Linear Elastic Finite Element Model Research Articles

Data-driven artificial neural network for elastic plastic stress and strain computation for notched bodies

An integration of artificial neural network (ANN) and finite element (FE) analysis was developed to predict elastic–plastic stress and strains at notch locations based on a linear elastic FE analysis solution. Two FE models were created for different materials and multiaxial load cases to produce hypothetical elastic and elastic–plastic stress and strain datasets. One model was based on an elastic state, and the other was based on an elastic–plastic state. The ANN was trained with the elastic stress data from the linear elastic FE model as input and the elastic–plastic stress–strain data from the nonlinear elastic–plastic FE model as output. The dataset was divided into three groups: training, verification, and testing data. The ANN was trained using the training data, evaluated using the verification data, and tested for generalizability using the testing data. The results showed that the proposed methodology can predict elastic–plastic stress and strain fields for notched bodies under multiaxial loadings accurately and efficiently using only the elastic FE analysis solution.

Mesh parameterization using elastic FEM with negative Poisson’s ratio material and triangle shape transformation

Linear mesh parameterization method with a free boundary is an attractive technology and a ubiquitous tool that is widely used in computer graphics and geometry processing. The existing methods always have the shortcoming of element flipping. In this study, a novel linear mesh parameterization method with a free boundary is proposed based on the linear elastic finite element model of a material with negative Poisson’s ratio. With appropriate parameter settings, the method can flatten a 3D mesh without element flipping to the most extent. The proposed method is divided into two steps: (1) each element of the 3D mesh is compressed to the origin point; (2) the degenerated mesh is gradually expanded in a plane under the two forces of equal magnitude and opposite directions based on a finite element model of an elastic membrane material with negative Poisson’s ratio. Subsequently, the causes of element flipping are analyzed at internal nodes and boundary nodes. The triangle shape transformation (TST) method is proposed to solve the problem of internal element flipping, and the stiffness enhancement method is presented to overcome the boundary element flipping caused by the severe mutual extrusion of the internal elements near the boundary. Finally, typical examples are tested to verify the effectiveness of the proposed mesh parameterization method.

Experimental analysis and numerical fatigue life prediction of 3D-Printed osteosynthesis plates.

The trend towards patient-specific medical orthopedic prostheses has led to an increased use of 3D-printed surgical implants made of Ti6Al4V. However, uncertainties arise due to varying printing parameters, particularly with regards to the fatigue limit. This necessitates time-consuming and costly experimental validation before they can be safely used on patients. To address this issue, this study aimed to employ a stress-life fatigue analysis approach coupled with a finite element (FE) simulation to estimate numerically the fatigue limit and location of failure for 3D-printed surgical osteosynthesis plates and to validate the results experimentally. However, predicting the fatigue life of 3D components is not a new concept and has previously been implemented in the medical device field, though without experimental validation. Then, an experimental fatigue test was conducted using a proposed modification to the staircase method introduced in ISO 12107. Additionally, a FE model was developed to estimate the stress cycles on the plate. The stress versus number of cycles to failure curve (S-N) obtained from the minimum mechanical properties of 3D-printed Ti6AI4V alloy according to ASTM F3001-14 to predict the fatigue limit. The comparison between experimental results and fatigue numerical predictions showed very good agreement. It was found that a linear elastic FE model was sufficient to estimate the fatigue limit, while an elastic-plastic model led to an accurate prediction throughout the implant's cyclic life. The proposed method has great potential for enhancing patient-specific implant designs without the need for time-consuming and costly experimental regulatory testing.

3-Dimensional analysis of fatigue crack fields and crack growth by in situ synchrotron X-ray tomography

The propagation rate of a fatigue crack in a nodular cast iron, loaded in cyclic tension, has been studied in situ by X-ray computed tomography and digital volume correlation. The semi-elliptical crack initiated from an asymmetric corner notch and evolved to a semi-circular shape, initially with a higher growth rate towards one edge of the notch before the propagation rate along the crack front became essentially independent of position. The phase congruency of the displacement field was used to measure the crack shape. The three-dimensional stress intensity factors were calculated via a linear elastic finite element model that used the displacement fields around the crack front as the boundary conditions. Closure of the crack tip region was observed. The cyclic change in the local mode I opening of the crack tip determined the local fatigue crack propagation rate along the crack front.

Finite Element Modelling of Wear Behaviors of Composite Laminated Structure

Three different laminated composites are used in this study: carbon fiber, woven glass fiber, and glass-fiber-reinforced epoxy. The composite laminate structures were fabricated using the hand lay-up technique at room temperature. The laminates were reinforced with epoxy resin, carbon fibers (CFRP), woven glass fibers (GFRP-W), and random-orientation glass fibers (GFRP-R) to obtain laminates with eight layers. The wear test was performed using a pin-on-disc tribometer with five different loads of 10, 20, 30, 40, and 50 N at room temperature and a constant speed of 3 m/s. In addition, three different surfaces were lubricated: dry, with grease, and with oil. The effect of lubrication on the weight loss of the laminates was measured. The linear elastic finite element model FEM was derived to simulate the pin on the disc and the failure mode in shear mode for the case of dry lubrication. In addition, the FEM allows the friction force to be measured to determine the friction coefficient numerically. For validation, a simple analytical model based on the shear stress induced by the laminates at the interfaces was extracted to measure the friction coefficients. Tensile strength is a characteristic property that is very important for the purpose of material description from FEM and the analytical model. Therefore, it was determined experimentally with a simple tensile test. The results show that the wear rate is better with GFRP-R composites. Moreover, the wear rate with grease is lower than with oil or dry. The FEM showed that the coefficient of friction decreases with normal force to a minimum value of 0.02 for the case of 50 N normal force and for GFRP-R, while the maximum value of the coefficient of friction was 0.55 for CFRP at 10 N normal load and the FEM results were in good agreement with the analytically determined data.

Simulation based compensation techniques to minimize distortion of thin-walled monolithic aluminum parts due to residual stresses

Thin-walled milled monolithic aluminum workpieces are common in the aerospace industry, because of their advantages such as favorable material properties, established design methods, good machinability, known performance and reliable inspection techniques. Machining-induced residual stresses (MIRS) and initial bulk residual stresses (IBRS) are known to be the key factor for causing distortion of those workpieces. In this study the effect of both types, the milling path strategy and the wall thickness on the distortion is analyzed. A developed 3D linear elastic finite element (FEM) model, considering both types of RS as input, and predicting the resulting part distortion, is extended by using the true milling path as well as all RS contained in the entire workpiece. The simulation outcome is validated by experiments and distortion minimization techniques are derived. The results show that the model predicts the distortion shape and level for different wall thicknesses and milling strategies with a high accuracy. The experiments indicated that the distortion of low IBRS parts with 3 mm wall-thickness could be minimized by 42% by only changing the milling path. The simulation highlighted, that for smaller wall thicknesses, the distortion minimization potential is even higher (e.g. 2 mm wall thickness: up to 69% distortion minimization). For high IBRS parts, milling the inverse form of the predicted shape on the backside of the workpiece represents an alternative, which led up to a reduction of the distortion by 77%. In general, three main categories for precontrol distortion techniques can be identified as the process parameters, the part topology and the process strategy.

Strain Measurement within an Intact Swine Periodontal Ligament

The periodontal ligament (PDL) provides support, proprioception, nutrition, and protection within the tooth–PDL–bone complex (TPBC). While understanding the mechanical behavior of the PDL is critical, current research has inferred PDL mechanics from finite element models, from experimental measures on complete TPBCs, or through direct measurement of isolated PDL sections. Here, transducers are used in an attempt to quantify ex vivo PDL strain. In-fiber Bragg grating (FBG) sensors are small flexible sensors that can be placed within an intact TPBC and yield repeatable strain measurements from within the PDL space. The objective of this study was to determine: 1) if the FBG strain measured from the PDL space of intact swine premolars ex vivo was equivalent to physical PDL strains estimated through finite element analysis and 2) if a change in FBG strain could be linearly related to a change in finite element strain under variable tooth displacement, applied to an intact swine TPBC. Experimentally, individual TPBCs were subjected to 2 displacements (n = 14). The location of the FBG was determined from representative micro–computed tomography images. From a linear elastic finite element model of a TPBC, the strain magnitudes at the sensor locations were recorded. An experimental ratio (i.e., FBG strain at the first displacement divided by the FBG strain at the second displacement) and a finite element ratio (i.e., finite element strain at the first displacement divided by the finite element strain at the second displacement) were calculated. A linear regression model indicated a statistically significant relationship between the experimental and finite element ratio (P = 0.017) with a correlation coefficient (R2) of 0.448. It was concluded that the FBG sensor could be used as a measure for a change in strain and thus could be implemented in applications where the mechanical properties of an intact PDL are monitored over time.

A simple analytical study of masonry viaducts

A new, simplified model of behaviour for masonry viaducts is proposed in this article. It recognises that the structural material at the head of a column, comprised of the arch and its backing, forms a very stiff component of the viaduct. The influence of this stiffness is demonstrated qualitatively through the use of two-dimensional, linear elastic finite element models. The implications from such analyses are considered in the context of explaining the reasons behind common forms of damage.

Dynamic load responses of perpetual pavement test roads on U.S. 23: Full-scale instrumentation and evaluation

Perpetual pavement experimental roads of varying asphalt concrete thicknesses (28 cm, 33 cm & 38 cm) were constructed and instrumented on U.S. Route 23 in Delaware County, Ohio. Controlled Vehicle Load (CVL) testing was performed to obtain dynamic load responses under vehicular load and to evaluate influence of vehicle speed, tire pressure and axle configuration. CVL tests were conducted in November 2012 and July 2013 to evaluate temperature effects on pavement responses. A linear elastic finite element model program, OpenPave was used to obtain layered elastic solutions of load responses with time history to validate measured results. Paired t-tests were performed to compare mean difference between measured and calculated strain responses. Factorial ANOVA test was performed to evaluate significance of truck speed and tire pressure on measured strain responses. It was found that the calculated strain responses were overall in good agreement with the measure values. A uniquely designed strain gage rosette was installed to obtain vertical strain in the pavement and was found to be effective. However, significant differences existed between measured and calculated strain responses in summer test due to unaccountability of the FE program for viscoelasticity of asphalt concrete materials. 33 cm section with stabilized subgrade performed the best with lowest strain responses. Tandem axle truck produced strains lower than single axle truck even though total weight was heavier. Transverse strain tends to increase as lateral wheel offset increases.

2D and 3D numerical models to evaluate trabecular bone damage

The comprehension of trabecular bone damage processes could be a crucial hint for understanding how bone damage starts and propagates. Currently, different approaches to bone damage identification could be followed. Clinical approaches start from dual X-ray absorptiometry (DXA) technique that can evaluate bone mineral density (BMD), an indirect indicator of fracture risk. DXA is, in fact, a two-dimensional technology, and BMD alone is not able to predict the effective risk of fractures. First attempts in overcoming this issue have been performed with finite element (FE) methods, combined with the use of three-dimensional high-resolution micro-computed tomographic images. The purpose of this work is to evaluate damage initiation and propagation in trabecular vertebral porcine samples using 2D linear-elastic FE models from DXA images and 3D linear FE models from micro-CT images. Results show that computed values of strains with 2D and 3D approaches (e.g., the minimum principal strain) are of the same order of magnitude. 2D DXA-based models still remain a powerful tool for a preliminary screening of trabecular regions that are prone to fracture, while from 3D micro-CT-based models, it is possible to reach details that permit the localization of the most strained trabecula.Graphical abstract

A stochastic micro to macro mechanical model for the evolution of bone-implant interface stiffness

Upon placement of an implant into living bone, an interface is formed through which various biochemical, biological, physical, and mechanical interactions take place. This interface evolves over time as the mechanical properties of peri-implant bone increase. Owing to the multifactorial nature of interfacial processes, it is challenging to devise a comprehensive model for predicting the mechanical behavior of the bone-implant interface. We propose a simple spatio-temporally evolving mechanical model – from an elementary unit cell comprising randomly oriented mineralized collagen fibrils having randomly assigned stiffness all the way up to a macroscopic bone-implant interface in a gap healing scenario. Each unit cell has an assigned Young's modulus value between 1.62 GPa and 25.73 GPa corresponding to minimum (i.e., 0) and maximum (i.e., 0.4) limits of mineral volume fraction, respectively, in the overlap region of the mineralized collagen fibril. Gap closure and subsequent stiffening are modeled to reflect the two main directions of peri-implant bone formation, i.e., contact osteogenesis and distance osteogenesis. The linear elastic stochastic finite element model reveals highly nonlinear temporal evolution of bone-implant interface stiffness, strongly dictated by the specific kinetics of contact osteogenesis and distance osteogenesis. The bone-implant interface possesses a small stiffness until gap closure, which subsequently evolves into a much higher stiffness, and this transition is reminiscent of a percolation transition whose threshold corresponds to gap closure. The model presented here, albeit preliminary, can be incorporated into future calculations of the bone-implant system where the interface is well-defined mechanically. Statement of significanceA simple, physically informed model for the mechanical characteristics of the bone-implant interface is still missing. Here, we start by extending the reported mechanical characteristics of a one cubic micrometre unit cell to a 250 µm long interface made of 1 µm thick layers. The stiffness of each cell (based on mineral content) is assigned randomly to mimic bone micro-heterogeneity. The numerical study of this interface representative structure allows for the simultaneous determination of the spatio-temporal evolution of the mechanical response at local (discrete element) and global (overall model) scales. The proposed model is the first of this kind that can easily be incorporated into realistic future models of bone-implant interaction with emphasis on implant stability and different loading conditions.

Interlocking birch plywood structures

Interlocking Particle Structures (IPS) are geometrically stable assemblies, usually fabricated from plate type elements that are interconnected by slotted joints. IPS are demountable and their components have the potential to be used and reused in different structures and configurations. This paper explores the applicability of birch plywood panels, which are characterized by a high surface hardness, for this type of structural system. Experimental tests were conducted to determine the mechanical properties of birch plywood plates. Moreover, IPS connections with different geometrical properties were investigated for two different load exposures: bending and rotation. The characteristics under bending exposure are influenced by the orientation of the face-veneers. For the rotational load exposure, very small strength and stiffness properties have been identified. A linear elastic finite element model is presented that shows a wide agreement with the test results. The study serves as an initial probe into the performance of IPS structures at the component level. Various aspects that are relevant for the design of IPS, such as the assembly, the accuracy and challenges regarding digital fabrication, the durability, and the structural performance are discussed.

A Bayesian Approach for Inferring Sea Ice Loads

AbstractThe Earth’s climate is rapidly changing and some of the most drastic changes can be seen in the Arctic, where sea ice extent has diminished considerably in recent years. As the Arctic climate continues to change, gathering in situ sea ice measurements is increasingly important for understanding the complex evolution of the Arctic ice pack. To date, observations of ice stresses in the Arctic have been spatially and temporally sparse. We propose a measurement framework that would instrument existing sea ice buoys with strain gauges. This measurement framework uses a Bayesian inference approach to infer ice loads acting on the buoy from a set of strain gauge measurements. To test our framework, strain measurements were collected from an experiment where a buoy was frozen into ice that was subsequently compressed to simulate convergent sea ice conditions. A linear elastic finite element model was used to describe the response of the deformable buoy to mechanical loading, allowing us to link the observed strain on the buoy interior to the applied load on the buoy exterior. The approach presented in this paper presents an instrumentation framework that could use existing buoy platforms as in situ sensors of internal stresses in the ice pack.

Experimental investigation on the structural response of RC slabs subjected to combined fire and blast

Reinforced concrete (RC) submerged floating tunnels (SFTs) represent a possible solution for crossing wide, deep fjords, and is considered for the E39 highway route along the Norwegian west coast. With regard to SFTs, the specific accidental scenario that is under investigation is the combined action of fire and subsequent internal explosion, as this is a crucial safety design condition for this type of structure. To assess the structural performance of reinforced concrete structures under combined fire and blast actions, gas burner equipment and a shock tube device were used to generate high temperature and blast loading, respectively, on RC circular slabs. A proper set of instruments consisting of thermocouples embedded in the specimens, accelerometers and ultrasonic pulse velocity (UPV) equipment made it possible to capture the behaviour of the slabs under the combined fire and blast actions and to distinguish the specific role of fire and blast. Simplified numerical tools such as an equivalent elastic single degree of freedom (SDOF) model and a linear elastic finite element (FE) model were used to interpret the experimental results. By considering all combinations of three fire exposure times and two shock waves, the effect of damage accumulation from a combined action of fire and subsequent internal explosion was mapped. A reliable benchmark for numerical models was obtained.

Notch static strength of additively manufactured acrylonitrile butadiene styrene (ABS)

The present theoretical/experimental investigation deals with the problem of performing the static assessment of notched components made of additively manufactured Acrylonitrile Butadiene Styrene (ABS). The notch strength of this 3D-printed material was investigated by testing a large number of specimens, with the experiments being run not only under tension, but also under three-point bending. The samples contained geometrical features of different sharpness and were manufactured (flat on the build plate) by changing the printing direction. Being supported by the experimental evidence, the hypothesis was formed that the mechanical response of 3D-printed ABS can be modelled effectively by treating it as a material that is linear-elastic, brittle, homogenous and isotropic. This simplifying hypothesis allowed the Theory of Critical Distances to be employed also to assess static strength of 3D-printed ABS containing geometrical features. The validation exercise based on the experimental results being generated demonstrates that this theory is highly accurate, with its use leading to predictions falling mainly within an error interval of about ±20%. This level of accuracy is certainly satisfactory especially because this static assessment methodology can be used in situations of engineering relevance by making use of the results obtained by solving standard linear-elastic Finite Element models.

Fatigue Strength Reduction Factors Based on Strain Energy Density Applied to Sharp and Blunt Notches under Multiaxial Loading

Real mechanical assemblies favor the initiation and propagation of fatigue cracks due to stress concentration phenomena arising from the geometrical features such as notches, corners, holes, welding toes, etc. Classical fatigue analysis of notched specimens is done using an empirical formula and a fitted fatigue strength reduction factor, which is experimentally expensive and lacks physical scene. In the present paper, a simple and meaningful methodology is proposed to assess notched components against multiaxial fatigue. In this method, by precisely defining a finite-size volume surrounding the fatigue crack initiation site (notch tip), over which the strain energy is averaged, the morphological effect on the process zone is fully addressed. Such a method takes into account the effect of combination of different modes (I, II, III) and the load ratio. In order to implement it for components with a sharp or blunt notch, it is enough to analyze a linear elastic finite element model and to know only the properties of materials obtained from simple uniaxial tests. New relationships for determining an effective (tensile-type) stress and fatigue strength reduction factors are derived for notched specimens. The accuracy of the proposed model is validated by experimental data available in the literature, related to tubular specimens weakened with sharp/blunt notches under combined bending-torsion loading. Such a situation widely appears in equipment used for various branches of industry such as piping, automotive, power plant, drilling, etc.

The Critical Distance Method to estimate the fatigue strength of notched additively manufactured titanium alloys

The present investigation deals with the problem of performing the fatigue assessment of notched components made of 3D-printed titanium alloy Ti6Al4V when it is used in the as-manufactured condition. The notch fatigue strength of this additively manufactured metallic material was investigated by testing under axial loading a large number of specimens containing geometrical features of different sharpness. This experimental programme was designed to investigate also the effect of non-zero mean stresses, so that the experimental results were generated under a load ratio not only equal to -1, but also equal to 0.1. Being supported by the experimental evidence, the hypothesis was formed that the mechanical response of the 3D-printed titanium alloy being investigated could be modelled effectively by treating it as a material that is linear-elastic, homogenous and isotropic. This simplifying hypothesis allowed the Theory of Critical Distances to be employed also to assess the notch fatigue strength of 3D-printed titanium alloy Ti6Al4V weakened by geometrical features of different kind. The validation exercise based on the experimental results being generated demonstrates that this theory is highly accurate, with its use leading to predictions falling mainly within the scatter bands associated with the fatigue curves used for calibration. This level of accuracy is certainly satisfactory especially because the Theory of Critical Distances can be employed in situations of engineering relevance by making use of the results obtained by solving standard linear-elastic Finite Element models.

Metamaterial topology optimization of nonpneumatic tires with stress and buckling constraints

SummaryThis article presents the design of a metamaterial for the shear layer of a nonpneumatic tire using topology optimization, under stress and buckling constraints. These constraints are implemented for a smooth maximum function using global aggregation. A linear elastic finite element model is used, implementing solid isotropic material with penalization. Design sensitivities are determined by the adjoint method. The method of moving asymptotes is used to solve the numerical optimization problem. Two different optimization statements are used. Each requires a compliance limit and some aspect of continuation. The buckling analysis is linear, considering the generalized eigenvalue problem of the conventional and stress stiffness matrices. Various symmetries, base materials, and starting geometries are considered. This leads to novel topologies that all achieve the target effective shear modulus of 10 MPa, while staying within the stress constraint. The stress‐only designs generally were susceptible to buckling failure. A family of designs (columnar, noninterconnected representative unit cells) that emerge in this study appears to exhibit favorable properties for this application.

Stress analysis of double-lap bi-material joints bonded with thick adhesive

Mechanics of double-lap Steel-to-CFRP adhesively-bonded joints loaded in tension are investigated experimentally using Digital Image Correlation (DIC) and Acoustic Emission (AE), analytically using a one-dimensional closed-form solution and numerically with Finite Element analysis. The double-lap bi-material joints are fabricated of a steel core adhesively bonded to two CFRP skins with adhesive thickness of ~ 8 mm, using an Epoxy-based and MMA-based adhesives. In order to capture the in-plane deformation of the joint, full field strain/displacement maps are obtained using DIC. This data is used to validate the shear-lag model predictions of the adhesive shear stress/strain distribution as well as the linear-elastic Finite Element Model (FEM) results. In addition, they are used to capture the susceptible damage locations and their effect on the displacement contour maps, strain distribution and load transfer between the joint's different constituents. A correlation between the DIC displacement and the AE signals is obtained for damage detection in both joints. Moreover, a good agreement amongst the analytical, FE and DIC strain/stress distributions along the bond-line is observed. This study introduces the analytical shear-lag model as an alternative to predict the stress state in thick-adhesive double-lap joints, with an acceptable level of accuracy and robustness.

High-resolution 3D weld toe stress analysis and ACPD method for weld toe fatigue crack initiation

Weld toe fatigue crack initiation is highly dependent on the local weld toe stress-concentrating geometry including any inherent flaws. These flaws are responsible for premature fatigue crack initiation (FCI) and must be minimised to maximise the fatigue life of a welded joint. In this work, a data-rich methodology has been developed to capture the true weld toe geometry and resulting local weld toe stress-field and relate this to the FCI life of a steel arc-welded joint. To obtain FCI lives, interrupted fatigue test was performed on the welded joint monitored by a novel multi-probe array of alternating current potential drop (ACPD) probes across the weld toe. This setup enabled the FCI sites to be located and the FCI life to be determined and gave an indication of early fatigue crack propagation rates. To understand fully the local weld toe stress-field, high-resolution (5 μm) 3D linear-elastic finite element (FE) models were generated from X-ray micro-computed tomography (μ-CT) of each weld toe after fatigue testing. From these models, approximately 202 stress concentration factors (SCFs) were computed for every 1 mm of weld toe. These two novel methodologies successfully link to provide an assessment of the weld quality and this is correlated with the fatigue performance.