3D Continuum Research Articles

Micro–macro FE modeling of damage evolution in laminated composite plates subjected to low velocity impact

A phenomenological-based micro–macro mechanical method, comprising the coupling of a 3D continuum damage mechanics (CDM) model with an original micromechanical FE model, is presented to predict low velocity impact response of composite laminates. The key point of the proposed method is the definition and computation of saturation crack density, which is used to scale impact-induced delamination instead of via expensive cohesive zone model based FEM. In order to gain the specific value of the saturation crack density, a micromechanical FE model is established based on the RVE technique. Additionally, the initiation of intralaminar failure including fiber fracture (FF) and inter-fiber fracture (IFF) is evaluated by Puck criteria, and its evolution, with considering effects of the fracture plane angle, is assumed to be controlled by equivalent strains on the fracture plane rather than the classic material principal axis plane. A good agreement between the experimental and simulated results shows correctness and effectiveness of the developed micro–macro mechanical method for predicting impact response and damage using a relatively coarse mesh. Furthermore, significant reduction of computational cost, compared with existing techniques, can be achieved with the novel mesh-independent method.

Non-Linear Numerical Analysis of Unreinforced Masonry Column and Masonry Column Reinforced by FRP Wrapping

A numerical model for unreinforced masonry columns and masonry columns reinforced by FRP wrapping is presented in this paper. Both, the bricks and the mortar are modeled as 3D continuum and to the interface between these two materials a non-linear contact law is assigned. The accurate 3D modeling of masonry units and mortar joints within the numerical model leads to high computational cost, but on the other hand, an appropriate analysis tool delivering detailed information about the behavior of masonry columns is obtained. A concrete damaged plasticity model was adopted for mortar and brick. External wrapping by a perfectly-adherent composite based strips and contact between strips and masonry is defined in the next step. The behavior of reinforcement was assumed isotropic and linearly elastic. The response and failure mechanism of masonry columns can be investigated. For all simulations the commercial software package ABAQUS was used. By comparison with results from experiments [1], the performance of the numerical model is evaluated and the obtained numerical results are discussed.

Masonry Column Reinforced by FRP Wrapping: Behavior and Numerical Analysis

A numerical analysis for masonry columns is presented in this paper. The behavior and character of deformation of compressed unreinforced masonry columns is investigated and compared with the deformation of masonry columns reinforced by FRP wrapping. The experimental program is part of a research project NAKI [1]. Both, the bricks and the mortar are modeled as 3D continuum and to the interface between these two materials a non-linear contact law is assigned. The contact between reinforcement and masonry support is considered as perfectly-adherent. Two different cases are simulated - the ratio of Young ́s modulus of brick and Young’s modulus of mortar is 5:1, respectively 1:5. For all simulations the commercial software package ABAQUS was used and the obtained numerical results are discussed.

Numerical modeling of dynamic rock fracture with a combined 3D continuum viscodamage‐embedded discontinuity model

SummaryThis paper deals with numerical modeling of dynamic failure phenomena in rate‐sensitive quasi‐brittle materials, such as rocks, with initial microcrack populations. To this end, a continuum viscodamage‐embedded discontinuity model is developed and tested in full 3D setting. The model describes the pre‐peak nonlinear and rate‐sensitive hardening response of the material behavior, representing the fracture‐process zone creation, by a rate‐dependent continuum damage model. The post‐peak response, involving the macrocrack creation accompanied by exponential softening, is formulated by using an embedded displacement discontinuity model. The finite element implementation of this model relies upon the linear tetrahedral element, which seems appropriate for explicit dynamic analyses involving stress wave propagation. The problems of crack locking and spreading typical of embedded discontinuity models are addressed in this paper. A combination of two remedies, the inclusion of viscosity in the spirit of Wang's viscoplastic consistency approach and introduction of isotropic damaging into the embedded discontinuity model, is shown to be effective in the present explicit dynamics setting. The model performance is illustrated by several numerical simulations. In particular, the dynamic Brazilian disc test and the Kalthoff–Winkler experiment show that the present model provides realistic predictions with the correct failure modes and rate‐dependent tensile strengths of rock at different loading rates. The ability of initial embedded discontinuity populations to model the initial microcrack populations in rocks is also successfully tested. Copyright © 2016 John Wiley & Sons, Ltd.

Modelling of Rotating Twisted Blades as 1D Continuum

Presented paper deals with modelling of a twisted blade with rhombic shroud as one-dimensional continuum by means of Rayleigh beam finite elements with varying cross-sectional parameters along the finite elements. The blade is clamped into a rotating rigid disk and the shroud is considered to be a rigid body. Since the finite element models based on the Rayleigh beam theory tend to slightly overestimate natural frequencies and underestimate deflections in comparison with finite element models including shear deformation effects, parameter tuning of the blade is performed.

Effect of Boundary Conditions in Segmental Lining Model on its Sectional Force

Nowadays, underground construction becomes popular as the demand for infrastructure in urban areas increases. To develop underground space in an urban area, it is important to investigate ground surface settlement and damage to existing neighbouring structures. Consequently, 3D finite element method (FEM) continuum models have been developed. This paper introduces a 3D FEM continuum model, which can consider, longitudinal joints, circumferential joints, and nontension boundary between lining and ground, and examines the effect of boundary condition at the tunnel end and ground stiffness on the lining behavior (i.e., bending moment, axial force, normal effective earth pressure, and segment displacement) in the case of staggered building. As a result, it was found that the boundary condition at the tunnel end does not significantly affect the sectional force, except for the axial force in the case of soft soil; The two-ring model provides the safe side results from the viewpoint of segment design; and it can be adopted for segmental lining design and lining behavior simulation.

Three-dimensional finite element analysis of the stress distribution in the endodontically treated maxillary central incisor by glass fiber post and dentin post.

Introduction:From the point of dental practice, the restoration of endodontically treated teeth has become an important aspect as it involves a range of treatment options of variable complexity. Restoring teeth with insufficient coronal tooth structure, it is always indicated to use the post to retain a core for definitive restoration. Fiber post has a modulus of elasticity in analogs to dentin structure, thus reducing the stress areas at the dowel dentin interface. However, the only material that can substantiate all these properties can be none other than dentin itself.Materials and Methodology:Three-dimensional (3D) models of the maxillary central incisor were developed incorporating all the nonlinearities. Continuum 3D elements were used in three dimensions. Maxillary central incisor was laser scanned, duplicated with the help of reverse engineering into STL format, and it was converted into 3D model for finite element analysis (FEA). For the model, fixed boundary conditions were applied at the outer bone, while 100 N static vertical occlusal loads were prescribed at 135° on the loading component of the simulated tooth. The stress distribution was evaluated using dentin and fiber post with prescribed materials, loading and boundary conditions in endontically treated teeth by 3D FEA.Results:The analysis for von Misses stress for dentin post showed that the stress in the dentin post at the cervical area was 127 MPa. The displacement in the dentin post was <0.025 mm. Von Misses stress for the fiber post at the cervical area was approximately 182 MPa and the displacement was <0.035 mm.Conclusion:The FEA results showed that the stress in the cervical area of the dentin was more for fiber post when compared to dentin post, and maximum displacement values were less for dentin post in comparison to fiber post.

Plane bias extension test for a continuum with two inextensible families of fibers: A variational treatment with Lagrange multipliers and a perturbation solution

In the present paper, a system constituted by two families of nearly inextensible fibers is studied. The interest towards this kind of structures, which can be suitably modeled by 2D continua with inextensible curves, comes form both theoretical and applicative motivations. Indeed, the advantageous weight/strength ratio and the particularly safe behavior in fractures make them attractive in many engineering fields, while the mechanical properties displayed by them are theoretically interesting and still not well understood in full generality. We focused on dead-loading traction boundary-value problems assuming particular forms for the deformation energy associated to every node of the structure. The main result of the paper consists in the determination of the nonlinear integral equations describing fibers directions for a specific class of deformation energies. A perturbative analysis of a particular solution is also performed, and some physical justification for one of the considered forms for the energy density are provided in the Appendix.

Novel continuum models for coupled shear wall analysis

Summary Replacement beam formulations represent a family of 1D continuum models suitable for approximate analyses of the structural arrangements of buildings. In this paper, an energy equivalence approach is applied to coupled shear walls to develop suitable replacement beam models. Assuming properly compatible coupling fields between walls, a novel three-field coupled two-beam approach, therein providing shear and axial deformations, is proposed. The corresponding mathematical formulation provides closed-form solutions for simple loading cases with homogenous properties. Considering slender coupled shear walls, as typically found in tall buildings, the coupled two beams can be reduced to a two-field formulation, i.e., a parallel assembly of an extensible Euler–Bernoulli beam and a rotation-constraining beam. The latter model is solved analytically, and expressions for the tip displacement and base bending moment are presented. A finite element model is then presented and demonstrated to be an efficient tool for static and dynamic analyses. The effects of the axial deformation and degree of coupling on slender coupled shear wall responses are described as being dependent upon two suitable parameters. Various approximate relations are also proposed for design purposes. Finally, the validity of both analytical solutions and the finite element model is confirmed via numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.

Morphometric structural diversity of a natural armor assembly investigated by 2D continuum strain analysis.

Many armored fish scale assemblies use geometric heterogeneity of subunits as a design parameter to provide tailored biomechanical flexibility while maintaining protection from external penetrative threats. This study analyzes the spatially varying shape of individual ganoid scales as a structural element in a biological system, the exoskeleton of the armored fish Polypterus senegalus (bichir). X-ray microcomputed tomography is used to generate digital 3D reconstructions of the mineralized scales. Landmark-based geometric morphometrics is used to measure the geometric variation among scales and to define a set of geometric parameters to describe shape variation. A formalism using continuum mechanical strain analysis is developed to quantify the spatial geometry change of the scales and illustrate the mechanisms of shape morphing between scales. Five scale geometry variants are defined (average, anterior, tail, ventral, and pectoral fin) and their functional implications are discussed in terms of the interscale mobility mechanisms that enable flexibility within the exoskeleton. The results suggest that shape variation in materials design, inspired by structural biological materials, can allow for tunable behavior in flexible composites made of segmented scale assemblies to achieve enhanced user mobility, custom fit, and flexibility around joints for a variety of protective applications.

Mineral precipitation-induced porosity reduction and its effect on transport parameters in diffusion-controlled porous media.

BackgroundIn geochemically perturbed systems where porewater and mineral assemblages are unequilibrated the processes of mineral precipitation and dissolution may change important transport properties such as porosity and pore diffusion coefficients. These reactions might alter the sealing capabilities of the rock by complete pore-scale precipitation (cementation) of the system or by opening new migration pathways through mineral dissolution. In actual 1D continuum reactive transport codes the coupling of transport and porosity is generally accomplished through the empirical Archie’s law. There is very little reported data on systems with changing porosity under well controlled conditions to constrain model input parameters. In this study celestite (SrSO4) was precipitated in the pore space of a compacted sand column under diffusion controlled conditions and the effect on the fluid migration properties was investigated by means of three complementary experimental approaches: (1) tritiated water (HTO) tracer through diffusion, (2) computed micro-tomography (µ-CT) imaging and (3) post-mortem analysis of the precipitate (selective dissolution, SEM/EDX).ResultsThe through-diffusion experiments reached steady state after 15 days, at which point celestite precipitation ceased and the non-reactive HTO flux became constant. The pore space in the precipitation zone remained fully connected using a 6 µm µ-CT spatial resolution with 25 % porosity reduction in the approx. 0.35 mm thick dense precipitation zone. The porosity and transport parameters prior to pore-scale precipitation were in good agreement with a porosity of 0.42 ± 0.09 (HTO) and 0.40 ± 0.03 (µ-CT), as was the mass of SrSO4 precipitate estimated by µ-CT at 25 ± 5 mg and selective dissolution 21.7 ± 0.4 mg, respectively. However, using this data as input parameters the 1D single continuum reactive transport model was not able to accurately reproduce both the celestite precipitation front and the remaining connected porosity. The model assumed there was a direct linkage of porosity to the effective diffusivity using only one cementation value over the whole porosity range of the system investigated.ConclusionsThe 1D single continuous model either underestimated the remaining connected porosity in the precipitation zone, or overestimated the amount of precipitate. These findings support the need to implement a modified, extended Archie’s law to the reactive transport model and show that pore-scale precipitation transforms a system (following Archie’s simple power law with only micropores present) towards a system similar to clays with micro- and nanoporosity.Graphical abstract:Electronic supplementary materialThe online version of this article (doi:10.1186/s12932-015-0027-z) contains supplementary material, which is available to authorized users.

Three-dimensional numerical analysis of geocell-reinforced soft clay beds by considering the actual geometry of geocell pockets

Due to its complex honeycomb structure, the numerical modeling of the geocell has always been a big challenge. Generally, the equivalent composite approach is used to model the geocells. In the equivalent composite approach, the geocell–soil composite is treated as the soil layer with improved strength and stiffness values. Though this approach is very simple, it is unrealistic to model the geocells as the soil layer. This paper presents a more realistic approach of modeling the geocells in three-dimensional (3D) framework by considering the actual curvature of the geocell pocket. A square footing resting on geocell reinforced soft clay bed was modeled using the “fast Lagrangian analysis of continua in 3D” (FLAC3D) finite difference package. Three different material models, namely modified Cam-clay, Mohr–Coulomb, and linear elastic were used to simulate the behaviour of foundation soil, infill soil and the geocell, respectively. It was found that the geocells distribute the load laterally to the wider area below the footing as compared to the unreinforced case. More than 50% reduction in the stress was observed in the clay bed in the presence of geocells. In addition to geocells, two other cases, namely, only geogrid and geocell with additional basal geogrid cases were also simulated. The numerical model was systematically validated with the results of the physical model tests. Using the validated numerical model, parametric studies were conducted to evaluate the influence of various geocell properties on the performance of reinforced clay beds.

Development of modelling strategies for two-way RC slabs

Analyses of tested two-way reinforced concrete (RC) slabs were carried out with varying modelling choices to develop better modelling strategies. The aim was to study how accurately the response of a slab subjected to bending could be predicted with nonlinear finite element (FE) analysis using three-dimensional (3D) continuum elements, and how the modelling choices might influence the analysis results. The load-carrying capacity, load–deflection response, crack pattern and reaction-force distribution of the two-way slab studied were compared to experimental data available. The influence of several modelling parameters was investigated, including geometric nonlinearity, element properties, concrete model, reinforcement model and boundary condition. The results show the possibility of accurately reflecting the experimental results concerning load-carrying capacity, load–deflection response and crack pattern giving proper modelling choices. Moreover, the reaction force distribution was found to be highly influenced by the stiffness of the supports.

Spiral arms in scattered light images of protoplanetary discs: are they the signposts of planets?

One of the striking discoveries of protoplanetary disc research in recent years are the spiral arms seen in several transitional discs in polarized scattered light. An interesting interpretation of the observed spiral features is that they are density waves launched by one or more embedded (proto)planets in the disc. In this paper, we investigate whether planets can be held responsible for the excitation mechanism of the observed spirals. We use locally isothermal hydrodynamic simulations as well as analytic formulae to model the spiral waves launched by planets. Then H-band scattered light images are calculated using a 3D continuum radiative transfer code to study the effect of surface density and pressure scaleheight perturbation on the detectability of the spirals. We find that a relative change of ∼3.5 in the surface density (δΣ/Σ) is required for the spirals to be detected with current telescopes in the near-infrared for sources at the distance of typical star-forming regions (140 pc). This value is a factor of 8 higher than what is seen in hydrodynamic simulations. We also find that a relative change of only 0.2 in pressure scaleheight is sufficient to create detectable signatures under the same conditions. Therefore, we suggest that the spiral arms observed to date in protoplanetary discs are the results of changes in the vertical structure of the disc (e.g. pressure scaleheight perturbation) instead of surface density perturbations.

Experimental and numerical studies on protection of buried pipelines and underground utilities using geocells

This paper presents the results of the laboratory model tests and the numerical studies conducted on small diameter PVC pipes, buried in geocell reinforced sand beds. The aim of the study was to evaluate the suitability of the geocell reinforcement in protecting the underground utilities and buried pipelines. In addition to geocells, the efficacy of only geogrid and geocell with additional basal geogrid cases were also studied. A PVC (Poly Vinyl Chloride) pipe with external diameter 75 mm and thickness 1.4 mm was used in the experiments. The vehicle tire contact pressure was simulated by applying the pressure on the top of the bed with the help of a steel plate. Results suggest that the use of geocells with additional basal geogrid considerably reduces the deformation of the pipe as compared to other types of reinforcements. Further, the depth of placement of pipe was also varied between 1B to 2B (B is the width of loading plate) below the plate in the presence of geocell with additional basal geogrid. More than 50% reduction in the pressure and more than 40% reduction in the strain values were observed in the presence of reinforcements at different depths as compared to the unreinforced beds. Conversely, the performance of the subgrade soil was also found to be marginally influenced by the position of the pipe, even in the presence of the relatively stiff reinforcement system. Further, experimental results were validated with 3-dimensional numerical studies using FLAC3D (Fast Lagrangian Analysis of Continua in 3D). A good agreement in the measured pipe stain values were observed between the experimental and numerical studies. Numerical studies revealed that the geocells distribute the stresses in the lateral direction and thus reduce the pressure on the pipe. In addition, the results of the 1-g model tests were scaled up to the prototype case of the shallow buried pipeline below the pavement using the appropriate scaling laws.

Comment on “Shape transition of unstrained flattest single-walled carbon nanotubes under pressure” [J. Appl. Phys. 115, 044512 (2014)

Recently, Mu et al. [J. Appl. Phys. 115, 044512 (2014)] have developed an analytic approach to describe some special shapes of a single-wall carbon nanotube (SWCNT) under hydrostatic pressure. These authors have found approximate analytic expressions for the parametric equations of the tube cross section profile and its curvature at the convex-to-concave transition pressure using a shell-like 2D continuum model describing the shapes of such nanotubes. In this comment, we provide additional insight into this problem taking into account the exact analytic representation of the shapes that a SWCNT attains when subjected to hydrostatic pressure according to the very same continuum model.

Phase-field model coupling cracks and dislocations at finite strain

A new 3D continuum model is developed to simultaneously describe cracks and dislocations in materials undergoing finite strain deformations. Significant advances are made to account for fracturing in a cubic symmetrical system and to correctly model the microscopic dislocation properties into a Time-Dependent Ginzburg–Landau formalism. In addition, the interaction between dislocations and free borders (crack lips, surfaces…) is naturally described. As an example, the model is used to investigate the effects of plasticity on the delamination and buckling of thin films deposited on substrates. It may also be helpful in any other situation where cracks and dislocations take place and in which finite strain effects must be considered.

Comparative study of finite element analysis in tube hydroforming of stainless steel 304

This research conducts a comparative study of finite element analysis (FEA) in tube hydroforming (THF). The investigated tube is stainless steel grade 304 (SS304) of as received and after annealing (AN). Three different finite element modeling techniques have been examined and compared with corresponding experimental results. The main modeling parameters of interest range from element technologies, symmetry modeling, and solving schemes. Other parameters being sensitive to each model are discussed. Formability issues have been investigated through FEA and forming limit diagram (FLD). Computational aspects have been illustrated and discussed for simulating THF and an intermediate AN. Prediction of the required forming pressure is challenging. Both shell and continuum elements have different advantages and drawbacks in simulating THF. A shell element with explicit time integration tends to underpredict the required forming pressure while both axisymmetric and 3D continuum elements with implicit time integration tend to overpredict the required forming pressure. The draw-in observation can also provide an insight of the state of deformation.

A unified stochastic framework for robust topology optimization of continuum and truss-like structures

In this article, a unified framework is introduced for robust structural topology optimization for 2D and 3D continuum and truss problems. The uncertain material parameters are modelled using a spatially correlated random field which is discretized using the Karhunen–Loève expansion. The spectral stochastic finite element method is used, with a polynomial chaos expansion to propagate uncertainties in the material characteristics to the response quantities. In continuum structures, either 2D or 3D random fields are modelled across the structural domain, while representation of the material uncertainties in linear truss elements is achieved by expanding 1D random fields along the length of the elements. Several examples demonstrate the method on both 2D and 3D continuum and truss structures, showing that this common framework provides an interesting insight into robustness versus optimality for the test problems considered.

A continuum shell model including van derWaals interaction for free vibrations of double-walled carbon nanotubes

This paper proposes the free vibration analysis of Double-Walled Carbon Nano Tubes (DWCNTs). A continuum elastic three-dimensional shell model is used for natural frequency investigation of simply supported DWCNTs. The 3D shell method is compared with beam analyses to show the applicability limits of 1D beam models. The effect of van der Waals interaction between the two cylinders is shown for different Carbon Nano Tube (CNT) lengths and vibration modes. Results give the van der Waals interaction effect in terms of frequency values. In order to apply the 3D shell continuum model, DWCNTs are defined as two concentric isotropic cylinders (with an equivalent thickness and Young modulus) which can be linked by means of the interlaminar continuity conditions or by means of an infinitesimal fictitious layer which represents the van der Waals interaction.