In-plane Loading Conditions Research Articles

Enhanced Crashworthiness Parameters of Nested Thin-Walled Carbon Fiber-Reinforced Polymer and Al Structures: Effect of Using Expanded Polypropylene Foam

The in-plane loading conditions of carbon fiber/epoxy composite (CFRP) and aluminum nested-tube-reinforced expanded polypropylene (EPP) blocks were empirically examined. This study used crashworthiness metrics to estimate the best design configuration under quasi-static loading rates. The experimental phase began with lateral loading testing of single and nested aluminum and CFRP specimen. In-plane crushing experiments were performed on EPP foam blocks reinforced with nested tubes. Both single and nested aluminum tubes had comparable force–response curves and maintained their load-bearing capacity throughout testing. Despite a load-carrying capacity drop above a particular displacement threshold, the CFRP specimens had superior specific energy absorption (SEA) values due to their lightweight nature. The triple-tube nested specimens with two smaller tubes exhibited the best SEA results (1.72 and 1.88 J/g, respectively, for the aluminum and CFRP nested samples). During concurrent tube deformation, the nested samples showed a synergistic connection that increased energy absorption, especially in the EPP foam blocks with reinforced tubes. The study also examined the effects of building nested specimens with aluminum exterior tubes and CFRP inner tubes, and vice versa. This method showed that CFRP tubes within aluminum outer tubes lowered specimen weight (from 93.1 g to 67.7 g) and energy absorption (from 160.2 J to 153.3 J). However, the weight reduction outweighed the energy absorption, increasing SEA values for certain composite material configurations (from 1.72 J/g to 2.26 J/g).

A quadrilateral inverse plate element for real-time shape-sensing and structural health monitoring of thin plate structures

The inverse finite element method (iFEM) emerged as a powerful tool in shape-sensing and structural health monitoring (SHM) applications with distinct advantages over existing methodologies. In this study, a quadrilateral inverse-plate element is formulated via a sub-parametric approach using bi-linear and non-conforming cubic Hermite basis functions for engineering structures, which can be modeled as thin plates. Numerical validation involves dense and assumed sparse sensor arrangements for in-plane, out-of-plane, and mixed general loading conditions. iFEM analysis reveals efficient monotonic convergence to analytical and high-fidelity finite element reference solutions. After successful numerical validation, defect detection analysis is performed considering minute geometric discontinuities and structural stiffness reduction because of latent subsurface defects under tensile and transverse loading conditions. The inverse formulation successfully resolves the presence of simulated defects under a sparse sensor arrangement. The proposed inverse-plate element is accurate in the full-field reconstruction of shape-sensing profiles and reliable in defect identification and quantification in thin plate structures.

A homogenized anisotropic constitutive model of perforated sheets for numerical simulation of stamping

Perforated sheets exhibit strong anisotropy related to the arrangement of holes during plastic deformation, which poses significant challenges for accurate prediction of the macroscopic plastic behavior in stamping. Addressing this, unit cell simulations were conducted to determine the homogenized yielding and hardening behaviors of perforated sheets with hexagonal or square arrays of circular holes under in-plane loading conditions. The local deformation mode, which determines the macroscopic anistropy, is unveiled. A mechanism-motivated homogenized yield criterion was proposed based on the local deformation modes, which provides a concise yet unified approach to modeling complex material anisotropic behavior with high accuracy. Additionally, a mixed hardening strategy was developed to capture the evolution of yield loci in term of size and shape. The proposed constitutive model demonstrates precise predictions of flow stress variations and the apparent r-value with loading angles during uniaxial tension. Furthermore, it successfully forecasts two distinct types of earing profiles in the deep drawing of perforated sheets with square arrays of circular holes at different hole fractions. This modeling approach provides a feasible way for predicting the deformation behavior of perforated sheets during stamping with high computational efficiency.

Phase-field approach for fracture prediction of brittle cracked components

The versatility of the phase-field method (PFM) in predicting elusive fracture trajectories has attracted researchers in recent years; however, limited focus has been directed toward fracture load prediction for brittle materials. This study presents a computationally low-cost and straightforward framework based on phase-field modeling to predict the fracture loads and fracture initiantion angles of brittle cracked components under in-plane loading conditions. The framework was assessed through a comprehensive comparison between numerical and experimental data for various specimens and test configurations. Despite using 1D analytical formulations for calculating phase-field parameters, great accordance between empirical data and simulation results demonstrated the effectiveness of the proposed model. A technique that restricts the computation of the phase-field variable merely around the crack tip was applied to significantly reduce the computational costs of PFM simulations. Furthermore, we examined different numerical aspects and confirmed the robustness of the proposed procedure.

Experimental and theoretical investigation of the influence of post-curing on mixed mode fracture properties of 3d-printed polymer samples

This study explores the mechanical properties and fracture characteristics of additively manufactured acrylonitrile butadiene styrene specimens, focusing on the impact of raster angle and post-process heat treatment. To this end, a large number of tensile and semi-circular bending samples with three distinct raster angles of 0/90°, 22/ − 68°, and 45/ − 45° were prepared and exposed to four types of heat treatments with different temperature and pressure conditions. Simultaneously, theoretical models of maximum tangential stress (MTS) and generalized MTS (GMTS) were developed to estimate the onset of specimen fracture under mixed-mode in-plane loading conditions. Recognizing the non-linear behavior within the stress–strain curve of tensile test samples, particularly in the annealed samples, an effort was undertaken to transform the original ductile material into a virtual brittle material through the application of the equivalent material concept (EMC). This approach serves the dual purpose of bypassing intricate and tedious elastoplastic analysis, while concurrently enhancing the precision of the GMTS criterion. The experimental findings have revealed that while the annealing process has a minimal effect on the yield strength, it considerably enhances energy absorption capacity, increases fracture toughness, and reduces the anisotropy. Additionally, the combined EMC-GMTS criterion has demonstrated its capability to predict the failure of the additively manufactured parts with an acceptable level of accuracy.

Enhancing crashworthiness characteristics of modified hexagonal honeycomb structural panels through stretching and bending of ribs

The effects of stretching and bending of concave, convex, and horizontal ribs on the energy absorption characteristics of modified hexagonal honeycomb structural panels are investigated under in-plane quasi-static compression loading conditions. In this regard, five hierarchical modified structural panel configurations were fabricated using polylactic acid material (PLA) via a fused filament 3D printer, ensuring uniform wall thickness in the 1.5–2 mm range. The panels included the regular hexagonal panel (RHP), regular hexagonal panel with concave rib (RHCP), regular hexagonal panel with convex rib (RHXP), regular hexagonal panel with concave and horizontal ribs (RHCRP), and regular hexagonal panel with convex and horizontal ribs (RHXRP). In-plane quasi-static compressive loading tests were conducted to analyze crush resistance characteristics, and buckling modes of the modified honeycomb panels were examined through experimental and finite element analysis procedures. The result indicates that the specific energy absorption capacity (SEA) of RHXRP is increasing significantly compared to the SEA capacity of other categories of the structures. The changes in failure modes and increased crush energy absorption characteristics of modified RHP with the introduction of concave, convex, and horizontal ribs are elaborated.

Experimental investigation of the shear force capacity of prismatic cross laminated timber beams

Experimental tests of Cross Laminated Timber (CLT) under in-plane beam loading conditions are presented. The influence of the element layup, the individual lamination width, and the beam overhang at the supports on the shear force capacity was investigated. All the CLT beams had the same gross cross section, and a 4-point-bending test setup was used. The experimentally determined load-bearing capacities are compared with the load-bearing capacities resulting from analytical methods proposed for structural design, focusing on shear failure in the crossing areas of flatwise bonded laminations (shear failure mode III). The test results indicate no or very small influence of the element layup and the lamination width on the shear force capacity. These results partly contradict the predictions of the proposed design methods. Of the three studied beam geometry parameters, the beam overhang at the support had the greatest influence on the load-bearing capacity.

A two-dimensional four-node quadrilateral inverse element for shape sensing and structural health monitoring

The inverse finite element method (iFEM) is a powerful tool for shape sensing and structural health monitoring and has several advantages with respect to some other existing approaches. In this study, a two-dimensional four-node quadrilateral inverse finite element formulation is presented. The element is suitable for thin structures under in-plane loading conditions. To validate the accuracy and demonstrate the capability of the inverse element, four different numerical cases are considered for different loading and boundary conditions. iFEM analysis results are compared with regular finite element analysis results as the reference solution, and very good agreement is observed between the two solutions demonstrating the capability of iFEM approach.

Enhancing buckling analysis of functionally graded plates using unified and generalized higher-order shear deformation theories

This paper introduces a comprehensive framework for stability analysis of functionally graded plates under diverse in-plane loading conditions while employing higher-order shear deformation theories. For this purpose, a unified model, including all shear deformation kinematics, has been proposed. This unified model incorporates any number or type of shear transverse functions, encompassing all existing plate shear deformation theories. This inclusivity is achieved through the introduction of a unique parameter, denoted by ”n” representing the number of shear deformation functions in the displacement model. Such a unified model allows great flexibility in choosing among higher order theories when modeling the behavior of plates subjected to shear deformation, making it a valuable tool for applications in engineering and materials science. Besides, this allowed us to easily introduce a fifth-order theory used for the first time in the buckling analysis of FGM plates. The critical buckling loads expressions corresponding to the employed kinematics were derived and the calculated values are compared to those computed using the numerical solver. The comparison demonstrates the effectiveness and accuracy of the formulated expressions in predicting critical buckling loads under uniaxial and biaxial loading conditions.

A Two-Dimensional Eight-Node Quadrilateral Inverse Element for Shape Sensing and Structural Health Monitoring.

The inverse finite element method (iFEM) is a powerful tool for shape sensing and structural health monitoring and has several advantages with respect to some other existing approaches. In this study, a two-dimensional eight-node quadrilateral inverse finite element formulation is presented. The element is suitable for thin structures under in-plane loading conditions. To validate the accuracy and demonstrate the capability of the inverse element, four different numerical cases are considered for different loading and boundary conditions. iFEM analysis results are compared with regular finite element analysis results as the reference solution and very good agreement is observed between the two solutions, demonstrating the capability of the iFEM approach.

A two-dimensional inverse crack tip element for shape sensing and structural health monitoring

inverse Finite Element Method (iFEM) is a powerful tool for shape sensing and structural health monitoring of marine structures and has several advantages with respect to some other existing approaches. However, current iFEM formulation is not suitable for marine structures having pre-existing cracks due to stress singularities at the crack tip. In this study, a two-dimensional inverse crack tip element formulation is presented. The element is suitable for thin structures under in-plane loading conditions. The inverse crack tip element allows determination of Stress Intensity factor values at the crack tip. To validate the accuracy and demonstrate the capability of the inverse crack tip element, six different numerical cases are considered for different geometry, loading and boundary conditions. iFEM analysis results are compared with regular finite element analysis results as the reference solution and very good agreement is observed between the two solutions demonstrating the capability of the current iFEM approach.

A simplified micro-model based on discrete elements and elastic bodies for non-linear static analysis of in-plane loaded masonry panels

In this paper, a simplified micro-model based on a combination of continuum (2D) and discrete elements was developed to estimate non-linear behavior and failure prediction of masonry panels subjected to in-plane loads. Bricks were substituted by 2D elastic elements which connected via eight bi-component non-linear springs to each other. Each spring has axial and shear behavior which is represented by mortar axial stress–strain curve, including softening and brick–mortar cohesion-friction law, respectively. Substantial simplifications are accomplished due to employing elastic panels and concentration non-linearity at the discrete elements in terms of the possibility of implementation in commercial software. The validation process was conducted at two levels; first: a masonry cell under possible in-plane loading conditions and second: ten experimental panels having different geometrical and mechanical properties subjected to vertical and horizontal actions simultaneously. The obtained results including global behavior and crack pattern were compared with experimental ones as well as available numerical predictions from the literature. High accuracy was observed despite convergence ease and reduction in both pre-processing and analysis time.

Towards reduction of bending-extension coupling in unsymmetrical laminates using multi-objective heat transfer search

The main advantage of composite materials is the ability to tailor the properties of stacking sequences. Unsymmetrical laminate involves an arbitrary even or odd number of fiber layers oriented at different angles wherein identical fiber orientation above and below mid-surface does not exist. In the case of these laminates, the coupling deformation is undesired during mechanical loads and symmetrical laminates may not be the best solution for all cases. In this work, an effort has been made to present the methodology to minimize the end effects of bending-extension coupling in the case of unsymmetrical laminates to make it widely applicable. The infinite plate containing the circular and elliptical hole is studied with various in-plane loading conditions. The end effect of bending-extension coupling is presented by the multi-objective problem of minimization of the normalized tangential force and moment. The non-dominated sorting heat transfer search algorithm is employed to solve this optimization problem wherein TOPSIS decision-making technique is used to obtain the best values from the Pareto solution. The different cluster-based methods are proposed to utilize the unsymmetrical laminates most effectively. The effects of these clusters on the bending-extensional coupling are investigated and results reveal that cluster design presenting each fiber angle value distinctly is the best design among all recommended in the present investigation. More than 70% of the bending-extensional coupling is reduced in most cases. A unique correlation is found between the cluster design and fiber angles of the optimum stacking sequences. The proposed approach and designs will support the potential use of unsymmetrical laminates by improving properties through tailoring stacking sequences.

Dynamic crashing behaviors of prismatic lithium-ion battery cells

With rapid rising use of lithium-ion batteries (LIBs) for electric vehicles (EV), the mechanical behaviors of LIBs have become more and more important to crash safety. This study aims to investigate dynamic crashing characteristics of prismatic LIB cells through compression tests and finite element (FE) modeling. First, the in-plane and out-of-plane constrained compressive tests of battery specimens without electrolyte are performed at various strain rates to characterize mechanical behaviors of LIB cells under the dynamic loading conditions. The experimental results indicated that the strain rate was of significant effect on the in-plane constrained compression tests but insignificant effect on the out-of-plane counterparts. The nominal stress–strain curves obtained from the dynamic in-plane loading conditions are generally higher than those from the quasi-static conditions. The nominal stress–strain curves obtained from the experimental tests were used to develop homogenized material models for the LIB cell components subject to dynamic crashing conditions. Second, the FE models for the prismatic LIB cell were created by incorporating the homogenized material model. The simulation results were compared with those obtained from in-house experiments including the in-plane and out-of-plane indentation tests on the LIB cell specimens, which exhibited fairly good agreement. Finally, based upon the validated FE models of LIB cell, the indentation of entire prismatic LIB was simulated to further characterize the mechanical behavior of the Lithium-ion batteries under dynamic crushing. The established FE models are anticipated to provide a useful approach for crash safety design in the LIB packs for different impact accidents of electric vehicles.

Assessment of dynamic instability of thin nanoplates considering size and surface energy effects

The stated goal of this study is to comprehensively understand the dynamic instability characteristics of thin nanoplate structures, taking into account the combined effects of both size and surface energy. To achieve this, we present a computational approach based on the non-classical Kirchhoff plate theory within the framework of NURBS-based isogeometric analysis (IGA). The modified couple stress theory, which includes one material length scale parameter, is implemented to adequately account for the size-dependent effect. Additionally, the Gurtin–Murdoch surface elasticity is effectively utilized to assess the influence of surface energy. For the first time, we explore the dynamic instability regions of thin nanoplates, accounting for both size and surface energy effects simultaneously. To obtain solutions from the Mathieu-Hill equations, the Bolotin method is applied in this research. A number of numerical investigations on square, circular and annular thin nanoplate models under periodic in-plane compressive loads are conducted to assess the influence of several crucial input factors on the regions of dynamic instability. The present outcomes reveal that both size and surface energy effects have a remarkable influence on the dynamic instability characteristics of the nanoplates. Accordingly, these effects contribute to an enhancement in structural rigidity at the small-scale level. Furthermore, we explore that in the case of ultra-thin nanoplates, the influence of surface energy becomes dominant. The obtained findings provide valuable insights into the behavior of thin nanoplates under dynamic in-plane loading conditions as well as can contribute to the design of more robust engineering structures.

Reduced polynomial invariant integrity basis for in-plane magneto-mechanical loading

The description of the behavior of a material subjected to multi-physics loadings requires the formulation of constitutive laws that usually derive from Gibbs free energies, using invariant quantities depending on the considered physics and material symmetries. On the other hand, most of crystalline materials can be described by their crystalline texture and the associated preferred directions of strong crystalline symmetry (the so-called fibers). Moreover, among the materials produced industrially, many are manufactured in the form of sheets or of thin layers. This article has for object the study of the magneto-mechanical coupling which is a function of the stress σ and the magnetization M. We consider a material with cubic symmetry whose texture can be described by one of three fibers denoted as θ, γ or α′, and which is thin enough so that both the stress and the magnetization can be considered as in-plane quantities. We propose an algorithm able to derive linear relations between the 30 cubic invariants Ik of a minimal integrity basis describing a magneto-elastic problem, when they are restricted to in-plane loading conditions and for different fiber orientations. The algorithm/program output is a reduced list of invariants of cardinal 7 for the {100}-oriented θ fiber, of cardinal 15 for the {110}-oriented α′ fiber and of cardinal 8 for the {111}-oriented γ fiber. This reduction (compared to initial cardinal 30) can be of great help for the formulation of low-parameter macroscopic magneto-mechanical models.

Comparison of different quasi-static loading conditions of additively manufactured composite hexagonal and auxetic cellular structures

Auxetic cellular structures have the potential to revolutionise sandwich panel cores due to their potential superior energy absorption capability. Because of their negative Poisson's ratio, auxetics behave counterintuitively and contract orthogonally under an applied compressive force, resulting in a densification of material in the vicinity of the applied load. This study investigates three cellular structures and compares their compressive energy absorbing characteristics under in-plane and axial loading conditions. Three unit cell topologies are considered; a conventional hexagonal, re-entrant and double arrowhead auxetic structures. The samples were additively manufactured using two different materials, a conventional Nylon and a carbon fibre reinforced composite alternative (Onyx). Finite element simulations are experimentally validated under out of and in-plane loading conditions and the double arrowhead (auxetic) structure is shown to exhibit comparatively superior energy absorption. For the carbon fibre reinforced material, Onyx, the specific energy absorbed by the double arrowhead geometry was 125% and 244% greater than the hexagonal (non-auxetic) and re-entrant (auxetic) structures respectively.

A general analytical solution of stresses around circular holes in functionally graded plates under various in-plane loading conditions

A general analytical solution of stresses around circular holes in functionally graded plates under various in-plane loading conditions

Experimental and FEM study on the in-plane and out-plane loaded reversible dual-material bio-inspired lattice structures with improved energy absorption performance

In the current study, bio-inspired lattice structures are derived from the architecture of the Euplectella aspergillum (sea sponge). All the lattice structures are fabricated using the fused filament fabrication (FFF) process. The fabricated structures are subjected to quasi-static uni-axial compressive in-plane and out-plane loading conditions. The results shows that energy absorption performance of lattice structures also depends on the structure's stiffness. When used in lattice structures, soft material like thermoplastic polyurethane (TPU) has good energy absorbing performance. However, the stiffness of soft materials is not good enough to increase energy absorption. Here an attempt has been made to increase the energy absorption capacity of lattice structures by using a combination of hard (PLA) and soft phase (TPU) material in the fabrication of structures. Overall, the mechanical properties and deformation behavior in the experimental and finite element studies are quite similar. Structures under in-plane loading conditions showed a shorter linear elastic region and longer plateau region, whereas the structures subjected to out-plane loading conditions showed longer nonlinear elastic regions and a shorter plateau region. Overall, the structures loaded in the in-plane condition have a more stable response, whereas those loaded in the out-plane loading conditions have higher mean plateau stress, higher energy absorption and better efficiency. In both in-plane and out-plane loaded structures, dual-material fabricated structures showed higher efficiency; in-plane structures showed the highest experimental efficiency of 0.453 whereas out-plane structures showed the highest efficiency of 0.470. Combination of dual-material showed improved performance without compromising the reversibility of the energy absorbers. Hence this study opens a field for the design and fabrication of better energy absorbers.

A unified design proposal for shear stress prediction in crossing areas for cross laminated timber at in-plane shear and beam loading conditions

Environmental and urbanization challenges during the last few decades encouraged steady growth of mass timber construction where attention is drawn to cross laminated timber (CLT) as one of the most interesting products in terms of mechanical properties, versatility, efficient prefabrication and sustainability. Standardisation and codification regarding testing and design of CLT elements are hence pointed out as one of the main issues within the ongoing revision procedure of Eurocode 5. A consistent and unified design approach for CLT at pure in-plane shear loading conditions (shear walls) and at in-plane beam loading conditions is however still missing. This paper deals with analytical models for the determination of stress components related to predictions of load bearing capacity of CLT with respect to shear failure mode III – shear failure in the crossing areas constituted by the flatwise bonded areas between laminations of adjacent layers. This failure mode is relevant for both pure in-plane shear loading and in-plane beam loading conditions. The paper presents a review of previously proposed models for the prediction of shear stresses in crossing areas of CLT, for both loading conditions. Comparisons between FE-results and model predictions are reviewed indicating significant differences between them concerning the predicted influence of the CLT element lay-up and values of maximum shear stresses. Based on simplifications of models previously presented, a unified design proposal that is based on a rational and consistent mechanical background for both loading situations and that shows overall good agreement with FE-results is presented.