Volume-averaged Stress Research Articles

Characterization of cellular responses and cell lysis to elevated hydrodynamic stress from benchtop perfusion bioreactors.

The effective design of perfusion cell culture is currently challenging regarding balancing the operating parameters associated with the hydrodynamic conditions due to increased system complexity. To address this issue, cellular responses of an industrial CHO cell line to different types of hydrodynamic stress in benchtop perfusion bioreactors originating from agitation, sparging, and hollow fibers (HF) in the cell retention devices were systematically investigated here with the analysis of cell lysis. It was found that cell lysis was very common and most associated with the sparging stress, followed by the HF and lastly the agitation, consequently heavily impacting the estimation of process descriptors related to biomass. The results indicated that the agitation stress led to a reduced cell growth with a shift toward a more productive phenotype, suggesting an energy redirection from biomass formation to product synthesis, whereas the sparging stress had a small impact on the intracellular metabolic flux distribution but increased the cell death rate drastically. For HF stress, a similar cell maintenance profile was found as the sparging while the activity of glycolysis and the TCA cycle was significantly impeded, potentially leading to the lack of energy and thus a substantial decrease in cell-specific productivity. Moreover, a novel concept of volume average shear stress was developed to further understand the relations of different types of stress and the observed responses for an improved insight for the perfusion cell culture.

Computer homogenization of porous piezoceramics of different ferrohardness with random porous structure and inhomogeneous polarization field

The article is concerned with the homogenization problems, in which the effective moduli of porous piezoceramic composites are determined taking into account the inhomogeneity of the polarization field. The homogenization problems are solved by the finite element method in the framework of the theory of effective moduli and the Hill energy principle using the ANSYS package. To this end, in static problems of electroelasticity, the displacements and electric potential, which are linear in spatial variables, are specified on the boundary of a representative volume to provide constant stress and electric induction fields for a homogeneous reference medium. After solving a set of boundary value problems under different boundary conditions and determining the volume-averaged stress components and the electric induction vector, a complete set of effective moduli for the piezoelectric composite is calculated. A representative volume of the piezocomposite is created in the form of a regular finite element mesh consisting of cubic elements. Pores in the representative volume are assumed to be filled with a piezoelectric material with extremely small moduli. Finite elements with pore properties are selected according to a simple random algorithm. The inhomogeneous polarization field is found by solving an electrostatic problem, in which the polarization process in the representative volume is modeled based on a simplified linear formulation. The local coordinate systems for individual finite elements of the composite matrix are specified by the directions of the polarization vectors. In the following, when solving the problems of electroelasticity, these local coordinate systems associated with the elements of the piezoelectric matrix allow recalculating the material properties according to the formulas of transformation of the tensor components as the coordinate systems rotate. In addition, consideration is given to different models describing the change in the moduli of the material from an unpolarized state to a polarized one as a function of the polarization vector. Computational experiments were carried out for three types of piezoceramics: soft ferroelectric piezoceramics PZT-5H, piezoceramics PZT-4 of medium ferrohardness, and piezoceramics PZT-8 with higher degree of ferrohardness. The dependences of the effective moduli on porosity are compared for different laws of polarization inhomogeneity and different kinds of piezoceramic material of the composite matrix.

Optimized structure design of asymmetrical Mg alloy cerebrovascular stent with high flexibility

In the treatment of cerebral artery stenosis via stent intervention, it is required that the stent can pass through the tortuous blood vessel with high curvature to reach the lesion position smoothly, and the damage to the artery should be as small as possible. This determines that the coronary artery stent cannot be directly applied to the diseased cerebrovascular, but a specialized cerebrovascular stent with high flexibility should be specifically designed. Differing from the commonly employed symmetrical structure, in this work, an asymmetrical and unequal-heigh stent structure was designed, which helps to improve the flexibility of the stent and reduces the self-contact phenomenon that occurs after the ordinary stent is bent. To balance the comprehensive properties of the stent, multi-objective optimization on the stent structure was carried out. The optimized stent structure shows better radial strength and flexibility and does not significantly affect equivalent plastic strain after stent expansion and volume average stress. In addition, this work provides a universal workflow for the customized stent structure.

Revaluating coal permeability-gas pressure relation under various gas pressure differential conditions

Identifying changes in coal permeability with gas pressure and accurately codifying mean effective stresses in laboratory samples are crucial in predicting gas-flow behavior in coal reservoirs. Traditionally, coal permeability to gas is assessed using the steady-state method, where the equivalent gas pressure in the coal is indexed to the average of upstream and downstream pressures of the coal, while ignoring the nonlinear gas pressure gradient along the gas flow path. For the flow of a compressible gas, the traditional method consistently underestimates the length/volume-averaged pressure and overestimates mean effective stress. The higher the pressure differential within the sample, the greater the error between the true mean pressure for a compressible fluid and that assumed as the average between upstream and downstream pressures under typical reservoir conditions. A correction coefficient for the compressible fluid pressure asymptotes to approximately 1.3%, representing that the error in mean pressure and effective stress can be on the order of approximately 30%, particularly for highly pressure-sensitive permeabilities and compressibilities, further amplifying errors in evaluated reservoir properties. We utilized this volume-averaged pressure and effective stress to correct permeability and compressibility data reported in the literature. Both the corrected initial permeability and the corrected pore compressibility were found to be smaller than the uncorrected values, due to the underestimation of the true mean fluid pressure, resulting in an overestimation of reservoir permeability if not corrected. The correction coefficient for the initial permeability ranges from 0.6 to 0.1 (reservoir values are only approximately 40% to 90% of laboratory values), while the correction coefficient for pore compressibility remains at approximately 0.75 (reservoir values are only approximately 25% of laboratory value). Errors between the uncorrected and corrected parameters are quantified under various factors, such as confining pressure, gas sorption, and temperature. By analyzing the evolutions of the initial permeability and pore compressibility, the coupling mechanisms of mechanical compression, adsorption swelling, and thermal expansion on the pore structure of the coal can be interpreted. These findings can provide insights that are useful for assessing the sensitivity of coal permeability to gas pressure as truly representative of reservoir conditions.

Effect of gingival height of a titanium base on the biomechanical behavior of 2-piece custom implant abutments: A 3-dimensional nonlinear finite element study

Statement of problemTitanium base (TiBase) abutments to restore an implant-supported single crown are available in different gingival heights, but information on the biomechanical effects of the gingival heights is lacking. PurposeThe purpose of this nonlinear finite element analysis study was to evaluate the effects of TiBase gingival heights on the biomechanical behavior of custom zirconia (CustomZir) abutments and TiBase, including von Mises stress and maximum and minimum principal stress. Material and methodsTiBases with different gingival heights (0.5 mm, 1 mm, 1.5 mm, and 2 mm) with internal hexagon Morse taper connections were simulated in 3-dimensional models. The simulations (ANSYS Workbench 2020; ANSYS Inc) included the OsseoSpeed EV implant (Ø5.4 mm) (AstraTech; Dentsply Sirona), restoration, and surrounding bone in the mandibular first molar region. An occlusal force of 200 N was applied with a 2-mm horizontal offset toward the buccal side and a 30-degree inclination from the vertical axis. ResultsHigh-stress concentration was observed in the uppermost internal connection area on the buccal side and the antirotational part of the titanium abutment on the lingual side in all models. CustomZir abutments with a shorter gingival height exhibited larger concentrated areas of volume average stress von Mises stress and higher magnitude of maximum and minimum principal stress compared with a taller gingival height. ConclusionsA TiBase abutment with a taller gingival height reduced the fracture risk of a CustomZir abutment without increasing any mechanical risk.

Determining elastic properties of CSEB masonry using FEA-based homogenization technique

The world today is embracing a sustainable approach in all sectors. The construction industry is grappling with the problem of minimizing energy consumption and lowering carbon emissions involved in the manufacture of construction materials. Soil blocks are an alternative to fired clay bricks. Soil bricks are inexpensive, recyclable, environmentally friendly, and provide better thermal comfort. However, masonry walls built with soil blocks have several drawbacks. They are bulky, have poor durability properties and their strength capacity reduces significantly when saturated due to rain. The remedy for this problem is a Cement Stabilized Earth Block (CSEB). An engineered mixture of soil-sand-cement-moisture compacted at predefined levels offers superior strength and durability properties. The percentage of cement added is minimal in comparison to the soil-sand mixture content. In this study, a numerical model to predict the elastic properties of masonry comprised of CSEB and soil–cement mortar is developed. Both the constituents, CSEBs, and soil–cement mortar have different elastic properties. The presence of bed joints and perpends lends orthotropic behavior to masonry. The present study considers the Finite element analysis (FEA)-based homogenization technique to predict the elastic properties of CSEB masonry. A small periodic part of masonry called a repetitive unit cell (RUC) is considered, which is representative of the block-mortar arrangement in masonry. The three-dimensional masonry RUC is modelled using FE-based ABAQUS-CAE software. A user-defined Python script is developed to apply PBCs (Periodic boundary conditions) to RUC. The six far-field unit strains are applied to the RUC model in three normal and three shear directions. Finally, volume-averaged stress components are computed to determine the elastic properties. The modulus of elasticity and Poisson’s ratio of CSEB masonry along three directions are determined. The proposed approach is governed by mechanics and not by empirical relationships and provides satisfactory results.

Viscoelastic damage evaluation of the axon.

In this manuscript, we have studied the microstructure of the axonal cytoskeleton and adopted a bottom-up approach to evaluate the mechanical responses of axons. The cytoskeleton of the axon includes the microtubules (MT), Tau proteins (Tau), neurofilaments (NF), and microfilaments (MF). Although most of the rigidity of the axons is due to the MT, the viscoelastic response of axons comes from the Tau. Early studies have shown that NF and MF do not provide significant elasticity to the overall response of axons. Therefore, the most critical aspect of the mechanical response of axons is the microstructural topology of how MT and Tau are connected and construct the cross-linked network. Using a scanning electron microscope (SEM), the cross-sectional view of the axons revealed that the MTs are organized in a hexagonal array and cross-linked by Tau. Therefore, we have developed a hexagonal Representative Volume Element (RVE) of the axonal microstructure with MT and Tau as fibers. The matrix of the RVE is modeled by considering a combined effect of NF and MF. A parametric study is done by varying fiber geometric and mechanical properties. The Young’s modulus and spacing of MT are varied between 1.5 and 1.9 GPa and 20–38 nm, respectively. Tau is modeled as a 3-parameter General Maxwell viscoelastic material. The failure strains for MT and Tau are taken to be 50 and 40%, respectively. A total of 4 RVEs are prepared for finite element analysis, and six loading cases are inspected to quantify the three-dimensional (3D) viscoelastic relaxation response. The volume-averaged stress and strain are then used to fit the relaxation Prony series. Next, we imposed varying strain rates (between 10/sec to 50/sec) on the RVE and analyzed the axonal failure process. We have observed that the 40% failure strain of Tau is achieved in all strain rates before the MT reaches its failure strain of 50%. The corresponding axonal failure strain and stress vary between 6 and 11% and 5–19.8 MPa, respectively. This study can be used to model macroscale axonal aggregate typical of the white matter region of the brain tissue.

A Multiscale Study of CFRP Based on Asymptotic Homogenization with Application to Mechanical Analysis of Composite Pressure Vessels.

The application of composites is increasingly extensive due to their advanced properties while the analysis still remains complex on different scales. In this article, carbon fiber reinforced polymer (CFRP) is modeled via asymptotic homogenization employing a representative volume element (RVE) with periodic boundary conditions. A multiscale mechanical model of CFRP is established to bridge the microscopic model, mesoscopic model, and macroscopic model. According to asymptotic homogenization, the coefficients of the material constitutive equation are calculated with volume-averaged stress and strain. Using the homogenized materials properties of CFRP, the tensile experiments of composite layers with the layout of [] are carried out to validate asymptotic homogenization method. The results indicated that the asymptotic homogenization approach can be used to calculate the homogenized elastic moduli and Poisson’s ratio of the whole structure, where the numerical results are basically consistent with test data. The sequent homogenized CFRP laminate model is applied to the mechanical analysis of type III composite pressure vessels, whereby burst pressure is accurately predicted. This work might shed some light on multiscale analysis of composite pressure vessels.

Effect of Number and Location on Stress Distribution of Mini Dental Implant-Assisted Mandibular Kennedy Class I Removable Partial Denture: Three-Dimensional Finite Element Analysis.

Purpose To investigate effects of number and location on patterns of von Mises stress distribution and volume average stress on abutment tooth, edentulous ridge, mini dental implant, and surrounding bone of mini dental implant-assisted mandibular Kennedy class I removable partial denture. Materials and Methods Eight three-dimensional finite element models of mandibular Kennedy class I with different numbers and locations of mini dental implants were constructed. Mini dental implants were generated in the area of second premolar, first molar, and second molar, respectively. A static load of 400 N was applied on all models. The von Mises stress and volumetric average stress were calculated by three-dimensional finite element analysis. Result The minimum volumetric average stress of abutment tooth was found in the model, where there was one mini dental implant at the second molar position and 2 mini dental implants at first molar and second molar positions. The model with three mini dental implants had reduced volumetric average stress of abutment tooth, which was not different from the model with two mini dental implants. However, the minimum volumetric average stress of mini dental implant and surrounding bone were found when three mini dental implants were applied, followed by two and one mini dental implants, respectively. Conclusion Placing at least one mini dental implant at a second molar position can help reduce stress transferred to the abutment tooth. Stresses around each implant and surrounding bone reduced with increased numbers of mini dental implants.

Macroscopic elastic stress and strain produced by irradiation

Using the notion of eigenstrain produced by the defects formed in a material exposed to high energy neutron irradiation, we develop a method for computing macroscopic elastic stress and strain arising in components of a fusion power plant during operation. In a microstructurally isotropic material, the primary cause of macroscopic elastic stress and strain fields is the spatial variation of neutron exposure. We show that under traction-free boundary conditions, the volume-average elastic stress always vanishes, signifying the formation of a spatially heterogeneous stress state, combining compressive and tensile elastic deformations at different locations in the same component, and resulting solely from the spatial variation of radiation exposure. Several case studies pertinent to the design of a fusion power plant are analysed analytically and numerically, showing that a spatially varying distribution of defects produces significant elastic stresses in ion-irradiated thin films, pressurised cylindrical tubes and breeding blanket modules.

The optimal activation of plastic aligner for canine distal movement: a three-dimensional finite element analysis.

This study aimed to investigate the optimal activation of plastic aligner for the canine distal movement by combining the stress and strain of periodontal ligament. Computer-aided design models of the upper canine, periodontal ligament, alveolar bone, and plastic aligner were constructed. The stresses and strains of periodontal ligament were acquired by fitting plastic aligner on the canine, which will cause the canine distal-direction movement. The activation of plastic aligner was set into 12 groups, including 0.050, 0.100, 0.125, 0.150, 0.175, 0.200, 0.225, 0.250, 0.275, 0.300, 0.350, and 0.400mm. Assuming the volume-averaged hydrostatic stress (VAHS) ranging from 4.7 to 16kPa to be the optimal stress, and an average strain no less than 0.3 to be the optimal strain. The optimal activation of plastic aligner was acquired based on the optimal stress and average strain. As the activation increased, the stress and strain of periodontal ligament increased visibly. The degree of activation of plastic aligner was nonlinearly and positively related to VAHS and average strain. According to the fitted curves, the activation corresponding to the optimal stress was 0.07-0.24mm and the activation was not less than 0.21mm based on the optimal strain. The optimal activation of plastic aligner for the canine distal movement was 0.21-0.24mm in this study. The degree of activation affects the force system of orthodontic tooth movement, and it should be taken into consideration to obtain healthy and efficient tooth movement. The activation with 0.21-0.24mm seems optimal for orthodontic tooth movement in the plastic aligner system in this study.

Characterization of size-affected non-uniform deformation of polycrystalline copper

In polycrystalline materials, with the increase in grain size relative to the macrostructure, the collective behavior of crystal grains affects their macroscopic deformation field. To investigate the effect of relative size on the mechanical behavior of polycrystalline materials, the interaction between the microstructure-induced non-uniform deformation and the specimen shape-induced non-uniform deformation was evaluated based on experimental and numerical studies of uniaxial tensile tests of polycrystalline copper specimens with a curved gauge section. The effects of the macroscopic stress gradient and grain size on the strain field of the specimen were evaluated using specimens with different curvature radii obtained from different thermal treatment conditions. The development of strain distribution was measured using the digital image correlation method. A high strain concentration was observed at the minimum cross-section region in the specimen with smaller grains, whereas such strain concentration was relaxed in the specimen with larger grains because a random strain distribution occurred owing to the polycrystalline structure. A full-scale crystalline plasticity finite element method simulation, under conditions similar to those in the experiment, was then performed. Deformation concentrated zone, in which the length and width depended on the grain size, occurred in the polycrystalline specimen. The cross-section of the specimen was locally reduced when the deformation concentrated zone reached the free surface, and the tensile force became smaller for the specimen with larger grains. To discuss the relative specimen size effect, the plastic strain was divided into local and nonlocal plastic strains. Both the experimental and simulation results clarified that the nonlocal plastic strain gradient evaluated in the finite volume region increased with the region-averaged stress. From these results, we proposed a constitutive equation for the plastic strain as a function of local stress and finite volume averaged stress. The nonlocal plastic work for the evaluation region, which is estimated using the nonlocal strain gradient, increased with the stress during the strain-hardening stage in both the simulation and experimental results.

Dilute dispersion of compound particles: deformation dynamics and rheology

Compound particles are a class of composite systems in which solid particles encapsulated in a fluid droplet are suspended in another fluid. They are encountered in various natural and biological processes, for e.g. nucleated cells, hydrogels, microcapsules etc. Generation and transportation of such multiphase structures in microfluidic devices is associated with several challenges because of the poor understanding of their structural stability in a background flow and the rheological characteristics of their dispersions. Hence, in this work, we analyse the flow in and around a concentric compound particle and investigate the deformation dynamics of the confining drop and its stability against breakup in imposed linear flows. In the inertia-less limit (Reynolds number, $Re \ll 1$ ) and assuming that the surface tension force dominates the viscous forces (low capillary number, $Ca$ , limit), we obtain analytical expressions for the velocity and pressure fields up to ${O}(Ca)$ for a compound particle subjected to a linear flow using a domain perturbation technique. Simultaneously, we determine the deformed shape of the confining drop correct up to ${O}(Ca^2)$ , facilitating the following. (i) Since ${O}(Ca^2)$ calculations account for the rotation of the anisotropically deformed interface, the reorientation dynamics of the deformed compound particles is determined. (ii) Calculations involving the ${O}(Ca^2)$ shape of the confining interface are found to be important for compound particles as ${O}(Ca)$ calculations make qualitatively different predictions in generalised extensional flows. (iii) An ${O}(Ca)$ constitutive equation for the volume-averaged stress for a dilute dispersion of compound particles was developed to study both shear and extensional rheology in a unified framework. Our analysis shows that the presence of an encapsulated particle always enhances all the measured rheological quantities such as the effective shear viscosity, extensional viscosity and normal stress differences. (iv) Moreover, linear viscoelastic behaviour of a dilute dispersion of compound particles is characterised in terms of complex modulus by subjecting the dilute dispersion to a small-amplitude oscillatory shear (SAOS) flow. (v) Various expressions pertaining to a suspension of particles, drops, and particles coated with a fluid film are also derived as limiting cases of compound particles.

A multiscale DEM\u2013FEM coupled approach for the investigation of granules as crash-absorber in ship building

This paper covers a numerical analysis of a novel approach to increasing the crashworthiness of double hull ships. As proposed in Schöttelndreyer (Füllstoffe in der Konstruktion: ein Konzept zur Verstärkung vonSchiffsseitenhüllen, Technische Uni-versitt Hamburg, Hamburg, 2015), it involves the usage of granular materials in the cavity of the double hull ship. For the modeling of this problem, the discrete element method (DEM) is used for the granules while the finite element method is used for the ship’s structure. In order to account for the structural damage caused by collision, a gradient-enhanced ductile damage model is implemented. In addition to avoid locking, an enhanced strain-based formulation is used. For large-scale problems such as the one in the current study, modeling of all granules with realistic size can be computationally expensive. A two-scale model based on the work of Wellmann and Wriggers (Comput Methods Appl Mech Eng 205:46–58, 2012) is applied—and the region of significant localization is modeled with the DEM, while a continuum model is used for the other regions. The coupling of both discretization schemes is based on the Arlequin method. Numerical homogenization is used to estimate the material parameters of the continuum region with the granules. This involves the usage of meshless interpolation functions for the projection of particle displacement and stress onto a background mesh. Later, the volume-averaged stress and strain within the representative volume element is used to estimate the material parameters. At the end, the results from the combined numerical model are compared with the results from the experiments given in Woitzik and Düster (Ships Offshore Struct 1–12, 2020). This validates both the accuracy of the numerical model and the proposed idea of increasing the crashworthiness of double hull vessels with the granular materials.

Micromechanics Analysis of Elastic Properties of Flexible Matrix TWF Composites

Using carbon fibers triaxial woven fabric (TWF) as a reinforcing material and compounding with a suitable flexible matrix material to form a composite shell film structure. It is a new type of high precision deployable antenna implementation. In this paper, the elastic properties of TWF composites using silicone rubber are studied. Using the micromechanics method, the three-dimensional unit cell characterizing the structural properties of the braided composite material is carried out. Homogenization finite element analysis will ultimately yield the elastic modulus of the entire composite. Firstly, considering the fiber bundle interlacing, the unit cell is finely geometrically modelled. Next, the unit cell is analyzed by finite element and periodic boundary conditions are applied. The method of homogenization is used to obtain the volume average stress and strain through six independent loading analysis, and the stiffness matrix is obtained, and the engineering constant is finally obtained. Finally, the effect of fiber volume fraction on elastic properties is analyzed. At present, there are few researches on flexible matrix TWF composites at home and abroad. The research on the elastic properties of the material has laid a solid foundation for further research on the performance of the material in the future.

Effect of different implant configurations on biomechanical behavior of full-arch implant-supported mandibular monolithic zirconia fixed prostheses

Mechanical failure of zirconia-based full-arch implant-supported fixed dental prostheses (FAFDPs) remains a critical issue in prosthetic dentistry. The option of full-arch implant treatment and the biomechanical behaviour within a sophisticated screw-retained prosthetic structure have stimulated considerable interest in fundamental and clinical research. This study aimed to analyse the biomechanical responses of zirconia-based FAFDPs with different implant configurations (numbers and distributions), thereby predicting the possible failure sites and the optimum configuration from biomechanical aspect by using finite element method (FEM). Five 3D finite element (FE) models were constructed with patient-specific heterogeneous material properties of mandibular bone. The results were reported using volume-averaged von-Mises stresses (σVMVA) to eliminate numerical singularities. It was found that wider placement of multi-unit copings was preferred as it reduces the cantilever effect on denture. Within the limited areas of implant insertion, the adoption of angled multi-unit abutments allowed the insertion of oblique implants in the bone and wider distribution of the multi-unit copings in the prosthesis, leading to lower stress concentration on both mandibular bone and prosthetic components. Increasing the number of supporting implants in a FAFDPs reduced loading on each implant, although it may not necessarily reduce the stress concentration in the most posterior locations significantly. Overall, the 6-implant configuration was a preferable configuration as it provided the most balanced mechanical performance in this patient-specific case.

Multiscale Thermoelastic Analysis of the Thermal Expansion Coefficient and of Microscopic Thermal Stresses of Mature Concrete

The thermal expansion coefficient and the microscopic thermal stresses of mature concrete depend on its microstructural composition and the internal relative humidity. This dependence is determined by means of thermoelastic multiscale analysis of concrete. The underlying multiscale model enables two types of scale transition. Firstly, bottom-up homogenization allows for the quantification of the thermal expansion coefficient and the elastic stiffness of concrete based on the Mori-Tanaka scheme. Secondly, top-down scale concentration gives access to the volume averaged stresses experienced by the cement paste, the fine and the coarse aggregates and, furthermore, to the stress states of the interfacial transition zones covering the aggregates. The proposed model is validated by comparing the predicted thermal expansion coefficient of concrete with independent sets of experimental measurements. Finally, sensitivity analyses are carried out to evaluate the influence of the volumetric composition and the internal relative humidity of concrete on the thermal expansion coefficient and the microscopic thermal stresses.

Stress analysis of a plain orthogonally woven textile composite under tension along the warp direction

A non-idealized finite element model of a plain orthogonally woven textile composite was subjected to tension along the warp direction, and the predicted stress state was investigated. The effect of refining the geometry and mesh on the volume average stresses and the percentage of each constituent at different stress levels was explored. For the particular textile architecture considered, which consisted of large reinforcement tows and complex tow cross sections, it was shown that the typical mesh refinement in the literature might suffice for volume average stresses, but a higher mesh refinement is needed to accurately capture stress concentrations. The locations of stress concentrations within each constituent were identified. For the three types of tows, [Formula: see text], transverse normal stress in the local coordinate system, in the wefts was predicted to be the most severe component of stress. For the layers of wefts that are crossed over or under by a binder, stress concentrations developed where the warps were the most distorted. Whereas, for the interior layer of wefts, stress concentrations developed where a binder came closest to the weft. In the matrix, [Formula: see text], the normal stress in the direction of the load, concentrations developed where a binder came close to a warp or weft. The locations of peak cross-sectionally averaged stresses along the tow paths were shown to match the locations of local stress concentrations. However, it was observed that many of the stress concentrations might be sensitive to the method used to create the finite element model, boundary conditions, or accounting for the variation of local fiber-volume fraction that results from a variation of cross-sectional area.

Computational analysis of mesoscale thermomechanical ignition behavior of impacted LLM-105 based explosives.

LLM-105 (2,6-diamino-3,5-dinitropyrazine-1-oxide) is an insensitive high explosive crystal which has performance between that of HMX and TATB. An elastoviscoplastic dislocation model is developed for LLM-105 crystal, which accounts for the dislocation evolutions at the crystal interior and crystal wall and strain-rate dependent work hardening. Three different crystal morphology (cubic, icosahedral, rodlike) of LLM-105 based explosive computational models were constructed and subjected to an impact velocity of 200 m s−1 and 500 m s−1. Effects of crystal morphology and initial dislocation density on thermomechanical ignition behavior of LLM-105 based explosives were analyzed. Dislocation density of both crystal interiors and crystal walls in the rodlike LLM-105 based explosive increases slower than that in the cubic and icosahedral explosives. Both the volume averaged and localized stress and dislocation density are the lowest for the rodlike explosive. At the impact velocity of 500 m s−1, a temperature rise due to volumetric work, plasticity work and chemical reaction is sufficiently high to lead to the ignition of the cubic explosive, which shows that the rodlike explosive is the least sensitive among the three explosives. Moreover, with the increase of initial dislocation density, the corresponding volume averaged and localized stress and temperature increase as well. Results presented bridge the macroscale thermomechanical ignition response with the mesoscale deformation mechanisms, which is essential for better understanding the ignition mechanisms and guiding the design of LLM-105 based formulations.

Effective Elastic Coefficients of an Inhomogeneous Solids

The first special boundary value problem (SBVP) of the theory of elasticity for an inhomogeneous body is considered. The effective elasticity coefficients are found from the solution of the SBVP. They form a fourth-rank tensor, namely the tensor of effective elasticity moduli that makes it possible to express the volume average stresses via the mean deformations. It is shown that the solution of the first SBVP and hence the effective coefficients of elasticity are expressed in terms of the integrals of the Green tensor. The integrals of the Green tensor with respect to one of the variables are called the structural functions. The auxiliary equations, the solutions of which are determined by the functional dependence of the elastic characteristics on the coordinates, have been obtained for these structural functions. It is shown that in the case when the elastic moduli are periodic functions of one, two, or three coordinates, then the structural functions, far from the body boundary, are also periodic functions of the same coordinates. The structural functions are transformed to be equal to zero on the all body border approaching the boundary. In other words, in an inhomogeneous body with a periodic structure, it is possible to distinguish the boundary layer, which separates the regions of periodic values of structural functions from non-periodic ones. The thickness of this layer is of the order of the characteristic size of the periodicity cell. The effective tensors are found due to the structural functions. It is proved that the tensor of effective elastic moduli satisfies all the conditions of symmetry and positive definiteness. The case of an infinite plate with non-uniform thickness is considered in detail.