Finite Element-based Approach Research Articles

Reduced and All-at-Once Approaches for Model Calibration and Discovery in Computational Solid Mechanics

Abstract In the framework of solid mechanics, the task of deriving material parameters from experimental data has recently re-emerged with the progress in full-field measurement capabilities and the renewed advances of machine learning. In this context, new methods such as the virtual fields method and physics-informed neural networks have been developed as alternatives to the already established least-squares and finite element-based approaches. Moreover, model discovery problems are emerging and can also be addressed in a parameter estimation framework. These developments call for a new unified perspective, which is able to cover both traditional parameter estimation methods and novel approaches in which the state variables or the model structure itself are inferred as well. Adopting concepts discussed in the inverse problems community, we distinguish between all-at-once and reduced approaches. With this general framework, we are able to structure a large portion of the literature on parameter estimation in computational mechanics -- and we can identify combinations that have not yet been addressed, two of which are proposed in this paper. We also discuss statistical approaches to quantify the uncertainty related to the estimated parameters, and we propose a novel two-step procedure for identification of complex material models based on both frequentist and Bayesian principles. Finally, we illustrate and compare several of the aforementioned methods with mechanical benchmarks based on synthetic and experimental data.

Vine copulas for accelerated prediction of composite strength variability

Composite materials are essential for many advanced engineering applications, but numerical quantification of strength variability can be computationally expensive. This paper proposes a novel methodology that drastically reduces the number of finite element simulations required to characterise composite material strength variability using the concept of vine copulas. This concept provides a flexible tool for the representation of high-dimensional dependencies. The methodology considers spatial scatter of three material variabilities: fibre volume fraction, fibre misalignment and fibre strength. First, the cross-correlation between stress, fibre volume fraction and fibre misalignment is fitted by a vine copula using results from a limited number of finite element simulations. Next, the vine copula is used to predict new conditional stress realisations when given realisations for the fibre volume fraction and fibre misalignment. This effectively replaces the finite element simulations with a vine copula that is much faster to evaluate. The methodology is verified by predicting the tensile failure load of a unidirectional composite coupon. Predictions are very similar to an exclusively finite element-based approach, while reducing the number of finite element simulations by a factor of 200.

VarSim: A fast process variation-aware thermal modeling methodology using Green’s functions

Despite temperature rise being a first-order design constraint, traditional thermal estimation techniques have severe limitations in modeling critical aspects affecting the temperature in modern-day chips. Existing thermal modeling techniques often ignore the effects of parameter variation, which can lead to significant errors. Such methods also ignore the dependence of conductivity on temperature and its variation. Leakage power is also incorporated inadequately by state-of-the-art techniques. Thermal modeling is a process that has to be repeated at least thousands of times in the design cycle, and hence speed is of utmost importance.To overcome these limitations, we propose VarSim, an ultrafast thermal simulator based on Green’s functions. Green’s functions have been shown to be faster than the traditional finite difference and finite element-based approaches but have rarely been employed in thermal modeling. Hence we propose a new Green’s function-based method to capture the effects of leakage power as well as process variation analytically. We provide a closed-form solution for the Green’s function considering the effects of variation on the process, temperature, and thermal conductivity. Additionally, we propose a novel way of dealing with the anisotropicity introduced by process variation by splitting the Green’s functions into shift-variant and shift-invariant components. Since our solutions are analytical expressions, we were able to obtain speedups that were several orders of magnitude more than state-of-the-art proposals with a mean absolute error limited to 4% for a wide range of test cases. Furthermore, our method accurately captures the steady-state as well as the transient variation in temperature.

Optimisation of an elastomeric pre-buckled honeycomb helmet liner for advanced impact mitigation

Advances in computational modelling now offer an efficient route to developing novel helmet liners that could exceed contemporary materials’ performance. Furthermore, the rise of accessible additive manufacturing presents a viable route to achieving otherwise unobtainable material structures. This study leverages an established finite element-based approach to the optimisation of cellular structures for the loading conditions of a typical helmet impact. A novel elastomeric pre-buckled honeycomb structure is adopted and optimised, the performance of which is baselined relative to vinyl nitrile foam under direct and oblique loading conditions. Results demonstrate that a simplified optimisation strategy is scalable to represent the behaviour of a full helmet. Under oblique impact conditions, the optimised pre-buckled honeycomb liner exceeds the contemporary material performance when considering computed kinematic metrics head and rotational injury criterion, by up to 49.9% and 56.6%. Furthermore, when considering tissue-based severity metrics via finite element simulations of a human brain model, maximum principal strain and cumulative strain density measures are reduced by 14.9% and 66.7% when comparing the new material, to baseline.

Fatigue tests and fatigue-life prediction models for hybrid welded-bolted demountable shear connectors

Four push out tests were conducted to assess the structural performance of a welded demountable shear connector (WDSC) under high-cycle fatigue loading. The primary failure mode observed was stud fracture at the base. The presence of grout inside the tube significantly increased the WDSC's fatigue life by 5.4 times. The study also analysed stiffness degradation and relative slip evolution during fatigue cycles. Two finite element-based approaches were employed for fatigue life prediction: the critical plane method for fatigue crack initiation life and fracture mechanics for crack propagation life. Based on the experimental and numerical results, fatigue life prediction formulas (Wöhler curves) are proposed for WDSCs with and without grout to aid in predicting fatigue failure in fatigue-sensitive structural designs.

Finite Element Analysis on Hydroforming of CFRP/SS304 Composite Tube with different Fiber Orientation Stacking Sequence

In this paper, a finite element-based approach to the tube hydroforming process of SS304/CFRP material with different stacking sequences was performed in an effort to reveal the failure phases at different stacking angles. The effort to produce hybrid composite tubes through tube hydroforming with composite reinforcement resulted in laminate failure at all the proposed fiber orientation angles. A comparative study of strain energy dissipation at these different stacking angles is further presented. The results show that the 00/900 stacking is considered the strongest stacking angle requiring the least strain energy absorption to initial failure of approximately 50 % more as compared to the ±300 and ±600 stacking angles. The proposed method was more adequate for predicting the strain energy, matrix deformation, and fiber damage when simulating the events.

A meshfree-based topology optimization approach without calculation of sensitivity

This paper presents a novel topology optimization approach without calculation of sensitivity for the minimum compliance problems, based on the meshfree Radial Point Interpolation Method (RPIM). Relying on the algorithm of Proportional Topology Optimization (PTO), material is distributed using only information of the objective function (which is the elastic strain energy). Material properties are interpolated by the well-known Solid Isotropic Material with Penalization (SIMP) technique; however the pseudo density (design variables) are not defined on the element center as usually encountered in finite element-based approaches, but on integration points. Since no element exists in meshfree analysis, this would be a natural choice. More importantly, the number of integration points is in general larger than that of elements or that of nodes, resulting in higher resolution of the density field. The feasibility and efficiency of the proposed approach are demonstrated and discussed via several numerical examples.

Assessment of fatigue crack growth based on 3D finite element modeling approach

Fatigue crack growth life assessment enables manufacturers to quantify damage tolerance capability of high-risk components. Reduced order models that are based on simple geometries (i.e. surface crack in a plate, corner crack at a bolt hole) and on the assumption that cracks maintain an elliptical shape during propagation, are commonly employed in the damage assessment. A more comprehensive modeling process should consider the component geometry, service loading conditions and, eliminate assumptions related to crack front shape or planarity of the crack growth path. A 3D finite element-based approach is evaluated in this study as a more accurate alternative to reduced order models. For verification purposes, an analytical solution-based model was developed and implemented in MATLAB to predict fatigue crack growth life and crack front evolution for three different crack types: surface, corner and internal. The analytical model solutions are compared against 3D finite element (FE) based approach implemented in SimModeler Crack. The 3D FE modelling approach has been further tested and validated against experimental fatigue crack growth measurements from two Al 2024-T3 specimens containing multiple cracks. The verification and validation data presented herein show that the 3D FE-based modelling approach provides an accurate and effective modelling tool for crack propagation life assessment of structural components.

A finite element-based analysis approach for computing the remaining strength of the pressure equipment with a local thin area defect

Upon facing a pressure equipment with a structure defect and the subsequent question as to if the equipment is qualified for continuous operation, the answer often resorts to enough strength. However, strength of a pressure equipment is never defined clearly. In API 579, in order for a pressure equipment with a local thin area (LTA) defect to be accepted for continuing use in operation, the remaining strength factor (RSF) of the equipment must exceed 0.9. RSF is defined as the ratio of the plastic collapse load (PCL) of equipment with defect to that of the equipment without any damage. Hence, accurate evaluation of the plastic collapse load is of utter importance to judge fitness of the equipment. In this research, a finite element (FEM) based methodology has been devised to obtain an accurate estimation of the plastic collapse load.What needs to be established first is a finite element model for the whole, undamaged vessel as the main model and the other is the surrounding region encompassing the LTA defect as the sub-model. Pressure loadings are incrementally and continuously applied to the main model through load steps until the model can no longer sustain, and the plastic collapse load is the maximum load that a structure can safely carry. The cut boundary data from the main model is then passed on to the sub-model, and calculation is resumed with the same load steps until the PCL of the LTA is obtained. Then RSF is determined as the PCL of the vessel with an LTA to that of the original, damage free vessel.API 579 and ASME FFS propose the use of RSF as an indicator for assessing fitness of an equipment. Concept-wise, the term RSF is not sophisticated and sometimes is treated as rough guidance for assessing the remaining strength of a structure. However, the same concept must be treated differently as it is applied to determine whether the defect is allowed and the remaining life is needed, which ought to be a finite element-based approach. In this research, it is achieved through:1. Representing the defect in the form of a submodel consisting of SOLIDS element in order to process the area of varied thicknesses, and.2. Computing the plastic collapse load for both the undamaged finite element model of SHELL elements and the submodel of SOLIDS elements simultaneously.

A Transmural Path Model Improves the Definition of the Orthotropic Tissue Structure in Heart Simulations

In the past decades, the structure of the heart, human as well as other species, has been explored in a detailed way, e.g., via histological studies or diffusion tensor magnetic resonance imaging. Nevertheless, the assignment of the characteristic orthotropic structure in a patient-specific finite element model remains a challenging task. Various types of rule-based models, which define the local fiber and sheet orientation depending on the transmural depth, have been developed. However, the correct assessment of the transmural depth is not trivial. Its accuracy has a substantial influence on the overall mechanical and electrical properties in rule-based models. The main purpose of this study is the development of a finite element-based approach to accurately determine the transmural depth on a general unstructured grid. Instead of directly using the solution of the Laplace problem as the transmural depth, we make use of a well-established model for the assessment of the transmural thickness. It is based on two hyperbolic first-order partial differential equations for the definition of a transmural path, whereby the transmural thickness is defined as the arc length of this path. Subsequently, the transmural depth is determined based on the position on the transmural path. Originally, the partial differential equations were solved via finite differences on structured grids. In order to circumvent the need of two grids and mapping between the structured (to determine the transmural depth) and unstructured (electromechanical heart simulation) grids, we solve the equations directly on the same unstructured tetrahedral mesh. We propose a finite-element-based discontinuous Galerkin approach. Based on the accurate transmural depth, we assign the local material orientation of the orthotropic tissue structure in a usual fashion. We show that this approach leads to a more accurate definition of the transmural depth. Furthermore, for the left ventricle, we propose functions for the transmural fiber and sheet orientation by fitting them to literature-based diffusion tensor magnetic resonance imaging data. The proposed functions provide a distinct improvement compared to existing rules from the literature.

Modelling Nuclear Morphology and Shape Transformation: A Review.

As one of the most important cellular compartments, the nucleus contains genetic materials and separates them from the cytoplasm with the nuclear envelope (NE), a thin membrane that is susceptible to deformations caused by intracellular forces. Interestingly, accumulating evidence has also indicated that the morphology change of NE is tightly related to nuclear mechanotransduction and the pathogenesis of diseases such as cancer and Hutchinson–Gilford Progeria Syndrome. Theoretically, with the help of well-designed experiments, significant progress has been made in understanding the physical mechanisms behind nuclear shape transformation in different cellular processes as well as its biological implications. Here, we review different continuum-level (i.e., energy minimization, boundary integral and finite element-based) approaches that have been developed to predict the morphology and shape change of the cell nucleus. Essential gradients, relative advantages and limitations of each model will be discussed in detail, with the hope of sparking a greater research interest in this important topic in the future.

A crystal plasticity finite element-based approach to model the constitutive behavior of multi-phase steels

Steels are the most commonly used multi-phase materials in the industry, and their mechanical behaviors depend on the microstructure, composition, and phase fractions. Generally, the material behaviors need to be measured by experiments like a tensile test or split Hopkinson bar test, which is very time-consuming and expensive. Once the heat treatment and phase fractions are changed, it needs to be tested again, and, to avoid this, a better method is required to obtain the material behavior quickly and easily. In this study, a novel multi-scale approach is described to predict the material behaviors of multi-phase steels based on the phase fractions. A crystal plasticity finite element method is used to obtain the material behavior of each phase at a micro-scale with elevated strain rates, which is validated with experimental data or theoretical models at static or quasi-static conditions. Then a homogenization procedure with the rule of mixture method, which is based on the phase fractions measured from the microstructure characterization, is used to get the macro-scale constitutive behavior, and it is then implemented into the commercial software Abaqus/Standard to simulate the process of tensile test and compared with the experimental data. Good agreements are obtained between simulation and experimental results.

A new 3D finite element-based approach for computing cell surface tractions assuming nonlinear conditions.

Advances in methods for determining the forces exerted by cells while they migrate are essential for attempting to understand important pathological processes, such as cancer or angiogenesis, among others. Precise data from three-dimensional conditions are both difficult to obtain and manipulate. For this purpose, it is critical to develop workflows in which the experiments are closely linked to the subsequent computational postprocessing. The work presented here starts from a traction force microscopy (TFM) experiment carried out on microfluidic chips, and this experiment is automatically joined to an inverse problem solver that allows us to extract the traction forces exerted by the cell from the displacements of fluorescent beads embedded in the extracellular matrix (ECM). Therefore, both the reconstruction of the cell geometry and the recovery of the ECM displacements are used to generate the inputs for the resolution of the inverse problem. The inverse problem is solved iteratively by using the finite element method under the hypothesis of finite deformations and nonlinear material formulation. Finally, after mathematical postprocessing is performed, the traction forces on the surface of the cell in the undeformed configuration are obtained. Therefore, in this work, we demonstrate the robustness of our computational-based methodology by testing it under different conditions in an extreme theoretical load problem and then by applying it to a real case based on experimental results. In summary, we have developed a new procedure that adds value to existing methodologies for solving inverse problems in 3D, mainly by allowing for large deformations and not being restricted to any particular material formulation. In addition, it automatically bridges the gap between experimental images and mechanical computations.

A complex-variable cohesive finite element subroutine to enable efficient determination of interfacial cohesive material parameters

A new complex-variable version of a cohesive element is presented that provides highly accurate first order derivatives of the nodal displacements with respect to the cohesive fracture parameters. These sensitivities are provided as a byproduct of the analysis using the complex Taylor series expansion method. This information is useful for inversely determining the cohesive fracture parameters from experimental or synthetic data using a finite element-based approach. In particular, the PPR cohesive element (Park et al., 2009), was extended using complex variables as a user element for the well-known commercial finite element program, Abaqus. The source code for the element is provided as an educational resource. The advantage of having accurate first order derivatives on both accuracy and efficiency is demonstrated through numerical examples.

An innovative contactless finite element simulation of the shot peening process

Shot peening is a major finishing treatment aiming to enhance parts’ life. However, the recourse to simulation to master the process and its effects still suffers from problems due to its complexity. The current paper presents a finite element-based approach that considers the random aspect of the shot peening process in association with a large number of shots, making it more realistic. The developed method is found to allow a computing time gain up to 70 % with comparable results to those obtained by the discrete element method, which has been reported as the most suitable for shot peening simulation. The comparison of both simulations results to experiment returned a good agreement. Simulations and experiences were concerned with C75 Almen-like strips.

Electromechanical response of multilayered piezoelectric BaTiO3/PZT-7A composites with wavy architecture

Electromechanical laminated composites with piezoelectric phases are increasingly being explored as multifunctional materials providing energy conversion between electric and mechanical energies. The current work explores thus-far undocumented combined microstructural effects of amplitude-to-wavelength ratio, volume fraction, poling direction of piezoelectric phases on both the homogenized properties and localized stress/electric field distributions in multilayered configurations under fully coupled electro-mechanical loading. In particular, the Multiphysics Finite-Volume Direct Averaging Micromechanics (FVDAM) and its counterpart, an in-house micromechanical multiphysics finite-element model, are utilized to investigate the homogenized and localized responses of wavy multilayered piezoelectric BaTiO3/PZT-7A architectures. These two methods generate highly agreeable results. Moreover, we critically examine the convergence of the finite-volume and finite element-based approaches via the Average Stress Theorem and Average Electric Displacement Theorem. The comparison shows the finite volume-based approach possesses a better numerical convergence. This study illustrates the FVDAM’s ability toward the analysis and design of engineered multilayered piezoelectric materials with wavy architecture.

Fatigue life prediction of rubber-sleeved stud shear connectors under shear load based on finite element simulation

Rubber-sleeved studs, which are headed studs wrapped with rubber sleeves, have been found to be prospective to overcome some challenges in the design of steel–concrete composite structures with ordinary stud shear connectors. A finite element-based approach was provided for the fatigue life prediction of rubber-sleeved stud shear connectors. After calculating the stress and strain state of the connector by finite element models, the fatigue crack initiation life was predicted based on the critical surface method, and fracture mechanics was adopted to predict crack propagation life. The prediction method was validated by fatigue push-out test results. The subsequent finite element parametric study revealed the effect of shear stress range, rubber sleeve height, and elastic moduli of rubber and concrete on the fatigue life of shear connectors. Further, fatigue life prediction formulas for ordinary stud and rubber-sleeved stud shear connectors were proposed for facilitating the engineering application. The reliability of these formulas was verified by comparing with S-N curves in the design codes and those obtained from fatigue push-out tests.

Eccentricity Faults Diagnosis in Permanent Magnet Synchronous Motors: a Finite Element-Based Approach

This paper addresses the effects of permanent magnet synchronous motor (PMSM) eccentricity faults on the induced normal magnetic field, flux density, and electromotive forces (EMFs). A 2D finite element method (FEM) is needed for PMSM modeling and three kind of eccentricity faults are considered; static, dynamic, and mixed eccentricities. The achieved simulation results allow distinguishing the three types of eccentricity based on the EMF power spectral density (PSD) computation. The highlighted fault characteristics allow carrying out detection and diagnosis. Sideband components amplitude extracted from the EMF PSD are proposed as faults index, allowing the three considered eccentricity faults to be both detected and distinguished.

Interaction of the Mechano-Electrical Feedback With Passive Mechanical Models on a 3D Rat Left Ventricle: A Computational Study.

In this paper, we are investigating the interaction between different passive material models and the mechano-electrical feedback (MEF) in cardiac modeling. Various types of passive mechanical laws (nearly incompressible/compressible, polynomial/exponential-type, transversally isotropic/orthotropic material models) are integrated in a fully coupled electromechanical model in order to study their specific influence on the overall MEF behavior. Our computational model is based on a three-dimensional (3D) geometry of a healthy rat left ventricle reconstructed from magnetic resonance imaging (MRI). The electromechanically coupled problem is solved using a fully implicit finite element-based approach. The effects of different passive material models on the MEF are studied with the help of numerical examples. It turns out that there is a significant difference between the behavior of the MEF for compressible and incompressible material models. Numerical results for the incompressible models exhibit that a change in the electrophysiology can be observed such that the transmembrane potential (TP) is unable to reach the resting state in the repolarization phase, and this leads to non-zero relaxation deformations. The most significant and strongest effects of the MEF on the rat cardiac muscle response are observed for the exponential passive material law.

Experimental and numerical investigation of a thermal storage medium for ground source heat pump applications

As a means of improving performance and alleviating thermal imbalance issues associated with ground source heat pump systems, ground thermal energy storage is becoming increasingly appealing. Moreover, an efficient means of transferring energy from the borehole to the surroundings is crucial. In this paper, an experimental and numerical investigation of the performance of a thermal storage medium for ground source heat pump applications is presented. A thermal storage tank of 1 m diameter and 1.5 m height equipped with temperature sensors at different radial positions and depths was used. It incorporates a 150 mm-dimeter steel pipe in which a 25.4 mm u-shaped pipe is placed to emulate a borehole. A numerical model was developed using a finite element-based approach and validated with the obtained experimental data. Different bentonite-sand mixtures with varying thermal conductivities were considered inside and around the emulated borehole. A reduction in the tank temperature difference of about 57% was achieved by using bentonite-sand mixtures inside the borehole and around the borehole (in the tank) compared to using only bentonite inside the borehole and sand around the borehole. Results further show that the heat transfer performance increases by about 320% with the use of the bentonite-sand mixtures compared to the separated bentonite and sand arrangement. Moreover, the potential for energy storage with phase change material around the emulated borehole has been demonstrated.