Combined Material Model Research Articles

The application of an isotropic crushable foam model to predict the femoral fracture risk.

For biomechanical simulations of orthopaedic interventions, it is imperative to implement a material model that can realistically reproduce the nonlinear behavior of the bone structure. However, a proper material model that adequately combines the trabecular and cortical bone response is not yet widely identified. The current paper aims to investigate the possibility of using an isotropic crushable foam (ICF) model dependent on local bone mineral density (BMD) for simulating the femoral fracture risk. The elastoplastic properties of fifty-nine human femoral trabecular cadaveric bone samples were determined and combined with existing cortical bone properties to characterize two forms of the ICF model, a continuous and discontinuous model. Subsequently, the appropriateness of this combined material model was evaluated by simulating femoral fracture experiments, and a comparison with earlier published results of a softening Von-Mises (sVM) material model was made. The obtained mechanical properties of the trabecular bone specimens were comparable to previous findings. Furthermore, the ultimate failure load predicted by the simulations of femoral fractures was on average 79% and 90% for the continuous and discontinuous forms of the ICF model and 82% of the experimental value for the sVM material model. Also, the fracture locations predicted by ICF models were comparable to the experiments. In conclusion, a nonlinear material model dependent on BMD was characterized for human femoral bone. Our findings indicate that the ICF model could predict the femoral bone strength and reproduce the variable fracture locations in the experiments.

Temperature-dependent model for ferroelectrics embedded into two-dimensional polygonal finite element framework

A two-dimensional constitutive model, which is based on micromechanical rotation of domains, is presented in this work to demonstrate the non-linear behavior of ferroelectric materials under different loading conditions. A temperature-dependent combined material model that incorporates both phases i.e., tetragonal and rhombohedral phases is embedded into two-dimensional polygonal finite element framework. The developed material model which has easily overcome shortcomings related to tetragonal model and rhombohedral model alone. This model is developed on the morphotropic phase boundary which has produced desired behavior based on macroscopic material parameters. Temperature effects on behavior of combined material model are obtained in the work. Furthermore, polarization rotation test and temperature effects on polarization rotation are also studied in present work. There are numerous studies conducted on ferroelectric materials. All of them incorporate behavior of ferroelectric material confined to specific conditions. Either tetragonal model or rhombohedral model has been used extensively to get the desired behavior based on macroscopic material parameters. This model has some limitations in either satisfying one or another condition related to experiments conducted to study the behavior of ferroelectric materials. The tetragonal material model is capable of producing results with microscopic material properties but in case of macroscopic material parameters the tetragonal model is insufficient to produce the desired behavior for PZT ceramics. The rhombohedral material model is sufficient to produce results based on macroscopic material parameters. Therefore, model is extended by rhombohedral phase, allowing a mixture of both phases with varying quantities inside the grain. Though, rhombohedral model is also not used to that extent. We have developed material model that gives desired behavior and overcomes the hurdles in the existing model.

Influence of Residual Stresses and Fiber Orientation on Smooth Muscle Contraction in Arterial Walls

AbstractIn this contribution, we present a combined material model which couples three aspects of the arterial wall: a smooth muscle model embracing a stretch‐dependent calcium function, residual stresses induced by growth, and fiber reorientation. The model enables the investigation of the respective influence of all three aspects on each other. For this purpose, simulation results of arterial rings under varying intravascular pressure are analyzed.

Non-Newtonian numerical modelling of solder paste viscosity measurement

PurposeThe purpose of this paper is to present the establishment of a computational fluid dynamics model for investigating different non-Newtonian rheological models of solder pastes by simulating solder paste viscosity measurement. A combined material model was established which can follow the measured, apparent viscosity values with lower error.Design/methodology/approachThe model included a parallel plate arrangement of rheometers. The diameter of the plate was 50 mm, whereas the gap between the plates was 0.5 mm. Only one quarter of the plate was modelled to enable using fine enough mesh, while keeping the calculation time low. Non-Newtonian properties were set using user defined function in Ansys, based on the Cross and Carreau–Yasuda material models. The viscosity values predicted by the mathematical models were compared to measured viscosity values of different types of solder pastes.FindingsIt was found that the Cross model predicts the apparent viscosity with a relatively high error (even approximately 50 per cent) at lower shear rates, whereas the Carerau–Yasuda model has higher errors at higher shear rates. The application of the proposed, combined model can result in a much lower error in the apparent viscosity between the calculated and measured viscosity values.Originality/valueThe error of Cross and Carreau–Yasuda material models has not been investigated yet in details. The proposed, combined material model can be applied for subsequent simulations via the described UDF, e.g. in the numerical modelling of the stencil printing. This can result in a more accurate modelling of the stencil printing process, which is inevitable considering the printing of solder paste for today fine-pitch, small size components.

High frequency mechanical impact treatment (HFMI) for the fatigue improvement: numerical and experimental investigations to describe the condition in the surface layer

Post-treatment techniques like the high frequency mechanical impact treatment (HFMI) exhibit a significant fatigue life enhancement of welded joints. The effectiveness of this mechanical impact treatment is primarily based on the combination of three effects: the local hardness increase, compressive residual stresses and reduced notch stress concentration at the weld toe. The goal of the present study was to develop a computationally efficient approach for predicting residual stresses induced by the HFMI process on steel specimens. For that purpose, explicit simulations of this post weld treatment technique were performed utilizing the software package ABAQUS. Although, the focus of this study is to find suitable process and material parameters as input for the numerical simulation. For this, the impact velocity, contact force and permanent indentation depth of a pneumatic HFMI-tool were measured. Concerning material modelling, an enhanced combined material model with strain rate dependency was applied. Furthermore, the simulated residual stress field was experimentally validated by X-ray diffraction and neutron diffraction residual stress measurement. The results of the simulations are in good agreement with the experimental results, showing that the material hardening model used for simulation has a high influence on the calculated residual stress values.

Investigation and Validation of Finite Element Analysis Material Modeling for Integrity Assessment of Indented Pipe Under Static and Cyclic Loading

Mechanical damage in transportation pipelines is a threat to its structural integrity. There are many parameters that affect the severity of the mechanical damage which are related to the pipe geometry and material properties, the defect geometry and boundary conditions, the loading cycle, and the pipe state of stress. To understand those effects, the utilization of numerical finite element analysis (FEA) has been used extensively to supplement the expensive; and thus, limited full-scale tests. The actual pipe material exhibits a number of special features including nonlinear elasticity, anisotropy, and cyclic softening which need advanced material modeling techniques. However, the success of the numerical material model to actually simulate the pipe material behavior could not be studied in detail previously due to the insufficient experimental data especially in cyclic pressure loading. The objective of this paper is to investigate the effect of material modeling using FEA on the integrity assessment of dented pipe under static and cyclic loading by simulating pipe denting followed by subsequent pressure cycles. Several material models are tested and calibrated against the measurements of full-scale tests to find the effects of material modeling assumptions (e.g. isotropy, yield point, hardening rule). The results show that a combined material model simulating all special features of nonlinear elasticity, anisotropy, and cyclic softening gives a very close representation of experimental data in terms of strain values and fatigue cycles to failure. Therefore, detailed material properties are needed to conduct accurate integrity assessments of dented pipes especially under cyclic conditions.

Lifetime Calculation of Thermo-Mechanically Loaded Materials (Al, Cu, Ni, and Fe Alloys) Based on Empirical Methods

Abstract Cyclic loading of metallic engineering components at constant elevated or fluctuating temperatures causes a complex evolution of damage, which cannot be described easily. In many engineering components, thermo-mechanical loading occurs, e.g., cooling components in metallurgy and metal forming, turbine blades, cylinder heads, exhaust systems, etc. At the same time, the thermal expansion is restricted in some regions due to the complex geometry of the components. Therefore, mechanical stresses take place, and the cyclic plastic deformation leads to thermo-mechanical fatigue of the material. A careful analysis and comparison of the experimental results, based on a systematic variation of the relevant influence factors, allow to develop empirical models for computing the fatigue life of thermo-mechanically loaded components made of AlSi cast alloys, Cu alloy, Ni alloy, and cast iron. Based on stress-strain loops from low cycle fatigue tests at different temperatures, a nonlinear combined material model was adopted to describe the cyclic deformation behavior. The simulated loading parameters of stress and strain were the basis for the subsequent lifetime simulation. Different lifetime approaches were tested and analyzed to fulfill the requirements for the fatigue analysis of components made of these alloys. In particular, strain based criteria, damage parameters as well as hysteresis energy criteria were investigated. Also, a new energy based parameter was developed to optimize the scatter band and standard deviation. In order to verify the simulation model for components, numerical results have to be compared, and—if necessary—it also has to be adapted to experimental results from component tests. In addition, the model parameters can be optimized by using these results.

Comparison of the Temperature and Pre-Aging Influences on the Low Cycle Fatigue and Thermo-Mechanical Fatigue Behavior of Copper Alloys (CuCoBe/CuCo2Be)

Abstract Typically thermo-mechanical fatigue (TMF) loaded components in power plants and steel works are made of copper alloys and are used in different applications (e.g. cooling systems in continuous casting, transformers). So a careful analysis and comparison of the experimental results and microstructure of thermo-mechanical loaded copper components, which are based on a systematic variation of the relevant influence factors, have been conducted to develop empirical models for computing the fatigue life. At specific low cycle fatigue (LCF) and thermo-mechanical fatigue test series on the copper alloys CuCoBe and CuCo2Be, the influence of pre-aging and temperature were investigated by means of the cyclic deformation and lifetime behavior. Based on stress-strain loops from LCF tests at different temperatures and aging conditions a non-linear combined material model was adopted to describe the cyclic deformation behavior. The simulated loading parameters of stress and strain were the basis for the subsequent lifetime simulation. A new energy based damage parameter for copper alloys has been developed to fulfill the requirements of lifetime simulation.

Adaptive computational meso–macro-scale modeling of elastic composites

We consider combined material model and FE-mesh adaptivity in the context of computational meso–macro-scale modeling (CMM), whereby the coupling between different geometrical scales is taken into account. The macro-scale model is then replaced by the homogenized response of a representative volume element (RVE). In practice, the RVE is analyzed as a “small-scale” finite element problem, which is solved for each (Gauss) point in the domain. The high cost of this strategy clearly motivates the use of adaptive techniques based on a posteriori error estimates for the combined model and discretization error, whereby the solution of an appropriate dual problem is utilized. The suggested adaptive procedure is applied to a particle/matrix composite with hyperelastic constituents.

A study of stresses in powder compacted components during and after ejection

A finite strain finite element method is used to examine the residual stresses in a cup-shaped powder compact. Two rate-independent strain hardening porous material models are used: the combined material model (Fleck, N.A., Kuhn, L.T., McMeeking, R.M., 1992a. J. Mech. Phys. Solids 40 (5), 1139–1162) and a material model which includes the dependency of inter-particle cohesive strength (Fleck, N.A., 1995. J. Mech. Phys. Solids 43, 1409–1431). The residual stress state in the unloaded cup is highly dependent on the compaction process and less dependent on the ejection route. The maximum principal stress plotted during ejection shows that higher stresses are found during the ejection process than those found in the completely unloaded specimen. The degree of inter-particle cohesive strength has hardly any effect on the porosity distributions in the compacts but it has a strong influence on the stress state in the cups before unloading. However, after unloading, the stress states become quite similar in the two types of materials.

A combined material model for numerical simulation of hot isostatic pressing

In modelling of hot isostatic pressing (HIP) of powder materials the constitutive model should be able to describe different deformation mechanisms during the consolidation process. In the early stage, the consolidation is dominated by granular behaviour. As temperature and pressure increase in the powder the deformation can be described by a viscoplastic model. Experimental observations show substantial time-independent deformation in the early stage. At this stage of the densification process, pores in the powder are still interconnected. This cannot be described properly by a viscoplastic model. The inconsistency between the deformation mechanisms can be treated by a combined elasto-plastic and elasto-viscoplastic model. Here a granular plasticity model is combined with a viscoplastic model. In previous works the viscoplastic model, power-law breakdown, has been used to describe the entire deformation process. The combined model is implemented into an in-house finite deformation code for the solution of coupled thermomechanical problems. The simulation of a hot isostatic pressing test with dilatometer is performed in order to compare calculated results with the experimental measurement. The results from previously performed analysis carried out with a viscoplastic model only are also compared. Analysis with the combined material model shows good agreement with the experiment for the whole densification process.