Finite Body Research Articles

Simulating Pelvis Kinematics from Belt and Seat Loading in Frontal Car Crash Scenarios: Important Boundary Conditions that Influence the Outcome.

The risk of submarining during automotive crashes, defined by the lap belt sliding off the pelvis to load the abdomen, is predicted to increase in future autonomous vehicles as greater variation in seating position is enabled. Biofidelic tools are required to efficiently design and evaluate new and/or improved safety systems. This study aims to evaluate the pelvis response sensitivity to variations in boundary conditions that directly influence the pelvis loads, deemed important for the submarining outcome, to facilitate a more precise comparison between finite element human body models (FE-HBMs) and post-mortem human subjects (PMHSs). A parameter study, using a one-variable-at-a-time analysis (low/high) of belt friction, seat friction, seat stiffness, and (on/off) for added belt bending stiffness, was performed using a state-of-the-art FE-HBM in four different test scenarios; one stationary, two sleds with upright occupant posture, and one sled with reclined occupant posture. In the stationary scenario, both belt friction and belt bending stiffness influenced the belt folding behavior, which consequently affected the belt-to-pelvis angle at submarining. In the sled scenarios, only seat friction was found to influence the pelvis kinematics and submarining outcome, with the most biofidelic response resulting from both the low (0.2) and high (0.5) friction coefficient depending on the scenario. To reduce uncertainty in boundary conditions affecting the external pelvis loads and increase confidence in FE-HBM to PMHS comparisons, it is recommended that future experiments evaluate the PMHS to seat friction coefficient and that new belt modeling methods that accurately capture belt folding when interacting with soft tissues are developed.

Dynamics Modeling and Motion Evaluation of a Near-Ground Tethered Balloon Cable System under Severe Wind Environments

Weather survival poses a significant challenge for the utilization of tethered balloons. The dynamic modeling of tethered balloon systems presents challenges due to the flexible nature of the cables and the intricate nature of gust forces. The present study introduces a new approach for modeling near-ground tethered balloon systems, which enables the analysis of their dynamic responses and performance evaluation under complex boundary conditions. First, finite cylindrical rigid bodies that are joined together by bushing forces to describe the dynamics of the tethered cable. The properties of the flexible cables under severe bending and translation can be illustrated by the dynamics model. Second, a three-dimensional dynamics model based on the multibody dynamics theory is created to deal with the interaction of the tethered balloon system and flexible cables. The dynamic responses of the tethered balloon system under challenging operating conditions are investigated, focusing on the number of cable segments and the place and direction of gust wind impacts. This model allows for precise assessment and optimization of the system’s overall performance to improve weather resistance. The results show that compared to computational fluid dynamics (CFDs) methods, the multibody system dynamics-based balloon model improved the solution time by 80%, with a pitch angle deviation of only 0.0016°. Moreover, the bushing model effectively reduced cable force and enabled accurate reflection of the system’s motion characteristics.

Effects of loading processes on contact forces when simulating static seating with a finite element human body model

Seat interface forces, particularly shear forces, play an essential role in predicting the risk of pressure ulcers and seating discomfort. When a finite element human body model (HBM) is used for static seating simulation, the most common loading method is to put the model in a position close to the desired final posture and then ‘drop’ it from just above the seat by applying the gravity (DROP). This does not represent how people sit in a seat. In addition, high coefficients of friction (COF) are often used to prevent sliding, which may lead to unrealistically high tangential forces. This study aims to investigate the effects of the loading process and the COF on seating simulations with a HBM. We propose a new loading approach called ‘drop and rotate’ (D&R) to better mimic people sitting on a seat. With the trunk more flexed than the desired posture, the model is dropped to establish the contact between the buttocks and thighs, and the seat pan first, and then between the back and the backrest by rotating the hip. Simulations were performed using a recently developed and validated adult male model in two different seat configurations. Results show that the proposed D&R method was less sensitive to COF and gave a better prediction of contact forces, especially on the seat pan. However, its computational time is higher than the DROP method. The study highlights the importance of the loading process when simulating static seating.

Erosion of surfaces by trapped vortices

Two two-dimensional free boundary problems describing the erosion of solid surfaces by the flow of inviscid fluid in the presence of trapped vortices are considered. The first problem tackles an initially flat, infinite fluid-solid interface with uniform flow at infinity and a vortex in equilibrium above the surface. The second involves flow around a finite body with a trailing Föppl-type vortex pair. The conformal invariance of the complex potential permits both problems to be formulated as a Polubarinova–Galin (PG) type equation in which the time-dependent eroding surface in the physical z-plane is mapped to the fixed boundary of the ζ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\zeta $$\\end{document}-disk. The Hamiltonian governing the equilibrium position of the vortex (or vortex pair in the second problem) is also found from the same map. In each problem, the PG equation giving the conformal map is found numerically and the time-dependent evolution of the interface and vortex location is determined. Different models governing the erosion of the interface are investigated in which the normal velocity of the boundary depends on some given function of the fluid flow velocity at the boundary. Typically, in the infinite surface case, erosion leads to the formation of a symmetric valley beneath the vortex which, in turn, moves downward toward the interface. A finite body undergoes erosion which is asymmetric in the flow direction leading to a flattening of the lee surface of the body so displaying some similarity to the experiments and associated viscous theory of Ristroph et al, Moore et al (Proc Natl Acad Sci 109(48):19606–19609, 2012, Phys Fluids 25(11):116602, 2013).

The Curie principle and the Shubnikov system – to the further development of their ideas

The Curie principle, which establishes a relationship between the symmetries of a cause and its effect, was originally developed for finite bodies (crystals), but Pierre Curie himself noted the possibility of its application to extended media. This direction was initiated by the works of A. V. Shubnikov (crystalline media) and I.I. Shafranovsky (mother solution), and it requires further development. The systems of limiting symmetries for finite bodies and extended media are compared. The former is partially correlated with the symmetry system of crystallographic point groups. For the latter, in addition to the known data from Curie and Shubnikov, the introduction of new types of limiting symmetries is theoretically justified, and a general systematization is proposed.

Nonuniqueness in defining the polarization: Nonlocal surface charges and the electrostatic, energetic, and transport perspectives

Ionic crystals, ranging from dielectrics to solid electrolytes to complex oxides, play a central role in the development of modern technologies for energy storage, sensing, actuation, and other functional applications. Mesoscale descriptions of these crystals are based on the continuum polarization density field to represent the effective physics of charge distribution at the scale of the atomic lattice. However, a long-standing difficulty is that the classical electrostatic definition of the macroscopic polarization — as the dipole or first moment of the charge density in a unit cell — is not unique; rather, it is sensitive to translations of the unit cell in an infinite periodic system. This unphysical non-uniqueness has been shown to arise from starting directly with an infinite system — wherein the boundaries are ill-defined — rather than starting with a finite body and taking appropriate limits. This limit process shows that the electrostatic description requires not only the bulk polarization density, but also the surface charge density, as the effective macroscopic descriptors; that is, a nonlocal effective description. Other approaches to resolve this difficulty include the popular modern theory of polarization that completely sets aside the polarization as a fundamental quantity in favor of the change in polarization from an arbitrary reference value and then relates the change in polarization to the transport of charge (the “transport” definition); or, in the spirit of classical continuum mechanics, to define the polarization as the energy-conjugate to the electric field (the “energetic” definition).This work examines the relation between the classical electrostatic definition of polarization, and the transport and energy-conjugate definitions of polarization. We show the following: (1) The transport of charge does not correspond to the change in polarization in general; instead, one requires additional simplifying assumptions on the electrostatic definition of polarization for these approaches to give rise to the same macroscopic electric fields. Thus, the electrostatic definition encompasses the transport definition as a special case. (2) The energy-conjugate definition has both bulk and surface contributions; while traditional approaches neglect the surface contribution, we find that accounting for the nonlocal surface contributions is essential to be consistent with the classical definition and obtain the correct macroscopic electric fields.

Construction of Short-Time Heat Conduction Solutions in One-Dimensional Finite Rectangular Bodies

Abstract The concept of both penetration and deviation times for rectangular coordinates along with the principle of superposition for linear problems allows short-time solutions to be constructed for a one-dimensional (1D) rectangular finite body from the well-known solutions of a semi-infinite medium. Some adequate physical considerations due to thermal symmetries with respect to the middle plane of a slab to simulate homogeneous boundary conditions of the first and second kinds are also needed. These solutions can be applied at the level of accuracy desired (one part in 10A, with A = 2, 3, …, 15) with respect to the maximum temperature variation (that always occurs at the active surface and at the time of evaluation) in place of the exact analytical solution to the problem of interest consisting of an infinite number of terms and, hence, unapplicable.

The I-PREDICT 50th Percentile Male Warfighter Finite Element Model: Development and Validation of the Thoracolumbar Spine.

Military personnel are commonly at risk of lower back pain and thoracolumbar spine injury. Human volunteers and postmortem human subjects have been used to understand the scenarios where injury can occur and the tolerance of the warfighter to these loading regimes. Finite element human body models (HBMs) can accurately simulate the mechanics of the human body and are a useful tool for understanding injury. In this study, a HBM thoracolumbar spine was developed and hierarchicallyvalidated as part of the Incapacitation Prediction for Readiness in Expeditionary Domains: an Integrated Computational Tool (I-PREDICT) program. Constitutive material models were sourced from literature and the vertebrae and intervertebral discs were hexahedrally meshed from a 50th percentile male CAD dataset. Ligaments were modeled through attaching beam elements at the appropriate anatomical insertion sites. 94 simulations were replicated from experimental PMHS tests at the vertebral body, functional spinal unit (FSU), and regional lumbar spine levels. The BioRank (BRS) biofidelity ranking system was used to assess the response of the I-PREDICT model. At the vertebral body level, the I-PREDICT model showed good agreement with experimental results. The I-PREDICT FSUs showed good agreement in tension and compression and had comparable stiffness values in flexion, extension, and axial rotation. The regional lumbar spine exhibited "good" biofidelity when tested in tension, compression, extension, flexion, posterior shear, and anterior shear (BRS regional average = 1.05). The validated thoracolumbar spine of the I-PREDICT model can be used to better understand and mitigate injury risk to the warfighter.

How real is incomputability in physics?

A physical system is determined by a finite set of initial conditions and “laws” represented by equations. The system is computable if we can solve the equations in all instances using a “finite body of mathematical knowledge”. In this case, if the laws of the system can be coded into a computer program, then given the initial conditions of the system, one can compute the system's evolution.Are there incomputable physical systems? This question has been theoretically studied in the last 30–40 years.In this paper, we experimentally show for the first time the strong incomputability of a quantum experiment, namely the outputs of a quantum random number generator. Moreover, the experimental results are robust and statistically significant.

Perturbative stability analysis of deformable charged bodies revealing the mathematical origin of Planck constant

This article considers elementary particles like electrons as finitely sized deformable bodies and analyzes the classical mechanics of their interior continuum. The consequent findings answer a long-standing question in physics by computing Planck constant mathematically. It also explains quantum phenomena like wave-particle duality, uncertainty principle and atomic stability without resorting to phenomenological relations like Planck’s law or Bohr’s postulates. The analysis introduces the criteria for perpetual stability under arbitrary perturbations to compensate for the lack of system-defining initial conditions typically available in a classical mechanics problem. Accordingly, unperturbed leading order field solutions are first constructed from steady rotation and axisymmetric electromagnetic potentials. Then, novel perturbation theories uniquely render the particulate geometry along with mass and charge distributions by exploiting the stability conditions. The approach reveals the perpetually stable body to have surface charges encapsulating a slender disk with a radius-to-thickness ratio 51.36 and a rim velocity of 0.09798c. The volumetric densities for rest-mass and charge are seen to vary with dimensionless radius (r) as (1−r2)−3/2 and (1−r2)−2 . The theory infers that the deformable system with many degrees of freedom would exhibit several pulsating modes. One such vibration, named quantum mode in this paper, causes spontaneous oscillation of the particulate center in the equatorial plane with a unique time period of oscillation. This wavy motion manifests wave-particle duality, whereas its probabilistic amplitude is identified as the reason behind quantum uncertainties. Moreover, in response to external fields, the charge deforms to create dipoles which can nullify radiation-inducing Poynting vector to ensure atomic stability. Finally, the Planck constant is retrieved after dividing the rest-energy by the frequency of the quantum mode. Thus, the paper concludes that a new detailed mechanics can potentially describe subatomic physics if charges are perceived as perpetually stable but readily deformable finite bodies, not rigid shape-less entities.

Influence of muscle activation on lumbar injury under a specific +Gz load

PurposeThe present study aimed to analyze the influence of muscle activation on lumbar injury under a specific +Gz load. MethodsA hybrid finite element human body model with detailed lumbar anatomy and lumbar muscle activation capabilities was developed. Using the specific +Gz loading acceleration as input, the kinematic and biomechanical responses of the occupant's lower back were studied for both activated and deactivated states of the lumbar muscles. ResultsThe results indicated that activating the major lumbar muscles enhanced the stability of the occupant's torso, which delayed the contact between the occupant's head and the headrest. Lumbar muscle activation led to higher strain and stress output in the lumbar spine under +Gz load, such as the maximum Von Mises stress of the vertebrae and intervertebral discs increased by 177.9% and 161.8%, respectively, and the damage response index increased by 84.5%. ConclusionIn both simulations, the occupant's risk of lumbar injury does not exceed 10% probability. Therefore, the activation of muscles could provide good protection for maintaining the lumbar spine and reduce the effect of acceleration in vehicle travel direction.

Developing Rib Bone Surrogates for High Dynamic Impact Assessment with Additive Manufacturing and Post-mortem Human Subjects (PMHS)-Based Evaluation

The conception of ballistic personal protective equipment requires a comprehensive understanding of the human body’s response to dynamic loads. The objective of this study is to develop rib bone surrogates enhancing new anthropomorphic test devices for personal protective equipment evaluation at high dynamic impacts. These are fabricated with additive manufacturing and compared to post-mortem human subjects (PMHS) data from literature. The 5th rib of the finite element Global Human Body Model Consortium (GHBMC) male 50th percentile (M50) model was extracted and transferred to a CAD model. This CAD model was divided into 30 sections with specific cortical bone thicknesses in all directions (caudal, cranial, cutaneous and pleural) from an equivalent rib of an M50 PMHS. Three different additive manufacturing technologies (direct metal laser melting, fused filament fabrication and multi jet modeling) were used to reproduce the M50 PMHS 5th rib surrogate. A total of 57 specimens were dynamically (500 mm/s) loaded to failure in a bending scenario imitating a frontal thoracic impact. Force, displacement, stiffness, and energy at failure were determined. Also, the strain distribution using 3D digital image correlation was recorded and compared to PMHS data from literature. The rib surrogates show deviations from the PMHS characteristic values. Nevertheless, there are also common characteristics in key variables to certain age groups of the PMHS data, which will facilitate the further development and improvement of adequate surrogates for a more realistic representation of the human body’s response to high dynamic loads.

Revisiting classical concepts of Linear Elastic Fracture Mechanics - Part II: Stretching finite strips weakened by single edge parabolically-shaped notches

This is the second part of a short three-paper series, aiming to revisit some classical concepts of Linear Elastic Fracture Mechanics. Being the intermediate step of the analysis between infinite domains (discussed in Part-I) and finite bodies (that will be discussed analytically in the third part of the series), the present part offers an alternative theoretical approach for the confrontation of problems dealing with both infinite and finite bodies with geometrical discontinuities. The method is here applied to a stretched, single-edge notched strip. Assuming that the strip is made of a linearly elastic and isotropic material, the complex potentials technique is used. The solution is achieved by extending Mushkelishvili’s procedure, for the confrontation of the prob­lem of an infinite perforated plane. Closed form, full-field formulae are obtained for the stresses all over the notched strip. Using these formulae, the stress concentration factor at the base (tip) of the notch is quantified and studied in terms of the geometrical features of the notch and its dimensions relatively to the respective ones of the strip. The stress distributions plotted along characteristic loci, resemble closely, from a qualitative point of view, the respective ones provided by well-established analytical solutions. Preliminary numerical analyses in progress provide results in very good agreement with those of the present analysis.

A unified bond–based peridynamic model without limitation of Poisson's ratio

The issue of fixed Poisson's ratio is a critical problem plaguing bond–based peridynamic (BB–PD) models. The popular approach of introducing the bond's tangential stiffness cannot completely remove Poisson's ratio limitation, but instead leads to some additional troubles, such as negative tangential stiffness and bond force density misalignment in finite rigid body rotation problems. To address the issue of fixed Poisson's ratio thoroughly, a unified bond–based peridynamics (UPD) was originally proposed. In the proposed model, a novelty pairwise force density function has been developed, in which dilatation and distortion are distinguished, and the model assigns different stiffnesses to the two deformation components. Arbitrary and reasonable values of Poisson's ratio can be achieved by adjusting the PD parameters that control the bulk and shear moduli of the material. The theoretical range of Poisson's ratio in the proposed model is (-1, 0.5], which is consistent with those in continuum mechanics. In addition, the absence of tangential stiffness prevents the proposed model from misalignment of bond force density due to rigid body rotation. Several numerical examples, including four two–dimensional and three–dimensional deformation analyses and three quasi–static fracture analyses, were implemented to verify the accuracy and reliability of the proposed model. The results show that the proposed model can accurately simulate the elastic properties of the material and obtain the deformation with high accuracy. The numerical examples also demonstrate the fracture prediction capability of the proposed model.

A First Step Toward a Family of Morphed Human Body Models Enabling Prediction of Population Injury Outcomes.

The injury risk in a vehicle crash can depend on occupant specific factors. Virtual crash testing using finite element human body models (HBMs) to represent occupant variability can enable the development of vehicles with improved safety for all occupants. In this study, it was investigated how many HBMs of different sizes that are needed to represent a population crash outcome through a metamodel. Rib fracture risk was used as an example occupant injury outcome. Morphed HBMs representing variability in sex, height, and weight within defined population ranges were used to calculate population variability in rib fracture risk in a frontal and a side crash. Two regression methods, regularized linear regression with second-order terms and Gaussian process regression (GPR), were used to metamodel rib fracture risk due to occupant variability. By studying metamodel predictive performance as a function of training data, it was found that constructing GPR metamodels using 25 individuals of each sex appears sufficient to model the population rib fracture risk outcome in a general crash scenario. Further, by utilizing the known outcomes in the two crashes, an optimization method selected individuals representative for population outcomes across both crash scenarios. The optimization results showed that 5-7 individuals of each sex were sufficient to create predictive GPR metamodels. The optimization method can be extended for more crashes and vehicles, which can be used to identify a family of HBMs that are generally representative of population injury outcomes in future work.

Static Analysis and Optimization Design of Bridge Structures under Different Load Conditions

The research is the optimization design of the bridge from the structure of the bridge, proper material utilization, and improving the performance of the bridge. First, the static model of the bridge structure was established, and then the finite analysis and rigid body mechanics models were utilized to separately detail the dead load, live load, and exceptional load. Based on the above analyses, optimization methods such as mathematical programming and genetic algorithms were used for optimizing the design of bridge structures. The tests demonstrated that the bridge’s weight can be significantly reduced by optimal design, the efficiency of usage in materials is enhanced, and the rigidity and stability of the structure advanced significantly. It is verified through checking the comparative analysis before and after optimization that the efficiency of the optimization method has been proved and the critical application value of optimization design in bridge engineering. The research conclusions provide new ideas and methods for bridge structure design, which has important theoretical and practical significance.

An investigation of tendon strains in jersey finger injury load cases using a finite element neuromuscular human body model.

Introduction: A common hand injury in American football, rugby and basketball is the so-called jersey finger injury (JFI), in which an eccentric overextension of the distal interphalangeal joint leads to an avulsion of the connected musculus flexor digitorum profundus (FDP) tendon. In the field of automotive safety assessment, finite element (FE) neuromuscular human body models (NHBMs) have been validated and are employed to evaluate different injury types related to car crash scenarios. The goal of this study is to show, how such a model can be modified to assess JFIs by adapting the hand of an FE-NHBM for the computational analysis of tendon strains during a generalized JFI load case. Methods: A jersey finger injury criterion (JFIC) covering the injury mechanisms of tendon straining and avulsion was defined based on biomechanical experiments found in the literature. The hand of the Total Human Model for Safety (THUMS) version 3.0 was combined with the musculature of THUMS version 5.03 to create a model with appropriate finger mobility. Muscle routing paths of FDP and musculus flexor digitorum superficialis (FDS) as well as tendon material parameters were optimized using literature data. A simplified JFI load case was simulated as the gripping of a cylindrical rod with finger flexor activation levels between 0% and 100%, which was then retracted with the velocity of a sprinting college football player to forcefully open the closed hand. Results: The optimization of the muscle routing node positions and tendon material parameters yielded good results with minimum normalized mean absolute error values of 0.79% and 7.16% respectively. Tendon avulsion injuries were detected in the middle and little finger for muscle activation levels of 80% and above, while no tendon or muscle strain injuries of any kind occurred. Discussion: The presented work outlines the steps necessary to adapt the hand model of a FE-NHBM for the assessment of JFIs using a newly defined injury criterion called the JFIC. The injury assessment results are in good agreement with documented JFI symptoms. At the same time, the need to rethink commonly asserted paradigms concerning the choice of muscle material parameters is highlighted.

A single-surface multi-failure strength domain for masonry

In this paper, we propose a simple approach to derive a single-surface multi-failure strength domain for the in-plane behaviour of masonry. The approach, that lays the basis for homogeneous continuum model developments relies on micro-mechanical analyses employing a block-based model for masonry in which blocks, modelled as finite strength continuum bodies, interact through zero-thickness interfaces. In order to derive the strength domain, firstly three failure mechanism typologies are identified, namely crushing failure, joint failure and mixed joint-block failure. Then, the limit surface for each mechanism is obtained relying on limit equilibrium considerations, also introducing a novel rational treatment of the mixed mechanism. Accordingly, a multi-surface strength domain is built by intersecting all the limit surfaces. Finally, such multi-surface strength domain is reduced to a single-surface one exploiting the RealSoftMax function, which allows to preserve the multi-failure nature of the approach, i.e. the explicit distinction between all the failure mechanisms. Following the proposed procedure, the resulting strength domain inherits the material parameters characterizing the block-based model. A finite element block-based model and available experimental data are employed to validate the proposed strength domain. The good agreement obtained with reference results confirms the soundness of the approach.

Weighted finite element method and body of optimal parameters for elasticity problem with singularity

Mathematical models with a singularity play a decisive role in predicting the development of processes in fracture mechanics. A weighted finite element method based on the introduction of the definition of an Rν-generalized solution for the system of Lamé equations with corner singularity is constructed. An estimate for the convergence of an approximate solution by a weighted finite element method to an Rν-generalized solution at a rate of O(h), that is, without loss of accuracy, is proved. For effective use of a weighted finite element method, it is necessary to correctly set the control parameters of the approach for performing calculations. An algorithm for determining the optimal parameters the weighted finite element method for finding an approximate solution to the Lamé system in domains with a boundary containing re-entrant corners ranging from π to 2π is developed. The general body of optimal parameters for weighted finite element method is determined.

A commercial finite element approach to modelling Glacial Isostatic Adjustment on spherical self-gravitating compressible earth models

SUMMARYThis paper presents a method that modifies commercial engineering-oriented finite element packages for the modelling of Glacial Isostatic Adjustment (GIA) on a self-gravitating, compressible and spherical Earth with 3-D structures. The approach, called the iterative finite element body and surface force (FEMIBSF) approach, solves the equilibrium equation for deformation using the ABAQUS finite element package and calculates potential perturbation consistently with finite element theory, avoiding the use of spherical harmonics. The key to this approach lies in computing the mean external body forces for each finite element within the Earth and pressure on Earth's surface and core–mantle boundary (CMB). These quantities, which drive the deformation and stress perturbation of GIA but are not included in the equation of motion of commercial finite element packages, are implemented therein. The method also demonstrates how to calculate degree-1 deformation directly in the spatial domain and Earth-load system for GIA models. To validate the FEMIBSF method, loading Love numbers (LLNs) for homogeneous and layered earth models are calculated and compared with three independent GIA methodologies: the normal-mode method, the iterative body force method and the spectral-finite element method. Results show that the FEMIBSF method can accurately reproduce the unstable modes for the homogeneous compressible model and agree reasonably well with the Love number results from other methods. It is found that the accuracy of the FEMIBSF method increases with higher resolution, but a non-conformal mesh should be avoided due to creating the so-called hanging nodes. The role of a potential force at the CMB is also studied and found to only affect the long-wavelength surface potential perturbation and deformation in the viscous time regime. In conclusion, the FEMIBSF method is ready for use in realistic GIA studies, with modelled vertical and horizontal displacement rates in a disc load case showing agreement with other two GIA methods within the uncertainty level of GNSS measurements.