in the flexural rigidity of the SFG beam. Also, decreasing the frequency is seen to have suppressed the deflection of the USFG type up to 90%. The current research presents a reliable computational framework to help provide an insight into the design of an optimum sandwich structure subject to a complicated state of loading.

Aiming for the development of experimentally validated computational models to predict the mechanical properties of 3D-printed composites, the present study proposes a micromechanical approach by using a simplified unit cell model to characterize the material properties and behavior of 3D-printed composites manufactured through fused deposition modeling. The effective properties of the voided polymer matrix phase of the material are computed by calculating the void density as a tensorial meso-structural variable. These effective properties along with those of the fiber are input into a simplified micromechanical model to predict the material properties of the 3D-printed composite. The predictions are seen to be in very good agreement with the experimental values. The present approach is much simpler and less computationally costly compared to the finite element homogenization method. In addition, the present approach has the potential to simulate the response of the 3D-printed composite under different loading conditions.

A new thermodynamic-based model for bone remodeling is introduced. This model is based on chemical kinetics and irreversible thermodynamics in which bone is treated as a self-organizing system capable of exchanging matter, energy and entropy with its surroundings. Unlike the previous works in which mechanical loading is regarded as the only stimulus for bone remodeling, this model establishes a coupling between mechanical loading and the chemical reactions involved in the process of bone remodeling. This model is then incorporated to the finite element software ANSYS in the form of a macro to study bone remodeling after total hip arthroplasty with four different implants: Custom-made titanium, composite, Exceter and Omnifit hip stems. Numerical computations of bone density distribution after total hip arthroplasty indicate that the Omnifit implant with carbon fiber polyamide 12 composite results in minimum resorption in the proximal femur and consequently minimum bone loss due to stress shielding.

A new class of advanced ultralight composite materials has recently emerged through the use porous polymer matrix reinforced by carbon nanotubes. In this article, the dynamic response of functionally graded porous polymeric cylinders, reinforced by randomly oriented single-walled carbon nanotubes, using a meshfree method is studied. Three different porosity distribution patterns are investigated: symmetric distribution (SYD), unsymmetric distribution, and uniform distribution. A thorough study on the effects of reinforcement volume fractions and porosity distribution patterns on the dynamic response of the structure has been carried out using the radial point interpolation meshfree method based on the 2D theory of elasticity. In addition, a Pareto front solution is obtained through a multiobjective optimization aimed at minimizing the weight and maximizing the natural frequency of the structure with porosity and reinforcement volume fraction as design variables. From a design perspective, the results indicate that the SYD porosity type is the best candidate for relatively thick cylinders because of its smaller mass and higher stiffness compared to the other distribution types. The current research presents a reliable computational framework to help provide an insight into the design of an optimum structure subject to dynamic loading.

The present study proposes a stochastic simulation scheme to model reactive boundaries through a position jump process which can be readily implemented into the Inhomogeneous Stochastic Simulation Algorithm by modifying the propensity of the diffusive jump over the reactive boundary. As compared to the literature, the present approach does not require any correction factors for the propensity. Also, the current expression relaxes the constraint on the compartment size allowing the problem to be solved with a coarser grid and therefore saves considerable computational cost. The modified algorithm is then applied to simulate three reaction-diffusion systems with reactive boundaries.

Polymer matrix composites (PMC’s) are widely used in critical aerospace structures due to their numerous advantageous mechanical properties. Recently, PMC’s have been considered for high temperature applications where viscoelasticity arising from the time dependent nature of the polymer matrix becomes an important consideration. This inherent viscoelasticity can significantly influence deformation, strength and failure response of these materials under different loading modes and environmental factors. With a potentially large number of plies of different fiber directions and perhaps material properties, determining a fatigue failure criterion of any degree of generality through experiments only, may seem to be an unrealistic task. This difficult situation may be mitigated through the development of suitable theoretical micro or macro mechanical models that are founded on considering the fatigue failure of the constituting laminas. The micro‐approach provides a detailed examination of the individual failure modes in each of the constituent materials i.e. fiber, matrix. In this work, a micromechanical approach is used to study the role of viscoelasticity on the fatigue behavior of polymer matrix composites. In particular, the study examines the interaction of fatigue and creep in polymer matrix composites. The matrix phase is modeled as a vicoelastic material using Schapery’s single integral constitutive equation. Taking viscoelsticity into account allows the study of creep strain evolution during the fatigue loading. The fatigue failure criterion is expressed in terms of the fatigue failure functions of the constituent materials. The micromechanical model is also used to calculate these fatigue failure functions from the knowledge of the S‐N diagrams of the composite material in longitudinal, transverse and shear loadings thus eliminating the need for any further experimentation. Unlike the previous works, the present study can distinguish between the strain evolution due to fatigue and creep. The results can clearly show the contribution made by the effect of viscoelasticity to the total strain evolution during the fatigue life of the specimen. Although the effect of viscoelsticity is found to increase with temperature, its contribution to strain development during fatigue is compromised by the shorter life of the specimen when compared to lower temperatures.

A numerically efficient globally averaged number density approach is used to simulate a reaction-diffusion system using a particle-based stochastic simulation algorithm called reactive multiparticle collision (RMPC) dynamics. Constant diffusivity of the particles is achieved through a time-varying rotation angle (also called collision angle). Variation in the diffusion coefficient between two different chemical species is achieved in one of two ways: (ⅰ) using a different kBT/m value for one species compared to the other, or (ⅱ) using the same kBT/m value for both species, but using a different probability to free-stream for one species compared to another. For smaller diffusivities and larger spatial inhomogeneities, bath particles were necessary for the model to agree with the PDE solution. The latter approach was further used without a bath, and shown to be capable of producing Turing patterns after long simulation times. The significance of our work is that RMPC can serve as a feasible simulation tool for both short and long-term simulations, can handle spatial inhomogeneities, can model a fairly large range of diffusivities in a reaction-diffusion scenario, and is capable of producing Turing patterns. An advantage of this method includes more detailed system information in feasible simulation times.

The present paper introduces a new micro-meso hybrid algorithm based on the Ghost Cell Method concept in which the microscopic subdomain is governed by the Reactive Multi-Particle Collision (RMPC) dynamics. The mesoscopic subdomain is modeled using the Reaction-Diffusion Master Equation (RDME). The RDME is solved by means of the Inhomogeneous Stochastic Simulation Algorithm. No hybrid algorithm has hitherto used the RMPC dynamics for modeling reactions and the trajectories of each individual particle. The RMPC is faster than other molecular based methods and has the advantage of conserving mass, energy and momentum in the collision and free streaming steps. The new algorithm is tested on three reaction-diffusion systems. In all the systems studied, very good agreement with the deterministic solutions of the corresponding differential equations is obtained. In addition, it has been shown that proper discretization of the computational domain results in significant speed-ups in comparison with the full RMPC algorithm.

The incapability of classical elasticity theory of accurately modeling the deformation behavior of structures at micro- and nanoscales has necessitated the development of more advanced theories. The strain gradient theory, being one of such theories, involves higher-order spatial derivatives of the field variables. However, except for few cases, there exists no analytical solution based on the strain gradient theory. This paper proposes a novel meshfree method with modified point interpolation functions possessing the Kronecker delta property; it is proposed to incorporate the strain gradient formulation into the Euler–Bernoulli beam theory. In the present method, the continuity of the shape function and its higher derivatives, appearing in the general form of the strain gradient theory, can be much more conveniently accommodated compared to the FEM. In addition, the present approach is based on the global weak form which is computationally less costly as compared to meshfree methods based on local weak form. The validity of the method is demonstrated by comparing the results with both analytical and experimental results for beams at macro- and microscales for static and dynamic loadings.

In the present study, an off-lattice particle-based method called the reactive multi-particle collision (RMPC) dynamics is extended to model reaction-diffusion systems with reactive boundary conditions in which the a priori diffusion coefficient of the particles needs to be maintained throughout the simulation. To this end, the authors have made use of the so-called bath particles whose purpose is only to ensure proper diffusion of the main particles in the system. In order to model partial adsorption by a reactive boundary in the RMPC, the probability of a particle being adsorbed, once it hits the boundary, is calculated by drawing an analogy between the RMPC and Brownian Dynamics. The main advantages of the RMPC compared to other molecular based methods are less computational cost as well as conservation of mass, energy and momentum in the collision and free streaming steps. The proposed approach is tested on three reaction-diffusion systems and very good agreement with the solutions to their corresponding partial differential equations is observed.

ABSTRACTA novel micromechanical approach is proposed to calculate the effective thermal conductivities of fiber reinforced composite materials. The key advantage of the present formulation is its ability to yield closed form solutions for the effective thermal conductivity of composites in both longitudinal and transverse directions for three dimensional heat transfer problems. The obtained results are in good agreement with the experimental data reported in the literature. When compared with analytical and finite element solutions, the results are seen to be in better agreement with the hexagonal packed array compared to the square packed array which thus represents a more realistic model of the fiber distribution in the matrix medium.

The use of Carbon Nanotubes as the reinforcing constituent for polymer matrix composites in place of conventional fibers has led to the emergence of a new generation of advanced composite materials. In this paper, the free vibration of functionally graded nanocomposite beams on elastic foundations are studied. Three different types of Carbon Nanotubes distributions in the polymer matrix material are studied; Uniform distribution, symmetrically functionally graded distribution and unsymmetrically functionally graded distribution. The analysis is carried out by a mesh-free method using the two-dimensional theory of elasticity. The Moving Least Square shape functions are implemented to approximate the displacement field. Due to the absence of the Kronecker delta property of the shape functions, a transformation technique is used to apply the essential boundary conditions. After validation, the effects of different design parameters such as Carbon Nanotubes distribution, slenderness ratios, boundary conditions and foundation stiffness on the vibrational behavior of the structure are investigated. It can be seen that from a design perspective, the vibrational response of a FG structure may be controlled in two ways; one way is through changing the distribution of the CNT's in the matrix material and the other way is by changing stiffness of the elastic foundation on which it is resting. A notable observation is that increasing the stiffness of the foundation will move the neutral axis away from the foundation support of the beam. The current approach can serve as a benchmark against which other semianalytical and numerical methods based on classical beam theories can be compared.

In this paper, the dynamic response of functionally graded nanocomposite beams under the action of a moving load are investigated. Three different types of Carbon NanoTubes (CNT's) distributions in a polymer matrix material are studied; Uniform Distribution (UD), Symmetrically Functionally Graded (SFG) distribution and Unsymmetrically Functionally Graded (USFG) distribution. The analysis is carried out by a mesh-free method using the two-dimensional theory of elasticity. After validation, the effects of different design parameters such as CNT's distribution, the velocity and position of the moving load on the dynamic behavior of the beam are examined. The results also highlight the importance of the reinforcement distribution type from a design perspective. The current approach can serve as a benchmark against which other semi-analytical and numerical methods based on classical beam theories can be compared.

Many chemical reactions, such as gene transcription and translation in living cells, need a certain time to finish once they are initiated. Simulating stochastic models of reaction-diffusion systems with delay can be computationally expensive. In the present paper, a novel hybrid algorithm is proposed to accelerate the stochastic simulation of delayed reaction-diffusion systems. The delayed reactions may be of consuming or non-consuming delay type. The algorithm is designed for moderately stiff systems in which the events can be partitioned into slow and fast subsets according to their propensities. The proposed algorithm is applied to three benchmark problems and the results are compared with those of the delayed Inhomogeneous Stochastic Simulation Algorithm. The numerical results show that the new hybrid algorithm achieves considerable speed-up in the run time and very good accuracy.

The viscoelastic behavior of a RP46 polyimide resin is characterized at high temperature and the results are used within a micromechanical model to predict the viscoelastic response of a RP46 based carbon fiber composite. The creep master curve of the neat resin is obtained using the time temperature superposition principle (TTSP) from creep tests at three different temperatures, namely 180, 220, and 270°C. The viscoelastic behavior of RP46 is modeled based on Schapery's single integral constitutive equation whose Prony Series coefficients are obtained from the master curve. The acquired properties are then incorporated into a Simplified Unit Cell Micromechanical model to study the creep response of a RP46 resin based composite system. The advantage of this particular micromechanical model lies in its ability to give closed form expressions for the effective viscoelastic response of unidirectional composites as well as each of their constituents. Two types of nonlinearities were observed, one due to stress and the other due to temperature. Both of these nonlinearities can be modeled through the use of proper coefficients in the constitutive equation of the matrix material. The model predictions are found to be in good agreement with experimental results obtained from tests conducted on the RP46 resin based composite system. POLYM. COMPOS., 37:1407–1414, 2016. © 2014 Society of Plastics Engineers

A micromechanical approach is adopted to study the role of viscoelasticity on the fatigue behavior of polymer matrix composites. In particular, the study examines the interaction of fatigue and creep in angle ply carbon/epoxy at 25 and 114 °C. The matrix phase is modeled as a vicoelastic material using Schapery’s single integral constitutive equation. Taking viscoelsticity into account allows the study of creep strain evolution during the fatigue loading. The fatigue failure criterion is expressed in terms of the fatigue failure functions of the constituent materials. The micromechanical model is also used to calculate these fatigue failure functions from the knowledge of the S-N diagrams of the composite material in longitudinal, transverse and shear loadings thus eliminating the need for any further experimentation. Unlike the previous works, the present study can distinguish between the strain evolution due to fatigue and creep. The results can clearly show the contribution made by the effect of viscoelasticity to the total strain evolution during the fatigue life of the specimen. Although the effect of viscoelsticity is found to increase with temperature, its contribution to strain development during fatigue is compromised by the shorter life of the specimen when compared to lower temperatures.

The present study introduces a progressive fatigue damage model within a multiscale framework by incorporating a Simplified Unit Cell Micromechanical model into a Finite Element program. The use of micromechanics will allow the study of damage at the micro-scale which can therefore identify modes of failure in each of the composite’s constituents, separately. The use of finite element method at the macro-scale enables the model to capture the geometric complexities including regions of stress concentration, which expedites the failure of the material. Damage progression is modeled through the degradation of the material property corresponding to the failure mode detected by the micromechanical model. The results of the model are in good agreement with the experimental data for both unidirectional and multidirectional laminates. The present approach is capable of predicting the fatigue life of composite laminates of any arbitrary geometry and lay-up configuration with minimum dependence on empirical parameters.

In this work, the thermomechanical viscoelastic response of a high temperature polymer matrix composite system made up of T650-35 graphite fibers embedded in PMR-15 resin is studied through a micromechanical model based on the assumptions of simplified unit cell method within a temperature range of 250–300℃ corresponding to aerospace engine applications. The advantage of this particular micromechanical model lies in its ability to give closed-form expressions for the effective viscoelastic response of unidirectional composites as well as each of their constituents. Using the experimental data of the creep behavior of thermostable PMR-15 polyimide, the micromechanical model is first calibrated to account for the effect of temperature. The resulting elastic and viscoelastic responses are found to be in good agreement with the existing experimental data. The validated model is then used to predict the behavior of the composite material under different combinations of thermal and mechanical loadings. The results clearly demonstrate the importance of accounting for the viscoelastic effect of the matrix material as the temperature increases. Current works on modeling temperature-dependent viscoelastic behavior of polymer matrix composites are mainly based on the assumption of thermorheologically simple material. However, through the present approach where the matrix is modeled as a thermorheologically complex material, the effect of temperature on the elastic and viscoelastic response of the composite system can be individually investigated.

In the present study, a generalized three-dimensional (3D) energy-based criterion for the creep failure of viscoelastic materials is developed. Unlike the existing approaches which are restricted to uniaxial loading, the proposed criterion can predict failure under any combination of loads. This criterion is then incorporated into a simplified unit cell micromechanical model to predict the time-delayed failure of unidirectional polymer–matrix composites at elevated temperatures. The composite material used in this study is T300/934 which is suitable for service at high temperatures in aerospace applications. The use of micromechanics can give a more accurate insight into the failure mechanisms of the composite materials, in particular at high temperatures, where the general behavior of the polymer–matrix composite is governed by matrix viscoelasticity and matrix time-dependent failure due to creep is a localized phenomenon. The micromechanical model is also used to estimate the ultimate strength of the constituents from the knowledge of the allowable strengths of the unidirectional composite in the principal material directions. The obtained creep failure stresses are found to be in reasonable agreement with the experimental data particularly for the 90° unidirectional laminate, where failure is totally matrix dominated.

In the present study, a novel micromechanical approach is introduced to study the time-dependent failure of unidirectional polymer matrix composites. The main advantage of the present micromechanical model lies in its ability to give closed-form solutions for the effective nonlinear response of unidirectional composites and to predict the material response to any combination of shear and normal loading. The creep failure criterion is expressed in terms of the creep failure functions of the viscoelastic matrix material. The micromechanical model is also used to calculate these creep failure functions from the knowledge of the creep behavior of the composite material in only transverse and shear loadings, thus eliminating the need for any further experimentation. The composite material used in this study is T300/934, which is suitable for service at high temperatures in aerospace applications. The use of micromechanics can give a more accurate insight into the failure mechanisms of the composite materials in particular at high temperatures where the general behavior of the polymer matrix composite is governed by matrix viscoelasticity and the time-dependent failure of the matrix is a localized phenomenon. The obtained creep failure stresses are found to be in reasonable agreement with the experimental data.