Mesoscopic Finite Element Research Articles

Mesoscopic simulation study on density gradient metallic foam sandwich panels under hypervelocity impact

The high stiffness of sandwich panel shield ensures the survival of satellites and spacecrafts, making them extensively utilized in practical aerospace engineering. Metallic foams are exceptionally appropriate for spacecraft debris shields owing to their light weight and superior energy absorption characteristics. The internal mesostructure of a metallic foam plays a crucial role in determining its protective performance. At the mesoscale, the density gradient metallic foam exhibits a greater potential for protection compared to uniform metallic foam under hypervelocity impact. Therefore, this study investigates the behavior of density-gradient foams under hypervelocity impact. By leveraging three-dimensional Voronoi tessellation in conjunction with the background mesh-mapping algorithm, this study constructed mesoscopic finite element models of the layered and continuous-density gradient metallic foam, considering the internal structure of randomness. Subsequently, the Finite Element-Smoothed Particle Hydrodynamics (FE-SPH) adaptive method in LS-DYNA was employed to conduct numerical simulations of the hypervelocity impact. First, the simulation was validated through a comparison with the experiment. Based on the results of the numerical simulations, the characteristics of the debris cloud and the damage within the foam were analyzed. It was determined that the protection mechanism of the density gradient foam sandwich panel under hypervelocity impact involved a coupling effect between the domino and microchannel effects. The different damage characteristics of layered density gradient foam sandwich panels were analyzed. According to this mechanism, foam sandwich panels with different density-gradient configurations were designed and their protective performances were compared to determine the optimal density-gradient configuration to provide valuable insights into the optimal design of protective structures.

A mesoscopic numerical analysis method for evaluating the electromagnetic transmission performance of cement mortar with varying sand particle sizes and content

This paper explores the impact of sand content and particle size on the electromagnetic transmission performance (ETP) of mortar samples. This study involves designing mortar samples with a water-cement ratio of 0.4 and varying sand volume content from 0 % to 50 %. Additionally, a mesoscopic finite element model is established to analyze the electromagnetic transmission behavior. The findings indicate that the particle size and content of sand influence the multiple reflections behavior of electromagnetic waves, while the particle size of sand has almost no effect on the electromagnetic transmission coefficient and dielectric response. Although sand enhances the ETP of cement paste, its impact is limited. Furthermore, the study reveals that the distribution of the electromagnetic field remains continuous regardless of sand particle size or content, and is unaffected by the differing dielectric properties of sand and cement paste phases. However, the induced current generated by sand and other phases differs, leading to noticeable variations in dielectric loss. Mesoscopic simulation results clearly demonstrate that cement paste is the primary contributor to electromagnetic energy loss.

Meso-FE modelling for homogenization of the nonlinear orthotropic behavior of PTFE-coated fabric based on virtual fiber method

Compared to traditional textile composites, the coated fabric used in fabric membrane structures is much more flexible. Its macroscopic mechanical behavior is highly nonlinear, anisotropic, and shows stress ratio dependence during the loading process. The main reason is that the yarns within the coated fabric are not completely solidified, and there is a significant crimp interchange process in the yarns under load. This paper proposes a novel mesoscopic finite element (FE) model to predict the nonlinear orthotropic mechanical behavior of PTFE-coated fabric using the virtual fiber method (VFM). By comparing with experimental data, it is shown that the virtual fiber defined by the truss element can visually and effectively simulate the mechanical behavior of the internal fibers and reflect the crimp interchange process between two-way yarns. Combined with PBCs, it can effectively predict the uniaxial and biaxial tensile behaviors of the PTFE-coated fabric. Moreover, a new multi-scale model suitable for structural scale analysis of fabric membrane structures has been attempted by combining the direct FE2 (D-FE2) method with the proposed mesoscopic FE model. Local deformation mechanisms and macro response of fabric membrane structures can be observed simultaneously from these analyses, which provide a better understanding of the mechanical behavior of the fabric membrane structures.

Determining appropriate level of detail of 3D aggregate model for accurate and efficient mesoscopic simulation of asphalt concrete

The levels of detail (LODs) of aggregate models significantly impact both the accuracy and efficiency of the mesoscale numerical simulation of asphalt concrete. This study proposed a quantitative evaluation framework to find an appropriate LOD that allows accurate simulation of asphalt concrete with relatively low model complexity. First, the coarse aggregates in asphalt concrete were reconstructed from computed tomography (CT) images, and their LOD was defined as level-0. Each reconstructed aggregate was then simplified using a surface simplification method that obtains aggregate models with four descending LODs (levels-1, 2, 3 and 4), consisting of 200, 100, 50 and 20 triangular facets respectively. The simulation accuracy was evaluated according to several aggregate geometric indexes and mesoscopic finite element (FE) compressive simulation results of asphalt concrete. The results indicate that compared to the level-1 model, the level-2 model can achieve a similar simulation accuracy with a 50% reduction in simulation time.

Numerical simulation study on mesoscopic metallic foam core sandwich panels under hypervelocity impact

Due to its lightweight and superior energy absorption characteristics, metallic foams are exceptionally suitable for the protective shielding of spacecraft against debris. The mesoscopic structure of such a foam plays a pivotal role in enhancing its outstanding protective performance. Numerical simulations permit us to explore the damage mechanism of its internal structure and the evolving characteristics of debris clouds. By adopting the three-dimensional Voronoi tessellation in conjunction with the algorithm of background mesh mapping, this study constructed mesoscopic finite element models that accurately reflect the internal randomness and variability in ligament width within the metallic foam. Subsequently, numerical simulations were executed employing the FE-SPH adaptive method within the LS-DYNA. Comparative experimental cases substantiated the validity of the simulations, and an exhaustive mesh sensitivity analysis was conducted. Optimizing results from these simulations following a normal impact, we delved into the propagation of stress waves within the foam core, alongside the subsequent internal structural damage. Furthermore, we explored the damage mechanism of foam sandwich panels subjected to hypervelocity impacts. According to the fragmentation process of the projectile and the evolution of debris clouds, it was discerned that the random internal structure of the foam engenders an asymmetric and skewed debris cloud, dispersing its energy and culminating in multiple concentrated particle clusters with a predilection towards a particular direction. Tracking the velocity fluctuations of these ‘dominant particles’ and the inflicted damage on the rear facesheet revealed that the agglomerated tiny fragments of the projectile are primarily responsible for perforating the rear facesheet.

Experimental and Numerical Investigation into the Mechanical Behavior of Composite Solid Propellants Subject to Uniaxial Tension.

To further explore the quasi-static mechanical characteristics of composite solid propellants at low strain rates, an investigation was conducted on the mechanical behavior and damage mechanisms of a four-component hydroxy-terminated polybutadiene (HTPB) propellant by means of experiments and numerical simulation. A uniaxial tensile test and scanning electron microscope (SEM) characterization experiment were carried out. A microstructural model, which accurately represents the mesoscopic structure, was developed via the integration of micro-CT scanning and image-processing techniques. The constructed microstructural model was utilized to conduct a numerical simulation of the mechanical behavior. The experimental results demonstrated that the maximum tensile strength increases with increasing strain rate, and the primary cause of propellant failure at low strain rates is the dewetting phenomenon occurring at the interface between the larger particles and the matrix. The maximum tensile strength is 0.48 MPa when the strain rate is 0.00119 s-1, and the maximum tensile strength is 0.37 MPa when the strain rate is 0.000119 s-1. The simulation results indicated a consistent trend in variation when comparing the simulation and experimental curves. This suggested that the established model exhibits a high level of reliability, and provides a promising approach for carrying out microstructural simulations of heterogeneous propellants in future. The mechanical behavior of the propellant can be effectively described by utilizing a mesoscopic finite element model that incorporates the superelastic constitutive model of the matrix and the bilinear cohesive model. This framework facilitates the representation of mesoscopic damage evolution, which consequently provides insights into the damage mechanism. Additionally, the utilization of such models assists in compensating for the limitations of damage evolution characterization experiments.

Modelling the gradual through thickness porosity formation and swelling during the thermal aggression of thermoplastic based laminates

Impacting thermoplastic-based laminates by a high thermal energy -e.g. a flame—essentially causes the progressive deterioration of the matrix, involving solid-state transformations and dramatic variations of the thermomechanical properties. Throughout this process and because it is associated with significant through thickness gradients, the laminates retains a substantial capacity to sustain a mechanical load, even after matrix has melted. For temperatures higher than the melting temperature, the dominant mechanism of the matrix thermal decomposition is the formation of voids. Whereas they constitute a weakness from the mechanical point of view, they act as thermal insulators and contribute to the protection of the matrix on the side opposite to thermal aggression. Thus, describing accurately the kinetics of their formation is the key to a reliable control of the laminates thermomechanical properties evolution under fire conditions. As a prerequisite to this objective, the formation process was experimentally investigated. Results have evidenced the strong dependence of the porosity content and of the related swelling phenomenon to the time and temperature of thermal exposure. A mesoscopic Finite Element model representing porosities at a structural level was developed based on these observations. The porosity nucleation and the induced swelling were reproduced using a probabilistic approach to drive the progressive transformation of elements into porosities according to their thermal state.

Prediction of triaxial mechanical properties of rocks based on mesoscopic finite element numerical simulation and multi-objective machine learning

The deformation and strength characteristics of rocks are crucial for the effective development of underground resources and the construction of underground engineering projects. In this study, a novel approach is proposed to predict the triaxial mechanical properties of rocks by utilizing mesoscopic finite element numerical simulation and multi-objective machine learning. First, the mesoscopic mechanical properties of rocks are obtained through microscale finite element simulations to generate a training dataset. Then, three machine learning algorithms, namely support vector regression (SVR), artificial neural network (ANN), and random forest (RF), are employed to perform multi-objective machine learning on the triaxial elastic modulus, Poisson's ratio, and compressive strength of rocks, using uniaxial elastic modulus, Poisson's ratio, tensile strength, compressive strength, and confining pressure as feature variables. The performance evaluation, based on 10-fold cross-validation, demonstrates that all three models exhibit excellent predictive capabilities, especially the SVR and RF models, which show high accuracy and correlation, respectively. Among the five feature variables, confining pressure is the most important feature, while uniaxial tensile strength is the least important feature. The absence of uniaxial tensile strength does not significantly impact the predictive performance of the models. These findings offer novel insights into the investigation of the triaxial mechanical properties of rocks.

Corrosion-induced cracking behavior of lightweight aggregate concrete: Experimental and numerical study

The corrosion-induced cracking potentially undermines the durability of concrete structures, while the fracture mechanism of lightweight aggregate concrete (LWAC) differs from that of the normal concrete subjected to expansive corrosion products due to the low-strength coarse aggregate. Eleven beams considering different diameters of LWA, the volume fraction of LWA, and surface crack widths were subjected to the accelerated corrosion setup, and the corrosion-induced cracks and steel mass loss were observed. The mesoscopic finite element model was established for the analysis of LWAC, and the model was verified according to the test results. The results of numerical study showed that decrease in the strength of LWA led to the inner damage of LWAC, while the increase in cover thickness made the cracking process of LWAC more rapid. On the basis of mesoscopic simulations, the critical cracking mass loss of steel bar and the empirical cracking parameter were derived, and then the linear equations were adopted for the establishment of relations between mass loss of corroded rebar and the corrosion-induced surface crack width by considering the effect of concrete cover and the rebar spacing.

Mesoscopic numerical simulation analysis of electromagnetic transmission properties of prefabricated glass microbeads-cement paste composites

Prefabricated composites with glass microbeads volume content of 0%, 20%, 40% and 70% were designed. The electromagnetic properties of the composites were tested. Meanwhile, 2D mesoscopic finite element model of electromagnetic transmission performance of composites was established. The results showed that the glass microbeads would affect the transmission path of electromagnetic wave, and the electric field strength, magnetic field strength and energy loss distribution of the composites. The main reasons for the glass microbeads to improve the electromagnetic transmission performance of the composites were that when the glass microbeads content was lower than 40%, the extreme value of the reflection coefficient reduced; When the content of glass microbeads exceeds 40%, the extreme value of the reflection coefficient and absorption coefficient reduced. The electromagnetic transmission coefficient of the composites was increased by 343.5% with the content of glass microbeads reaches 70%.

Thermal and Mechanical Properties of Plain Woven Ceramic Matrix Composites by the Imaged-Based Mesoscopic Model

The mesoscopic finite element model of ceramic matrix composites is developed by reconstructing computed tomography images. The relationship between microstructure and macroscopic properties and their dispersion are explored. Firstly, a three-dimensional reconstructed computed tomography model was carried out to calculate the orientation of the components. Secondly, the orientation and gray value of images were used to identify the basic structure of composites including fiber tows, matrix, and porosities. Finally, the two-dimensional finite element model was developed to analyze the macroscopic thermal and mechanical properties. The numerical results showed that: (1) the geometries and distributions of pores had a significant effect on the through-thickness modulus and thermal conductivity; (2) the stress and heat flow concentration area on the material surface usually occurred in narrow gaps between closely spaced longitudinal tows; (3) the elastic modulus and thermal conductivity were dispersive, and their distribution followed by two-parameter Weibull distribution.

Tensile behavior and failure mechanism of 3D woven fabric reinforced aluminum composites

This paper aims to study the mechanical behavior and the complicated failure mechanism of a novel Al matrix composites reinforced with 3D orthogonal woven carbon fiber. The quasi-static tensile behavior, local stress response and progressive failure process are investigated via numerical and experimental approach. According to the microstructure at fiber and yarn scale, microscopic and mesoscopic finite element models were established to carry out multiscale simulation. The calculated tensile stress-strain curve is basically in accordance with the experimental curves, where the elastic moduli, tensile strength, and elongation are 118.6 GPa, 777.3 MPa and 0.84%, respectively. Local stress distribution of the matrix pocket and yarns exhibits apparent periodicity and heterogeneity, which is related to the specific fabric architecture. Interface debonding induces the local damage of matrix alloy and transverse cracking of binder and weft yarns successively, resulting in nonlinear response of the tensile curves. The catastrophic rupture of the composites is caused by the axial fracture of warp yarns that resulted from the combination of matrix failure and transverse yarns cracking. The fracture morphology of binder and weft yarns is flat and that of warp yarns exhibits limited fiber pull-out, which can be interpreted by the predicted failure mode. Based on the validated model, the influence of fabric structure parameters on the macroscopic properties was further evaluated. The results indicate that the increase of warp or weft density could improve the tensile strength and elastic modulus, but the tensile elongation decreases with the increase of weft density.

Fracture prediction of NM450TP wear-resistant steel plates during air bending using a mesoscopic heterogeneous model

A mesoscopic finite element model considering material heterogeneity based on microstructure features was constructed to predict the fracture of NM450TP plates during air bending. The fracture morphology and crack initiation and propagation were specifically addressed from two typical planes of the viewing direction, namely, the section plane orthogonal to the bending axis and the bending (outer) convex surface under tension during bending. The results demonstrated that the model could accurately reproduce the initiation, propagation and final fracture morphology. In the section plane, strain shear bands appeared and then developed into the onset of the initial crack with an inclined angle of 45° to the convex surface. As bending developed, the crack randomly expanded towards the through-thickness direction, ascribed to the interaction between the stress mode and material heterogeneity. In the bending convex surface, the fracture morphology dramatically changed with the relative position between the bending axis and rolling directions. When the bending axis was perpendicular to the rolling direction, a serrated fracture line was formed. When the bending axis was parallel to the rolling direction, a nearly linear fracture line was finally formed along the bending axis.

Anti-blast analysis and design of a sacrificial cladding with graded foam-filled tubes

Foam-filled tubes are excellent energy absorption structures for impact resistance, and graded foam may have superiority for the design of anti-blast sacrificial cladding. The anti-blast response of density-graded foam-filled tubes as a core layer is investigated numerically and theoretically. Mesoscopic finite element models for graded foam-filled tubes are constructed, and their constant-velocity compression and anti-blast performance are simulated. One-dimensional analytical shock models based on an empirical force–displacement relationship are developed to analyze the axial collapse wave propagation in graded foam-filled circular tubes. Single-/double-wave deformation patterns are observed for graded foam-filled tubes under blast loading, especially the negatively graded foam-filled tubes with gradient parameters close to zero may also show a single-wave deformation pattern. The results demonstrate that the negatively graded foam-filled tube with a small density gradient is a good choice to design anti-blast sacrificial cladding with a small critical length and a low transmitted force. A contour map of the critical length required to absorb the impulse of blast loading for different gradient parameters and diameter-thickness ratios of the outer tube is established. This study proposes a new design guideline for superior blast resistance structures in engineering applications.

Calculation and Analysis of Temperature Damage of Shimantan Concrete Gravity Dam Based on Macro-Meso Model.

Considering that ANSYS software will automatically quit or the computer will freeze when generating random aggregate models of concrete by using some existing methods that are based on the ANSYS parametric design language (APDL), a new method of random aggregate placement using the ESEL command in APDL and the rotation of the local coordinate system is proposed in this paper. According to this method, a multiscale macroscopic and mesoscopic finite element model of the No. 9 non-overflow dam section of Shimantan dam is constructed. In addition, considering that most of the damage models adopted by the existing mesoscale simulation of concrete damage and fracture cannot take into account the interaction between aggregates, interfacial transition zone (ITZ), and mortar, an improved anisotropic temperature damage model is proposed in this paper. The aggregate placement simulation results show that the method presented in this paper can quickly generate two-dimensional (2D) random concrete aggregates, and the generation of three-dimensional (3D) aggregates can also be completed in a very short time, which can greatly improve the aggregate generation efficiency. Moreover, the aggregate shape generated by this method is very close to the real concrete aggregate shape. The crack propagation simulation results show that the sudden rise and fall of temperature can cause damage in the mortar and ITZ of concrete inside the dam body, which is the main reason for the generation of macroscopic through-cracks in the No. 9 non-overflow dam section of Shimantan dam during the operation period. Finally, it can be learned from the results that the method presented in this paper is reasonable and feasible, and can be extended to the crack propagation simulation of some other concrete gravity and arch dams.

Shape memory property and mechanism of the knitting-fabric reinforced epoxy composites subjected to tensile loading

Shape memory polymers (SMPs), as stimulus-responsive shape-shifting materials, are generally reinforced with particles and fibers to fabricate the shape memory polymer composites (SMPCs) for better mechanical and shape-recovery properties. However, many continuous fibers reinforced SMPCs have good shape recoverability subjected to bending loading but limited shape recoverability under tensile loading due to limitation of tensile deformation of continuous fibers. Here, we developed the continuous fiber knitting-fabric reinforced shape memory epoxy composites and investigated their shape memory property and mechanism subjected to large tensile strain. The effect of epoxy component ratios, tensile strains, and course(0°)/wale(90°) directions on the shape memory behavior, recovery stress, and mechanical property of the shape memory epoxy (SMEP) and its composite (SMPC) were studied. The results show that the SMEPs and SMPCs with the tensile strain up to 30% have good shape fixation rates of above 99% and final recovery ratios of above 98%. A mesoscopic finite element model of knitting-fabric reinforced SMPC was established to study the shape memory mechanism. The recovery stress of the SMPC can improve up to 5.8 times as compared with pure SMEP. The knowledge gained in this work will benefit future development and application for better actuators.

A predictive model for strain hardening and inertia effect of aluminum tubes filled with aluminum foam

Studies on strain hardening and inertia effect of foam-filled tube (FFT) remain limited. Therefore, this work has conducted mesoscopic finite element analyses on FFTs. The 7075-T651 aluminum alloy is chosen for tube material and the 1100-H14 aluminum is employed for the base material of closed-cell foam. The deformation mechanism of the interaction between tube and foam, and the inertia effect on compressive response of FFTs, are both revealed. Results show that due to the interaction, FFT has a higher compressive stress compared with the sum of empty tube and individual foam under the same mass. As more material is involved, the load-bearing capacity, strain hardening, and interaction stress of FFTs all increase with the relative density of infilled foam. A predictive model is established to predict the compressive stress and strain hardening of FFTs. The load-bearing capacity of tube, the plastic hardening of foam, and the interaction effect between tube and foam are all considered in this model. Moreover, due to the inertia effect, the stress at the impact end is significantly higher than that at the support end under high-velocity impact. The one-dimensional shock wave theory is added to the model, enabling the prediction under high-velocity impact.

Developing a model for chloride transport through concrete considering the key factors

The corrosion of chloride-induced on concrete is affected by many factors. In this research, an innovative empirical model was developed to predict the long-term chloride migration behavior in concrete, considering the effects of water-cement ratio, time, bonding effect, temperature, relative humidity, and concrete deterioration. The reliability and validity of the results evaluated by the empirical prediction model were verified by the chloride concentration data in concrete specimens exposed to the marine environment for 3, 5, and 10 years reported in the literature. Combined with the established empirical prediction model, the concrete model was regarded as a three-phase composite material composed of mortar, coarse aggregate, and interfacial transition zone. The effects of key factors on chloride migration were further analyzed by using the mesoscopic finite element numerical simulation method. It was observed that when temperature increases from 5 ℃ to 65 ℃, chloride diffusion depth rises by 3.3 times. When relative humidity increases from 20% to 100%, chloride diffusion depth rises by 4.3 times. Also, the water-cement ratio, concrete deterioration, and chloride binding effect have a non-negligible impact on chloride migration.

On the elastic modulus of rock-filled concrete

Rock-filled concrete (RFC) is constructed by placing large rocks into the prescribed formwork then pouring self-compacting concrete (SCC) to fill interstitial voids. The prelaid rock skeleton transfers forces and provides a certain degree of stiffness at the beginning of the hardening process, which makes the elastic modulus evolution of RFC different from that of conventional concrete. This study aims to reveal the elastic modulus evolution of RFC at early ages, bridging the gaps of RFC research in the numerical computational field. Firstly, RFC is modeled using a mesoscopic finite element approach in which prelaid rocks, SCC, and interfacial transition zone are represented explicitly. This model is validated by onsite full-scale test results. Secondly, the hardening process of RFC is simulated using the validated model, and a qualitative evolution function is obtained. Finally, the advanced Dual Eigenstrain method is employed and calibrated based on the simulation results to predict the elastic modulus of RFC at any curing age.

An energy–momentum couple stress formula for variational-based macroscopic modelings of roving-matrix composites in dynamics

In dynamical systems, fiber-reinforced materials with fiber rovings in a cured matrix material, woven or manufactured by the technology of tailored fiber placement (TFP), for instance, have gained great significance for engineers. Therefore, many finite element simulations are currently in progress during the design of composite parts. But, standard finite element formulations do not take into account dimensions and the direction-dependent flexure and twist stiffness of the rovings. In order to avoid computationally costly mesoscopic finite element models with a discretization of roving-matrix interior boundary interfaces, a macroscopic material model can be derived by introducing micropolar rotation degrees of freedom. Micropolar rotation degrees of freedom allow for a separate constitutive description of the direction-dependent stiffness and inertia of the rovings in the cured matrix material. This continuum model represents an extended continuum formulation with an extended set of balance laws. In its computational setting, the discrete preservation of the complete set of balance laws can be realized by a mixed principle of virtual power in connection with energy–momentum tension stress and couple stress formulas. The guaranteed algorithmic energy–momentum consistency then allows an one-off virtual parameter identification of the macroscopic material constants with the mesoscopic model based on the error of the balance functions. Therefore, a mixed finite element formulation with independent micropolar rotation degrees of freedom is recently published, which are able to simulate dynamical problems by taking into account flexure and twist of the rovings. In this previously published paper, the constitutive laws are at most quadratic such that energy–momentum time integrations are possible without a special couple stress approximation. If a nonlinear strain energy function for flexure and twist of the rovings is considered, a new special couple stress approximation is necessary. Therefore, the present paper completes this mixed finite element formulation with a new couple stress approximation and shows its application by means of that numerical experiments with unidirectional rovings, which are designed for the virtual parameter identification. These fully dynamical examples with large translations, rotations and deformations demonstrate the flexure and twist stiffness of the rovings with roving curvature–twist strain energy functions of Kauderer-type by parameter studies. The complete set of discrete balance laws are satisfied independent of boundary conditions in order to allow the upcoming virtual parameter identification.