Dependent Material Model Research Articles

An elastoplastic damage ice material model based on modified Tsai-Wu yield criterion: Experiment, theory and numerical application

Ice, as a novel green and sustainable building material, has attracted more and more attention in building engineering. Appropriate ice material models are crucial for the performance analysis of the increasing ice structures. There is still challenging in modelling ice responses due to the complexity of ice. This study aims to present a nonlinear elastoplastic damage model for ice material. First, a triaxial compression test of artificial ice is conducted. Based on the test results, the modified Tsai-Wu failure criterion with better performance in the tensile zone and physical meaning for hydraulic strength is established. Then, combining plasticity theory with damage mechanics, an elastoplastic damage constitutive law considering the difference between tensile and compressive properties is proposed. The piecewise damage model and the Weibull exponential damage model are employed for compression and tension damage, respectively. Moreover, the numerical iterative algorithm is developed and a user-defined material subroutine (UMAT) is embedded in the finite element software ABAQUS to simulate the mechanical properties of ice. Furthermore, the constitutive model is verified by comparing the FEM results with the results of uniaxial compression, triaxial compression, and three-point bending tests. The results show that the constitutive model can well describe the stress-strain nonlinear behavior and capture the basic failure mode of ice materials. Finally, considering temperature affecting on the failure surface, a temperature dependent ice material model is developed. The current study would help in the design, operation and maintenance of ice structures.

Study of effect of loading rate on mechanical properties of SS316LN and evaluation of parameters of Johnson-Cook model using parametric FE analysis and experimental data

The objective of this work is to evaluate the parameters of strain rate dependent Johnson-Cook material model using a hybrid procedure which uses finite element analysis as well as experimental data. The large strain rate tests were conducted to using split Hopkinson pressure bar test setup, whereas the quasi-static test was carried out using conventional testing machines. Johnson-Cook material model has been used to simulate the plastic deformation behavior of material under the high strain loading. This model provides the flow stress of the material as a function of equivalent plastic strain, plastic strain rate and temperature. The parameters, i.e., A, B, n, C and m of the model have been determined using a hybrid procedure as mentioned earlier. One of the important issues in split Hopkinson pressure bar testing is the variation of strain rate during the duration of loading. Due to decrease in reflected strain magnitude, the strain rate continuously decreases (as strain rate is proportional to reflected strain signal) and it is a characteristic of the above test method. However, this creates problem in evaluation of parameters of Johnson-Cook material model using conventional procedure. In this work, a modified procedure has been developed in order to take into account of this variation in strain rate as function of applied strain. The results of the method has been validated with experimental data. The parameters have been evaluated only for room temperature data and the effect of temperature shall be studied in future.

Parametric CAD-integrated simulation of masonry structures based on the isogeometric analysis

This publication presents a novel numerical avenue for the assessment of masonry structures. To circumvent the labor-intensive finite element method modeling and pre-processing step, the isogeometric analysis is enhanced within this contribution to cope with the necessities for masonry structures. This incorporates the study of apparent kinematic shell formulations, including their respective properties. Additionally, the connection towards non-linear material laws is outlined, and an empirically evaluated approach for the element size regularization is proposed. This generic approach would be inherently valid for other size dependent constitutive material models, as e.g. concrete models.The current paper is explored in the context of a number of experimental problems. These validation examples are used to provide structural assessments that extend beyond the scope of the experiment. Finally, a potential example that provides an outlook towards anticipated applications is presented.

Prediction of skull fractures in blunt force head traumas using finite element head models.

Traumatic head injuries remain a leading cause of death and disability worldwide. Although skull fractures are one of the most common head injuries, the fundamental mechanics of cranial bone and its impact tolerance are still uncertain. In the present study, a strain-rate-dependent material model for cranial bone has been proposed and implemented in subject-specific Finite Element (FE) head models in order to predict skull fractures in five real-world fall accidents. The subject-specific head models were developed following an established image-registration-based personalization pipeline. Head impact boundary conditions were derived from accident reconstructions using personalized human body models. The simulated fracture lines were compared to those visible in post-mortem CT scans of each subject. In result, the FE models did predict the actual occurrence and extent of skull fractures in all cases. In at least four out of five cases, predicted fracture patterns were comparable to ones from CT scans and autopsy reports. The tensile material model, which was tuned to represent rate-dependent tensile data of cortical skull bone from literature, was able to capture observed linear fractures in blunt indentation loading of a skullcap specimen. The FE model showed to be sensitive to modeling parameters, in particular to the constitutive parameters of the cortical tables. Nevertheless, this study provides a currently lacking strain-rate dependent material model of cranial bone that has the capacity to accurately predict linear fracture patterns. For the first time, a procedure to reconstruct occurrences of skull fractures using computational engineering techniques, capturing the all-in-all fracture initiation, propagation and final pattern, is presented.

Site response analysis of liquefiable stratified ground comprising silt and sand: Numerical investigations

Most of the times in situ ground comprises layers of saturated silt and sand. Present study investigates effect of thickness and position of these layers on the site response of the ground. The constitutive response of both materials has been modelled by pressure dependent multi yield material model that captures typical cyclic mobility response under undrained seismic loading. For the homogeneous sandy ground, hydraulic gradient along the depth was found to be constant and equal to the submerged unit wight of the soil (i.e., 6.86). However, when 0.5 m thick silt seam was introduced at different depths, hydraulic gradient increased to as high as 57. It is inferred that a water film under sustained high pressure may get formed beneath the silt seam. With passage of time, further increase in the hydraulic gradient across the silt seam was noted. A re-liquefaction of the overlying soil is likely to happen due to breaking of the silt seam and pressurized soil ejecta. Locally negative hydraulic gradients were also observed implying that in a soil domain there could be locally downward flow of water even though top soil gets liquified. In all cases, a zone of zero hydraulic gradient was observed near the bottom of the model. The maximum horizontal acceleration at the ground surface was found to be 0.10 g irrespective of the stratification of the ground. Wavelet coherence revealed that the acceleration record across the silt seam was in phase over entire shaking and for frequency up to 25 Hz. The input acceleration record and the acceleration record at the ground surface were found to be almost in no phase, for all cases. Spectral analysis revealed that liquefaction reduces the spectral accelerations.

A strain rate dependent and anisotropic failure material model for short fiber reinforced plastics based on energy density accounting for local fiber orientation

A failure model for SFRP for FEM simulations is developed to describe the strain rate dependency, the influence of the local fiber orientation and of the stress state on the failure behavior. The material is considered as a continuum while internally calculating the micro-mechanics analytically. The described micro-mechanics are based on experimental observations and on analyzation with numerical studies. In particular the strain rate dependent delamination of fibers and matrix is incorporated in the model. The distortion energy density is defined as the driving value for failure and estimated by the model. This is achieved with the analytic solution by Eshelby for the stress field in the matrix and by introducing an additional phase for the plasticly deformed volume. The validation on characterization specimens as well as component test demonstrates that the influence of strain rate, fiber orientation, and stress state on the failure behavior can be described with only one material parameter, the critical distortion energy density.

Numerical calculation of [formula omitted] to simulate fatigue crack growth under large scale viscoplastic deformations

Crack propagation under low cycle fatigue and thermomechanical fatigue is characterized by high plastic and creep strains that extend over large regions around the crack, so that concepts of linear-elastic fracture mechanics cannot be applied. In these cases, the cyclic crack tip opening displacement ΔCTOD is a promising loading parameter to quantify crack growth. In this work, suitable definitions and Finite Element techniques are investigated and compared for an accurate calculation of ΔCTOD under cyclic mechanical and/or thermal loading. A viscoplastic temperature dependent material model of Chaboche-type is used along with large strain settings, specified for the austenitic cast iron Ni-resist. Extensive two-dimensional analyses of Single Edge Notch Tension specimens revealed that collapsed special crack tip elements are superior compared with commonly used regular quadrilateral 8-node elements. At the same level of accuracy of ΔCTOD, they require an about ten times coarser mesh and show less sensitivity w.r.t. element size for both stationary and propagating cracks. In order to simulate fatigue crack growth, an efficient, fully automated FE-technique is developed for an incremental crack propagation by successive remeshing, whereby the deformations and internal state variables are mapped from the old mesh onto the new one. Recommendations are made regarding important numerical control parameters like optimal size of crack tip elements, length of crack growth increment in relation to plastic zone size and ΔCTOD value.

A Strain Rate Dependent Damage Model for Evaluating the Dynamic Response of CFRTP Laminates with Different Stacking Sequence

Carbon fiber reinforced thermoplastic polymer (CFRTP) laminates can be used in packaging electronics components to reduce weight and shield external disturbance. The CFRTP structures in operation are inevitably to suffer dynamic loading conditions such as falling rocks, tools and impacts. In this study, a strain rate dependent material model for accurately evaluating the dynamic response of CFRTP laminates with different stacking sequence was proposed. The model was composed of three components: a strain rate dependent constitute model, a strain rate related damage initiation model and an energy-based damage evolution model. The strain rate effect of modulus and strength was described by a stacking sequence related matrix, and the damage initiation model could describe the matrix, fiber and delamination damage of CFRTP laminates without introducing cohesive elements. The material model was implemented into finite element software ABAQUS by user defines subroutine VUMAT. The low velocity impact tests of CFRTP laminates with quasi-isotropic and angle-ply stacking sequence were used to provide validation data. The dynamic response of CFRTP laminates from numerical results were highly consistent with the experimental results. The mechanical response of CFRTP laminates were affected by stacking sequence and impact energy, and the numerical error of proposed material model significantly decreased with the increasing impact energy especially for the laminae with damage occur.

Analysis of factors influencing on performance of solid tires: Combined approach of Design of Experiments and thermo-mechanical numerical simulation

Excessive loading conditions and internal heat build-up are the major causes of failures in solid resilient tires. Both operational and design related factors can affect tire performance including internal stress generation and heat build-up. In spite of their limitations, experimental techniques are still the most common method of identifying the factors that affect tire performance. This study explores a combined approach of numerical modelling and Design of Experiments (DoE) to identify the impact of several key design and operational factors on the performance of solid tires under different temperature levels. First, 3D Finite Element (FE) static and thermal models of the solid resilient tires are developed by incorporating suitable temperature dependent hyperelastic material models and relaxation properties. The temperature-dependent mechanical behaviours of rubber material are obtained by using Dynamic Mechanical Analyzer (DMA) and the William Landel Ferry (WLF) parameters. The developed FE thermal model is used to predict the tire performance, including the tire blasting region, which is then validated with experimental data. Secondly, a two-level fractional factorial DoE analysis is developed using response readings of maximum stresses, deformations and contact pressure obtained from the validated FE thermal model. The factors used in the DoE include the number of rubber layers, applied load, rolling speed, ramp angle and aperture level. The results provide optimal operational and design parameters of the solid resilient tire at different environmental temperatures and show the potential for considerable stress reduction with minimal changes to tire deformation and contact area. These results highlight the capability of the combined FEM and statistical design approach to drastically reduce the number of physical experiments required for obtaining optimal tire performance thus saving significant time and cost.

A hybrid approach to derive macro- and meso-mechanic cell models for vibrational investigations of lithium-ion pouch cells

Lithium-ion batteries are the core component of every energy storage system in modern electric vehicles. In order to represent the multi-physical processes in these battery systems in simulations, different modeling approaches are needed depending on the application area. In this work, two methods are presented to derive state-of-charge dependent material models for lithium-ion pouch cells suitable for modal analysis using the finite elements method. As a starting point, the non-destructive measurement method of experimental modal analysis is performed at different states of charge. Using the Dakota optimization framework, material models are derived by minimizing the deviations between measured and calculated natural frequencies. On a meso-mechanic level, a homogenization approach is presented, which makes it possible to use material parameters from tensile and compression tests of the individual cell layers to derive material models for the calculation of natural frequencies at cell level. A method is described to perform state-of-charge dependent modal calculations on pouch cells. Thus, a practical approach was created to derive models for vibrational investigations from low-cost, standardized tests.

Quasi-static and dynamic investigation of an advanced high strength and corrosion resistant 10 % Cr nanocomposite martensitic steel

The mechanical response of an advanced high strength and corrosion resistant 10 % Cr nanocomposite steel (ASTM A1035CS Grade 120) is measured under uniaxial tension and compression at the strain rates of 10−4 s−1, 10-2 s-1, 100 s−1, 700 s−1, and 3000 s−1. The experiments are performed at 22 °C as well as 80 °C to investigate the material behavior at the expected temperature rise due to adiabatic deformation at 15 % strain. Additionally, different compression-shear hat-shaped specimens are tested at quasi-static and dynamic strain rates to investigate the localization behavior of this material. The material exhibits small strain rate sensitivity (SRS) during quasi-static loading, but a pronounced SRS between quasi-static and dynamic strain rates. Tension-compression asymmetry is also observed at both temperatures. Experiments at 80 °C reveal a decrease in flow stress in both tension and compression indicating the material is sensitive to thermal softening due to adiabatic heating. Load-Unload-Reload (LUR) and strain rate jump experiments are performed to investigate the reasoning behind the approximate rate insensitivity of ASTM A1035CS steel during quasi-static strain rates. A new constitutive model is also developed using a novel rate dependent material model with a modified Hockett-Sherby (MHS) hardening model and incorporating Lode angle dependence to capture the tension-compression asymmetry. The model is also used to predict the LUR and strain rate jump experiments. Finally, reasoning behind the unique rate dependent thermo-mechanical behavior of ASTM A1035CS steel is discussed in regards to adiabatic heating, strain-partitioning, and phase transformation.

Fundamentals of chemical reactor engineering: A multi-scale approach

The mechanical response of an advanced high strength and corrosion resistant 10 % Cr nanocomposite steel (ASTM A1035CS Grade 120) is measured under uniaxial tension and compression at the strain rates of 10−4 s−1, 10-2 s-1, 100 s−1, 700 s−1, and 3000 s−1. The experiments are performed at 22 °C as well as 80 °C to investigate the material behavior at the expected temperature rise due to adiabatic deformation at 15 % strain. Additionally, different compression-shear hat-shaped specimens are tested at quasi-static and dynamic strain rates to investigate the localization behavior of this material. The material exhibits small strain rate sensitivity (SRS) during quasi-static loading, but a pronounced SRS between quasi-static and dynamic strain rates. Tension-compression asymmetry is also observed at both temperatures. Experiments at 80 °C reveal a decrease in flow stress in both tension and compression indicating the material is sensitive to thermal softening due to adiabatic heating. Load-Unload-Reload (LUR) and strain rate jump experiments are performed to investigate the reasoning behind the approximate rate insensitivity of ASTM A1035CS steel during quasi-static strain rates. A new constitutive model is also developed using a novel rate dependent material model with a modified Hockett-Sherby (MHS) hardening model and incorporating Lode angle dependence to capture the tension-compression asymmetry. The model is also used to predict the LUR and strain rate jump experiments. Finally, reasoning behind the unique rate dependent thermo-mechanical behavior of ASTM A1035CS steel is discussed in regards to adiabatic heating, strain-partitioning, and phase transformation.

Ballistic penetration simulation of a 3D woven fabric using high strain-rate dependent yarn model

3D woven fabric has great application potential in military armor systems. Here we report numerical simulation of 3 D angle interlock woven fabric(3DAWF) subjected to the ballistic impact using LS-DYNA. We employed membrane elements to construct the mesoscale yarn-level 3DAWF model to improve computational efficiencies and accuracy. The simplified Johnson-Cook (SJC) material model was proposed for simulating yarns' dynamic behaviors under high-speed impact loadings. The SJC material model and commonly used strain-rate dependent material model Cowper-Symonds (CS) were taken into the FEA model to simulate the fabric's ballistic impact behaviors separately. The ballistic impact tests of 3DAWF subjected to the Full Metal Jacket (FMJ) projectile under the strike velocity 190 ∼ 320 m/s were carried out to validate the new material model. Comparing the results between the tests and theoretical model found that the FEA model using the SJC material model can accurately predict projectile's residual velocities and fabric's deformation and damages. The numerical model using SJC yarn constitutive models can precisely capture the impact mechanism of 3DAWF.

A strain rate dependent nonlinear elastic orthotropic model for SFRC structures

A strain rate dependent orthotropic model for steel fiber reinforced concrete (SFRC) structures subjected to impact or blast loads is proposed in this paper. Based on the previously introduced orthotropic model for plain concrete, an improved strain rate dependent material model for SFRC is developed to account for the effect derived from the addition of steel fibers in the concrete matrix and to cope with the multiaxial strain rate dependent behavior of SFRC. In addition to verification of the constructed multiaxial strength envelope of SFRC through correlations with experimental data, improved failure strains in the uniaxial stress-strain relation are also introduced to minimize the mesh size dependency in the numerical results. Finally, the proposed orthotropic model is incorporated into LS-DYNA as a user defined material model. Numerical analyses were performed for experiments of RC and SFRC slabs under projectile impact and blast loading, and the obtained results show that the addition of the steel fibers provides a considerable improvement in the structural resistance and the proposed model effectively simulates the structural responses of SFRC structures while minimizing the mesh size dependency in the numerical results.

A numerical solver for coupled dynamic simulation of glacial ice impacts considering hydrodynamic-ice-structure interaction

Glacial ice features pose great threats on the safety of ships and offshore structures in the arctic. House sized bergy bits or growlers are of particular concern because of the detection capability limits of marine radars. Analysis and design of structures against collisions from such glacial ice bodies has always been challenging due to the complicated hydrodynamic-ice-structure interaction.This paper proposes a numerical solver for coupled simulation of glacial ice impacts accounting for the effects of hydrodynamic-ice-structure interaction. The solver adopts user subroutines provided in LS-DYNA and combines three different modules, i.e. the BWH (Bressan-Williams-Hill) criterion for the prediction of fracture of steels, a hydrostatic pressure dependent plasticity-based material model for constitutive modelling of ice, and the linear potential flow theory for hydrodynamic loads.The proposed solver is verified and calibrated to ice resistance data from field tests and is then applied to simulate ice collisions on a semi-submersible platform column. Collision scenarios with both in-plane 3DOF and full 6DOF ice motions are considered. The results are discussed with respect to ice motion trajectories, ice crushing and structural damage under the combined action of ice indentation and sliding loads. The dissipated energy predicted by external dynamic models is compared with simulation results and discussed.

Dynamic behaviors and protection mechanisms of sulcata tortoise carapace

This paper presents the compressive behavior of tortoise carapace at high strain rates and its protection mechanisms under impact loading. Both experimental and numerical results are reported. Tortoise is a land-based desert-dwelling animal taxonomically classified in the order of Testudines. The carapace is the dome-shaped upper part of the tortoise shell that protects its body from predator attacks. The carapace structure is composed of four layers formed as a composite structure with a porous core. The outer surface is keratin scutes made of fibrous structural proteins. The remaining layers are bone-like materials which are dorsal cortex, cancellous interior and ventral cortex. The compressive behavior at high rate of deformation is examined using split Hopkinson pressure bar (SHPB) technique. The results shown in the stress-strain plot illustrate a strain-rate hardening effect. The impact test is conducted using a gas gun with 6.35-mm diameter steel bearing balls as projectiles. The responses of carapace sample under a range of impact velocities are investigated to analyze its protection mechanisms. The numerical model of impact test is created to obtain an insight into mechanical behaviors of the carapace structure that cannot be observed in the experiments. The strain rate dependent material model is defined based on the SHPB test results. The distributions of stress and rebound velocity are presented and discussed.

Coupled simulations for lifetime prediction of board level packages encapsulated by thermoset injection moulding based on the Coffin-Manson relation

A fibre orientation dependent material model of the thermoset is implemented to predict the lifetime of electronic components as a part of 2nd level encapsulated packages. Experimental data are used in combination with coupled simulations (process simulation – fibre orientation dependant material model – thermo-mechanical simulation) for defining this lifetime prediction model. An already existing lifetime prediction model based on the Coffin-Manson relation is used initially to evaluate the prediction accuracy. The prediction model is then adjusted and fitted for the current application.

Strain-path dependent hardening models with rigorously identical predictions under monotonic loading

Accurate sheet metal simulation often requires advanced strain-path dependent material models, in order to predict the material response under complex loading conditions, including monotonic, reverse and orthogonal paths. More and more flexible models imply higher and higher costs in terms of parameter identification, computer implementation and simulation time, and robust comparison is often compromised by the inconsistent predictions of advanced models under monotonic loading. In this paper, a simple and general approach is proposed for the alteration of advanced hardening models in order to make them rigorously identical to each other under monotonic loading. This objective was reached without any drawback other than the addition of the corresponding equations. On the contrary, the flexibility and accuracy of the selected models was improved, and the parameter identification procedure became simpler, more accurate and more robust. Three material models of increasing complexity were selected to demonstrate the interest of this approach with respect to a complete set of characterisation experiments for a DP600 sheet steel.

Numerical investigation of high velocity impact on foam-filled honeycomb structures including foam fracture model

An appropriate finite element model is developed to simulate the high velocity impact of projectiles on polyurethane foam filled aluminum honeycomb. First, the numerical model of the high velocity impact of the projectiles on the empty aluminum honeycomb is developed using a strain rate dependent material model. A VUMAT subroutine including two different fracture criteria proposed by researchers is developed. The fracture criterion that shows similar behavior to experimental observations, is selected. The numerical model of the projectiles impact on the foam-filled honeycomb is compared with available experimental results, and the ballistic limit velocities are predicted with good accuracy.

A machine learning based plasticity model using proper orthogonal decomposition

Data-driven material models have many advantages over classical numerical approaches, such as the direct utilization of experimental data and the possibility to improve performance of predictions when additional data is available. One approach to develop a data-driven material model is to use machine learning tools. These can be trained offline to fit an observed material behaviour and then be applied in online applications. However, learning and predicting history dependent material models, such as plasticity, is still challenging. In this work, a machine learning based material modelling framework is proposed for both elasticity and plasticity. The machine learning based hyperelasticity model is developed with the Feed forward Neural Network (FNN) directly whereas the machine learning based plasticity model is developed by using of a novel method called Proper Orthogonal Decomposition Feed forward Neural Network (PODFNN). In order to account for the loading history, the accumulated absolute strain is proposed to be the history variable of the plasticity model. Additionally, the strain–stress sequence data for plasticity is collected from different loading–unloading paths based on the concept of sequence for plasticity. By means of the POD, the multi-dimensional stress sequence is decoupled leading to independent one dimensional coefficient sequences. In this case, the neural network with multiple output is replaced by multiple independent neural networks each possessing a one-dimensional output, which leads to less training time and better training performance. To apply the machine learning based material model in finite element analysis, the tangent matrix is derived by the automatic symbolic differentiation tool AceGen. The effectiveness and generalization of the presented models are investigated by a series of numerical examples using both 2D and 3D finite element analysis.