Elastic Material Behavior Research Articles

Dynamic acoustoelastic testing (DAET) with a thermal strain pump for characterization of closed fatigue cracks

Dynamic acoustoelastic testing (DAET) is a nonlinear acoustic technique used to characterize the nonlinear elastic behavior of materials. To enable the in-situ implementation of DAET, we propose a modification to the conventional DAET setup by replacing the mechanical strain pump with a thermal strain pump. This study presents the feasibility of the proposed thermal-pump DAET setup for in-situ detection of closed fatigue cracks in an aluminum test specimen. Our setup employs a hot air blower to induce a small (∼4 °C) thermal gradient near the surface of the specimen. The surface temperature evolution is captured by an infrared camera allowing thermal strain evaluation on the surface. A pair of high frequency angle-beam Rayleigh surface wave transducers are used to probe the thermal strain-induced changes in near-surface elastic properties. The slope of the relative change in Rayleigh wave speed with the applied thermal strain is taken as a measure of nonlinearity (γ) evaluated at several locations across the specimen along the intact and cracked regions. Our results show that γ measures higher near the crack and decreases as the probe moves towards the crack tip, demonstrating the potential of thermal-pump DAET for in-situ evaluation of closed fatigue cracks.

Investigation on the impact of electrical faults on the loads and exposures of wind turbine gears

For the design of a wind turbine, it is necessary that the design process takes into account the stresses of real operation to a high degree of detail so that targeted dimensioning can be carried out. Depending on its design, the drivetrain of a wind turbine includes a gearbox that connects the rotor to the generator. During operation of a wind turbine, transient load conditions can occur due to loopback from the power grid and faults in the frequency converter. The influence of the resulting stress and possible damage to the gears used in the gearbox is unclear in the design phase. While the stresses on the gears can often be simulated with a high degree of accuracy for constant operating conditions and can thus be integrated into the drivetrain design, this is not the state of the art for dynamic load conditions. The objective of this report is a method for considering dynamic loading events in the design of the cylindrical gear stage used in wind turbine gearboxes using a coupled multi-body simulation and a finite element based tooth contact analysis. Afterwards the method is used to quantify the stress on the tooth flank and tooth root due to special electrical events such as short circuits between the frequency converter and generator or power grid faults for various converter designs. The simulation analyses show that different converter concepts have different effects on the resulting gear load during electrical faults, but are not significantly decisive for the accumulated damage due to elastic material behavior between generator and gear.

Factors influencing the dynamic stiffness in short‐fiber reinforced polymers

AbstractIn short‐fiber reinforced polymers, fatigue damage is typically characterized by measuring the dynamic stiffness and its degradation under cyclic loading. Computational homogenization methods may be used to characterize the fatigue behavior of the composite via numerical predictions. Such an approach may reduce the experimental effort significantly. In the previous works, the authors proposed an elastic fatigue damage model for predicting the relative stiffness degradation of short‐fiber reinforced materials. However, the absolute value of the dynamic stiffness within the first cycle showed deviations from the expected elastic material behavior. Thus, the effect of viscoelastic polymer behavior as well as different microstructure descriptors on the dynamic stiffness is studied in the work at hand.

Prediction of Effective Elastic and Thermal Properties of Heterogeneous Materials Using Convolutional Neural Networks

The aim of this study is to develop a new method to predict the effective elastic and thermal behavior of heterogeneous materials using Convolutional Neural Networks CNN. This work consists first of all in building a large database containing microstructures of two phases of heterogeneous material with different shapes (circular, elliptical, square, rectangular), volume fractions of the inclusion (20%, 25%, 30%), and different contrasts between the two phases in term of Young modulus and also thermal conductivity. The contrast expresses the degree of heterogeneity in the heterogeneous material, when the value of C is quite important (C >> 1) or quite low (C << 1), it means that the material is extremely heterogeneous, while C= 1, the material becomes totally homogeneous. In the case of elastic properties, the contrast is expressed as the ratio between Young’s modulus of the inclusion and that of the matrix (C = EiEm), while for thermal properties, this ratio is expressed as a function of the thermal conductivity of both phases (C = λiλm). In our work, the model will be tested on two values of contrast (10 and 100). These microstructures will be used to estimate the elastic and thermal behavior by calculating the effective bulk, shear, and thermal conductivity values using a finite element method. The collected databases will be trained and tested on a deep learning model composed of a first convolutional network capable of extracting features and a second fully connected network that allows, through these parameters, the adjustment of the error between the found output and the expected one. The model was verified using a Mean Absolute Percentage Error (MAPE) loss function. The prediction results were excellent, with a prediction score between 92% and 98%, which justifies the good choice of the model parameters.

Numerical optimization-based design studies on biaxial tensile tests

Biaxial tensile tests are of great significance for the characterization of materials. For ductile materials, they allow the representation of the yield strength curve separating elastic and plastic material behavior. Contrary demands regarding the specimen design arise, if a biaxial stress state with the equivalent stress equal or close to the yield strength shall be obtained. On one hand, the specimen shall be of constant thickness and stiffness, in order to allow an unconstrained deformation without undesired lateral strains. On the other hand, stress concentrations arising from the load introduction make a thickened border region necessary, in order to avoid a premature failure of the specimen. The present paper addresses this problem by a multi-objective structural optimization using Evolutionary Algorithms. Well-defined parametric models of biaxial tensile test specimens allow to systematically investigate the influence of the thickness distribution and the sizing of the border region. Additionally, the influence of actuators of constant force compared to actuators of constant displacement are quantified. In all cases, the minimization of the stress difference as well as the actuation effort are considered as objectives. The results allow a deep insight to the optimal definition of biaxial tensile test specimens and are summed up in well-defined design proposals.

Crack initiation in PMMA plates with circular holes considering kinetic energy and nonlinear elastic material behavior

The coupled criterion (CC) of finite fracture mechanics (FFM) is extended to assess crack initiation in PMMA specimens with holes under quasi-static loading considering nonlinear elastic (NLE) material model and considering the kinetic energy variation in the energy balance. If dynamic aspects are disregarded, the failure stress predicted using the CC for either linear elastic (LE) material model or NLE material model is underestimated compared to the one measured experimentally. A better representation of the failure stress variation as a function of the hole size is obtained considering constant crack velocity profiles and velocities in the range [550–900] m/s (LE material model) or [400–600] m/s (NLE material model). The predicted failure stresses also depend on the crack velocity profile.

A numerical methodology to predict the lateral load response of monopiles installed in SAND considering soil stiffness degradation

Most of the routine work concerning the design of laterally loaded monopile foundations is conducted using simplified one-dimensional (1D) models based on p-y curves. However, many of these curves have been derived from slender piles typically used in the oil and gas industry, which behave differently than rigid monopiles used as offshore wind turbine foundations. Moreover, these curves usually represent the soil response without considering its degradation, which may significantly modify the monopile lateral response. Hence, this work proposes a numerical methodology based on the finite element method to derive suitable curves for 1D models of monopiles installed in sand. First, a three-dimensional (3D) finite element model (FEM) of the monopile and the surrounding soil was constructed. In this model, the monopile had an elastic and linear material behavior. The soil response was addressed using the Mohr-Coulomb criterion combined with three different soil stiffness degradation models. For extracting the p-y curves from the 3D FEM, a 10th-order polynomial was used to fit the bending moment profiles; consequently, an 8th-order polynomial described the soil reaction profiles. Results obtained using the proposed 3D FEM and a 1D model based on the derived p-y curves were then verified against experimental results obtained through centrifuge modeling. Furthermore, the proposed 1D model adequately matched the experimental results, especially for small displacement conditions.

TH Analyses and Simplified Approach for Precast RC Frames Retrofit with Dissipative Fuse Devices Sismocell

Precast RC structures are a typology of construction widely spread in Italy among industrial buildings, made of single-storey isostatic RC frames built, in past decades, without any connection between beams and columns. The Emilia Earthquake (2012) caused extensive damages in this kind of buildings that have a significant mass located at roof level and lack of connections between horizontal and vertical elements. The recent seismic events highlighted that the lack of connections is the main vulnerability of existing precast RC buildings and at the same time that large displacements are determined between beams and columns. In order to improve the seismic performance of precast RC buildings a cost-effective solution is to dissipate energy at roof level, avoiding at the same time any loss of support between elements. Dissipative fuse devices (Sismocell) placed at beam-column joints are able to dissipate energy and guarantee an effective connection between elements. To evaluate the improvement achieved with the use of Sismocell devices, non-linear time history analyses are usually performed, taking into account the plastic hinges at column base. This work aims to quantify the improvement that can be obtained using Sismocell devices, in terms of reduction of effect of actions in different typologies of structures, remaining in the range of elastic behavior of materials. The TH analyses have been performed on different frame configurations with different seismic input, comparing the behavior of models with hinged connections and connections equipped with dissipative fuse devices. In order to define the optimal force of plastic activation of Sismocell devices, different device sizes have been considered. The results have been analyzed in terms of reductions of shear and moment at base of the columns, with different scaling factor applied to seismic input. Finally, a proposal of a simplified approach based on linear analyses has been compared to TH results.

Influence of Vertical Load on Lateral-Loaded Monopiles by Numerical Simulation

Monopiles are the most common foundation form of offshore wind turbines, which bear the vertical load, lateral load and bending moment. It remains uncertain whether the applied vertical load increases the lateral deflection of the pile. This paper investigated the influence of vertical load on the behaviour of monopiles installed in the sand under combined load using three-dimensional numerical methods. The commercial software PLAXIS was used for simulations in this paper. Monopiles were modelled as a structure incorporating linear elastic material behaviour and soil was modelled using the Hardening-Soil (HS) constitutive model. The monopiles under vertical load, lateral load and combined vertical and lateral loads were respectively studied taking into account the sequence of load application and pile slenderness ratio (L/D; L and D are the length and diameter of the pile). Results suggest that the sequence of load application plays a major role in how vertical load affects the deflection behaviour of the pile. Specifically, when L/D ratios obtained by lengthening the pile while keeping its diameter constant are 3, 5 and 8, the relationships between lateral load and the deflection behaviour of the pile under the effect of vertical load demonstrate a similar trend. Furthermore, the cause of increased lateral capacity of the pile under the action of applied vertical load in the common practical application case and in the VPL case was analyzed by studying the variation law of soil stress along the pile embedment. Results confirm that the confining effect of vertical load increases means effective stress of the soil around the pile, thus increasing soil stiffness and pile capacity.

Mixed mode (I/III) fracture studies using a new specimen setup

In the present work, mixed mode (I/III) fracture studies have been investigated using a new specimen and an out-of-plane loading fixture that can be used with the conventional uniaxial universal testing machines. The proposed specimen is a single edge cracked circular (SECC) specimen which can be employed on both metallic and non-metallic materials under static and fatigue loads. A large number of three-dimensional finite element analyses have been performed on the proposed specimen setup to demonstrate the efficacy of the proposed setup. Experimental fracture studies have also been performed under mixed mode (I/III) loading conditions. The present experimental results are in very good agreement with the available mixed mode (I/III) fracture criteria. Experimental results indicate that the pure mode III fracture toughness is nearly 1.46 times greater than that of the mode I. This has been found due to an increase in the inelastic region around the crack tip in pure mode III and is in accordance with the published results. Detailed analyses of the fractured surfaces have also been carried out. It has been demonstrated that the fractured surfaces become more rough as the mode III component increases. Preliminary results of mixed mode (I/III) fatigue crack growth studies on Al 7075-T6 using the metallic SECC specimen have also been presented. The results of the present study confirm that the proposed specimen setup can be used to study the mixed mode fracture behavior of linear elastic materials under static and fatigue loading.

Heat aging effect on tensile behavior at different strain rates of thermoplastic styrene elastomer

Thermoplastic elastomers (TPEs) are a class of polymer materials used for interior, exterior and under the hood automotive applications which have the elastic behavior of elastomeric materials and the processability the same as for thermoplastics. TPEs have become the most rapidly growing segment of polymer industry. This paper focuses on obtaining the tensile test response of a heat aged compared to as delivered state of SEBS/TPS (Styrene-Ethylene-Butylene-Styrene/Thermoplastic Styrene Elastomers). Samples were analyzed before and after aging through thermal analysis and scanning electron microscopy to observe the chemical degradation of the materials.The dumb-bell samples used for the experimental program were prepared according to ISO 37 type 2 (overall length of 75 mm, length of the narrow portion of 25 mm, width of narrow portion: 4 mm). The samples were subjected to heat-aging according to ISO 188 with the following parameters: 168 h at 100 °C. Tensile tests were performed on the as delivered samples and the heat aged samples. Different values of strain rate (5 mm min−1; 50 mm min−1; 500 mm min−1) were used to determine the difference in the response of the thermoplastic elastomer sample.The ultimate tensile strength of the aged samples is higher than the virgin samples values. Displacement values are lower for the aged materials as the elongation at break is reduced due to the stiffening of the material after heat aging. There was no visible structural difference between aged and virgin samples.

Determination of optimal dimensions of polymer-based rectangular hollow sections based on both adequate-strength and local buckling criteria: Analytical and numerical studies

Most studies have focused on determining optimal dimensions of metal- or composite-based rectangular hollow sections (RHSs) by considering only the design requirement of strength. Different from those, an analytical procedure for the determination of optimal sectional dimensions of polymer-based RHS beams by accounting for both adequate-strength and local buckling for the first time has been presented in the context of this study. Analytical expressions which give the optimal sectional dimensions simultaneously satisfying the adequate-strength and local buckling conditions have been derived for two different loading configurations such as a pure major axis bending and a combined axial compression and major axis bending. The analytical procedure proposed in this study depends on the idea of preventing the polymer-based RHS from buckling prior to its compressive strength. This has been achieved by increasing the critical buckling stress of the RHS up to its compressive strength via optimizing its sectional dimensions. During the optimum design, different elastic and plastic material behaviors of polymers in tension and in compression have been taken into calculations. The results attained analytically have been validated against numerical predictions obtained from linear elastic eigenvalue buckling and postbuckling analyses implemented in Abaqus engineering finite element code. Thus, the analytical procedure reported in this study can be used as a benchmark in identifying the optimal dimensions of RHS members manufactured from polymers. Communicated by Davide Spinello.

The effect of pore sizes on the elastic behaviour of open-porous cellular materials

The influence of the pore structure characteristics in open-porous cellular materials on their macroscopic elastic behaviour is investigated by considering three important microstructural features viz. the relative density, the pore-size distribution, and the pore-wall thickness. To this end, a microstructure-informed modelling approach is presented, where all elements of the three-dimensional (3-d) pore structure can be controlled effectively. The results show that while density does dictate the mechanical properties of open-porous solids, the effects of the pore-wall thickness and the pore-size distribution are not negligible and must be considered while developing such materials, in particular those that exhibit a poly-disperse nature and require load-bearing capabilities under finite strains.

The effect of Lode parameter on the yield surface of Schoen's IWP triply periodic minimal surface lattice

Owing to the advancements in additive manufacturing and increased applications of additively manufactured structures, it is essential to fully understand both the elastic and plastic behavior of cellular materials, which include the mathematically-driven sheet lattices based on triply periodic minimal surface (TPMS) that have received significant attention recently. The compressive elastic and plastic behaviors have been well established for many TPMS latticed structures, but not under multiaxial loading. Furthermore, TPMS lattices are computationally expensive to model explicitly when used in latticing various structures for enhanced multi-functionality, and hence the need to develop accurate yield surfaces in order to capture their plastic behavior in a homogenized approach. The majority of previous yield surfaces developed for cellular materials originate from cellular foams, and limited attempts has been made to develop yield surfaces for TPMS lattices. In this study, a numerical modeling framework is proposed for developing the initial yield surface for cellular materials and is used to develop the initial yield surface for Schoen's IWP sheet-based TPMS cellular lattices. The effect of different loading conditions on the effective yield strength of the IWP sheet-based (IWP-s) TPMS lattice is numerically investigated, based on a single unit cell of IWP-s under fully periodic boundary conditions, assuming an elastic-perfectly plastic behavior of the base material, for relative densities (ρ‾) ranging from 7% to 28%. In order to account for different loading conditions, the stress state is characterized in a generalized fashion through the Lode parameter (L). The effect of L is studied over a range of mean stress values (σm) to understand the effect of both L and σm on the effective yield strength. An initial yield surface is developed incorporating the effect of L, σm and ρ‾, and is validated numerically showing rather good agreement. In the 3D principal stress space, the shape of the yield surface for the IWP-s lattice resembles the shape of a cocoa pod.

A Review of Simplified Numerical Beam-like Models of Multi-Storey Framed Buildings

Modern computational techniques have greatly influenced the numerical analyses of structures, not only in terms of calculation speed, but also in terms of procedural approach. In particular, great importance has been given to structural modelling, that is, the process by which a structure and the actions to which it is subjected are reduced to a simplified scheme. The use of a simplified calculation scheme is necessary since the structures are, in general, considerably complex physical systems whose behaviour is influenced by a large number of variables. The definition of a structural scheme that is at the same time simple enough to be easily computable as well as sufficiently reliable in reproducing the main characteristics of the behaviour of the analysed structure is, therefore, a crucial task. In particular, with reference to multi-storey framed buildings, the extensive use of three-dimensional finite element models (FEM) has been made in recent decades by researchers and structural engineers. However, an interesting and alternative research field concerns the possibility of studying multi-storey buildings through the use of equivalent beam-like models in which the number of degrees of freedom and the required computational effort are reduced with respect to more demanding FEM models. Several researchers have proposed single or coupled continuous beams to simulate either the static or dynamic response of multi-storey buildings assuming elastic or inelastic behaviour of the constitutive material. In this paper, a review of several scientific papers proposing elastic or inelastic beam-like models for the structural analyses of framed multi-storey buildings is presented. Considerations about limits and potentialities of these models are also included.

A semi-empirical approach model for neo-Hookean solids

The neo-Hookean materials change their behaviour at large stress values to give more strain than linear trend (Hook’s region) and plastic deformations appear and ultimately fail. A Mooney-Rivlin model successfully describes this behaviour based on theoretical derivations deduced from Kinetic theory. Although the model takes into account that the deformation involves a change in the volume of rubber, their relationship is quite fitting for a small stress-strain region (Gaussian region). In the present work, a peer model to Mooney-Rivlin one was presented, which covers the full behaviour of the stress-strain relationship. It is based on the theoretical derivation of the critical elongation value, which has been noticed previously in many earlier works but not theoretically defined. The internal friction coefficient, as a mechanical property of the material, was introduced in this model. Unexpectedly, the behaviour of elastic materials at small stress values is not Hookean but shows constant strain as the stress increases in a very small region. HIGHLIGHTS The critical elongation value is theoretically driven. Internal friction, which is a mechanical property of the material, is presented as a variable in the stress-strain model. Showing the behaviour of elastic materials at small stress values. Extend the well-known Mooney-Rivlin model to cover the stress-strain regime.

Effect of architecture disorder on the elastic response of two-dimensional lattice materials.

We examine how disordering joint position influences the linear elastic behavior of lattice materials via numerical simulations in two-dimensional beam networks. Three distinct initial crystalline geometries are selected as representative of mechanically isotropic materials with low connectivity, mechanically isotropic materials with high connectivity, and mechanically anisotropic materials with intermediate connectivity. Introducing disorder generates spatial fluctuations in the elasticity tensor at the local (joint) scale. Proper coarse-graining reveals a well-defined continuum-level scale elasticity tensor. Increasing disorder aids in making initially anisotropic materials more isotropic. The disorder impact on the material stiffness depends on the lattice connectivity: Increasing the disorder softens lattices with high connectivity and stiffens those with low connectivity, without modifying the scaling between elastic modulus and density (linear scaling for high connectivity and cubic scaling for low connectivity). Introducing disorder in lattices with intermediate fixed connectivity reveals both scaling: the linear scaling occurs for low density, the cubic one at high density, and the crossover density increases with disorder. Contrary to classical formulations, this work demonstrates that connectivity is not the sole parameter governing elastic modulus scaling. It offers a promising route to access novel mechanical properties in lattice materials via disordering the architectures.

Water ageing effects on the elastic and viscoelastic behaviour of epoxy-based materials used in marine environment

Both experimental tests and numerical simulations have been performed in this study to analyze the influence of long-term immersion (over 500 days) on the hygro-elastic and hygro-viscoelastic behaviour of epoxy resin samples. First, a diffusive and swelling campaign was carried out with water immersion at 25 °C and 60 °C. Various experimental tests have also been undertaken at different stages of ageing to highlight and quantify the influence of water diffusion on elastic and viscoelastic properties. A model is then proposed to simulate the hygro-viscoelastic behaviour of the studied material through finite element simulations. A good agreement between the experimental and numerical results is observed.

An improved recoil pressure boundary condition for the simulation of deep penetration laser beam welding using the SPH method

Deep penetration laser beam welding is simulated using the mesh-free Lagrangian Smoothed Particle Hydrodynamics (SPH) method. The physical phenomena modeled are the elastic material behavior of the solid phase, the fluid dynamics of the liquid phase including temperature-dependent surface tension, heat transfer by heat conduction, and the phase transitions melting, solidification, and evaporation. The energy input of the laser beam is determined by a ray-tracing scheme that calculates the absorbed irradiance distribution in the capillary. Based on the locally absorbed irradiance, an improved recoil pressure model is introduced and compared with a temperature-dependent model frequently used in the literature. To transfer the momentum of the recoil pressure to the surrounding melt, two boundary conditions based on either dynamically detected boundary particles or surface forces are presented and validated using simple examples. The results show that the recoil pressure is a key factor for the formation of a deep capillary and the acceleration of the melt around the capillary. Comparison of capillary geometry and melt pool size from simulation and experiment shows good agreement for the irradiance-dependent recoil pressure model.

Numerical simulation of axially impacted elastic bar

This numerical analysis considers a model of an elastic cylindrical bar impacted by rigid mass, where the accuracy of the model is benchmarked by a closed-form solution developed for this impact process. The analytical solution provides theoretical background and understanding, however, practical problem is not always restricted to a simple one-dimensional geometry and boundary conditions of a purely elastic material behaviour. Hence, the current work numerically simulates the impacted elastic bar, then explores parameters which are not considered in its theoretical model. A two-dimensional (2D) solid axisymmetric system is considered, in which rigid impactor is assigned with initial velocity corresponding to certain drop height and a 2D contact type is defined between interacting bodies. Both elastic and time-dependent viscoelastic material models are considered in this study. The simulation results reveal time intervals gradually increase in every sequential intervals, while relatively small discrepancies are recorded for peak load and pulse width outputs. The parameters of impactor’s mass, drop height and structural stiffness are varied; showing how these parameters individually affect the resulting force response at end struck. The models then evaluate time-dependent viscoelastic material model; showing stiffer response of the resulting force in comparison to models assigned with long-term elastic moduli. Derived elastic modulus-output variable relations show comparable mathematical forms to corresponding equations formulated analytically.