Homogeneous Material Properties Research Articles

Composite Pressure Vessel Failure Simulation Considering Spatial Variability

Carbon fiber-reinforced polymers offer lightweight solutions for demanding applications, but material imperfections affect structural reliability. In this study, an efficient uncertainty propagation framework is applied to predict composite behavior. The framework accounts for spatial variability of fiber misalignment, uneven fiber distribution, and single-fiber strength. Spatial variability is represented at both the micro- and mesoscale. Macroscale simulations incorporate this spatial variability indirectly using homogenized material properties. The framework was applied to composite pressure vessels, whose stochastic burst pressure was predicted. The predictions were validated by experimental measurements. These measurements show that the actual burst pressure was underpredicted by an average of 5.8%. Several hypotheses were investigated to explain this discrepancy.

A Survey of Multimaterial Treatments for Thermal Radiative Transfer

Arbitrary Lagrangian-Eulerian methods are a popular choice for hydrodynamic modeling in radiation (rad-hydro) simulations. Because these methods involve a relaxation step that moves the mesh relative to material boundaries, multimaterial spatial zones are generally present. Accurate treatments of these zones are needed to resolve various physical phenomena of interest for inertial confinement fusion applications. However, these codes are often paired with single-material, deterministic thermal radiative transfer (TRT) codes that are oblivious to the material compositions of each zone. These single-material TRT codes can only accept homogenized material properties (opacities, specific heats, etc.) from the hydrodynamic code and output homogenized solutions. After each TRT time step, the multimaterial hydrodynamic code must dehomogenize the quantities computed by the TRT package in order to update subzonal material temperatures. The process by which hydrodynamic codes perform this dehomogenization has not been well documented in previous literature, and the methods can vary significantly from code to code. The purpose of this paper is to document, study, and compare existing techniques used for rad-hydro simulations as well as present a new method with potentially promising results. We summarize several methods and give comparisons on infinite-medium problems as well a finite-medium problem for two of the methods.

Multiscale computational modelling of nano-silica reinforced cement paste: Bridging microstructure and mechanical performance

This study presents a systematic model to optimise nano-silica utilisation in cement paste and predict its nonlinear behaviour. The model integrates a hydration model, which calculates the dissolution rate of each clinker mineral, with a thermodynamic model that simulates the hydration reaction and interaction between hydrates and nano-silica. The investigation considered different replacement levels of nano-silica (2 and 4% by weight of cement) to analyse the phase assemblages and porosity of nano-silica reinforced cement paste. The reaction between nano-silica and the hydrate (portlandite) was meticulously accounted for by incorporating the formation of calcium-silica-hydrate (C-S-H) with a realistic transition from jennite-type C-S-H (Si/Ca ratio of 0.58) to tobermorite C-S-H (Si/Ca ratio of 0.67). The coupled model was validated against the experimental results obtained from thermogravimetric analysis, X-ray diffraction, and scanning electron microscopy, ensuring its reliability. Subsequently, the model was used to compute the volume fractions of various phases including hydrates, unhydrated clinkers, pores, and unreacted nano-silica. A representative volume element (RVE) was formulated for the cement pastes with and without nano-silica using MATLAB. The RVE was further evaluated through finite element analysis using COMSOL Multiphysics, enabling the computation of homogenised material properties such as compressive strength, and this aligned well with experimental findings. In summary, the proposed systematic model provides a realistic prediction of the nonlinear behaviour of cement pastes with different nano-silica replacement levels. Its applicability extends to the optimisation of cement-based composites for diverse engineering applications.

A statistical analysis of human talar shape and bone density distribution.

The shape of the talus, its internal structure, and its mechanical properties are important in determining talar behavior during loading, which may be significant for the design of surgical tools and implants. Although recent studies using statistical shape modeling have described quantitative talar external shape variation, no similar quantitative study exists to describe the density distribution of internal talar structure. The goal of this study is to quantify statistical variation in talar shape and density to benefit the design of talar implants. To this end, weight-bearing computed tomography (CT) scans of the ankle were collected in neutral, bilateral standing posture, and three-dimensional models were generated for each talus. Local density derived from the Hounsfield unit of each CT voxel was extracted. A weighted spherical harmonic analysis was performed to quantify the talar external shape. One hundred and seventy-nine volumes of interest were placed in the same relative position within each talus to quantify the talar density. Additionally, a finite element analysis (FEA) was conducted on a talus with both heterogeneous and homogeneous material properties to observe the effect of these properties on the stress and strain response. Significant differences were found in the talar density in sex and age, as well as in the stress and strain response between homogeneous and heterogeneous FEA. These differences show the importance of considering heterogeneity when examining the load response of tarsal bones.

Numerical analysis of functionally graded piezoelectric bionic fishtail based on Hermite element-free method

Piezoelectric bionic fishtails have good flexibility, response speed, anti-interference ability, and have great application prospects in ocean exploration. However, the inherent drawbacks of the mechanical properties of traditional homogeneous piezoelectric materials significantly affect the propulsion performance and reliability of the piezoelectric bionic fishtails. To fill this gap, this paper develops a functionally graded piezoelectric bionic fishtail (FGPBF) by imitating the tail characteristics of groupers. The geometric structure and working principle of the FGPBF are introduced in detail. Based on the first-order shear deformation theory and Hermite element-free method, an element-free model for the FGPBF is established. The effects of gradient factor, substrate material, substrate thickness and electrical load on the propulsion performance of the FGPBF are addressed. The results show that the current results are in good agreement with the finite element results. The deformation of the FGPBF is negatively correlated with the thickness and stiffness of the substrate and linearly positively correlated with the electrical load. As the gradient factor increases, the deflection of the FGPBF first increases and then decreases. When the gradient factor is 2, the potential is 200 V, the dimensionless aluminum substrate thickness is 1, the propulsion performance of the FGPBF is improved by 28% compared to the homogeneous piezoelectric bionic fishtail.

Effect of porosity on the modal response of doubly-curved laminated shell structures made of functionally graded materials employing higher order theories

The manuscript investigates the modal response of laminated anisotropic doubly-curved shell structures of variable thickness made of Functionally Graded Materials (FGM), according to an efficient equivalent single layer strategy where the displacement field is described employing a condensed unified formulation, accounting for a higher order through-the-thickness expansion. A generalized power law distribution is adopted for the assessment of the FGM layers, whereas the presence of voids is considered starting from different homogenization assumptions. Unlike previous works which presented a variation of the homogenized material properties within the shell solid, in this paper the problem of material porosity is addressed, therefore a general distribution of the volume fraction of the constituent materials is considered, along with the presence of voids. To this end, both linear and trigonometric through-the-thickness distributions are here assumed. The fundamental governing equations are derived starting from a proper set of curvilinear principal coordinates, while a generalized set of blending functions accounts for arbitrarily shaped structures. Non-conventional boundary conditions are, here, modelled with a distribution of linear springs along the shell edges. The numerical implementation of the problem is performed with the generalized differential quadrature method. A systematic set of validating examples is presented, whose results are compared to predictions based on refined models, as well as some experimental evidence. After a validation step, an extensive parametric analysis points out the sensitivity of the porosity parameters on the modal response of structures with different curvatures and external constraints, with valid findings for engineering design purposes.

Multiscale Analysis of Composite Structures with Artificial Neural Network Support for Micromodel Stress Determination.

Structures made of heterogeneous materials, such as composites, often require a multiscale approach when their behavior is simulated using the finite element method. By solving the boundary value problem of the macroscale model, for previously homogenized material properties, the resulting stress maps can be obtained. However, such stress results do not describe the actual behavior of the material and are often significantly different from the actual stresses in the heterogeneous microstructure. Finding high-accuracy stress results for such materials leads to time-consuming analyses in both scales. This paper focuses on the application of machine learning to multiscale analysis of structures made of composite materials, to substantially decrease the time of computations of such localization problems. The presented methodology was validated by a numerical example where a structure made of resin epoxy with randomly distributed short glass fibers was analyzed using a computational multiscale approach. Carefully prepared training data allowed artificial neural networks to learn relationships between two scales and significantly increased the efficiency of the multiscale approach.

Near‐Nozzle Mixing for Additive Manufacturing of Cementitious Mortar: A Homogeneity Study

AbstractThis paper investigates the Near‐nozzle Mixing (NNM) technique for 3D printing cementitious mortar, focusing on achieving continuous and homogeneous material properties. The NNM's ability to print Natural Sand Mortar (NSM), Recycled Aggregate Mortar (RAM), and Lightweight Mortar (LWM) was assessed. Fresh and hardened properties of each mortar were examined, emphasizing standard deviation (STD) and coefficient of variation (CV) to measure material homogeneity. Fresh properties included slump flow, yield stress, air void volume, density, and water‐to‐cement ratio, while hardened properties covered compressive strength, flexural strength, hardened density, and thermal conductivity. Results showed low CV values for all mortar types, indicating high consistency and homogeneity. NNM showed is capability to print of various materials with customized properties. NSM showed the highest compressive strength, RAM balanced strength and sustainability, and LWM provided the best thermal insulation. The study highlights NNM's versatility and potential for construction applications requiring tailored properties, proving it a promising additive manufacturing solution. The research serves as a foundation for future studies on graded multi‐material printing.

Numerical simulation of CLT moisture uptake and dry-out following water infiltration through end-grain surfaces

Cross-laminated timber (CLT) offers the potential to construct advanced load-bearing walls and floors made of wood, as its larger dimensions and homogenized material properties expands the application possibilities. As for wood in general, CLT can be negatively affected by moisture. End-grain wetting of CLT coupled with conditions that trap moisture can be particularly problematic due to hindered drying. However, CLT end-grain wetting and subsequent moisture dry-out are hardly investigated and conventional models have not been able to simulate these conditions sufficiently. Here, we show that the moisture uptake and dry-out under this unfavorable condition can be realistically simulated using a moisture transport model including free water. We modeled a basic configuration of one-week wetting, followed by two weeks of dry-out in different climatic conditions. To refine the simulations, the mass transfer coefficients of water vapor and free water were calibrated. In a sensitivity analysis, the influence of both coefficients on moisture development was investigated, revealing that the most significant effect on moisture changes originates from the mass transfer coefficient of free water. Furthermore, the influence of glue lines connecting the layers of CLT panels on moisture transport was examined. The results suggest that the glue line has a minor influence on the moisture behavior of CLT surface layers, but the effects increase towards the middle layer.

A black-box optimization strategy for customizable global elastic deformation behavior of unit cell-based tri-anti-chiral metamaterials

Metamaterials are a class of materials with a distinctive unit cell-based periodic architecture, often resulting in unique mechanical properties. The potential of metamaterials can be further improved by using gradients of unit cell parameters and thereby creating a specific distribution of material properties in a part. This design freedom comes with the challenge of finding new suitable design and optimization strategies. In this study, a Finite Element simulation-based optimization framework to create a predefined deformation behavior of unit cell-based metamaterials is presented. The framework consists of a numerical homogenization method to create an efficient linear elastic material representation, an interpolation scheme for a fast correlation of unit cell parameters with homogenized material properties and a black-box based optimization part. The framework is tested on a tri-anti-chiral metamaterial with additional geometric parameters and a newly developed transition unit cell. Several specified lateral deformations of simple 2D rectangular test specimens under tensile load are used as primary optimization targets and the homogenized results are validated against Finite Element simulations of fully modeled tri-anti-chiral structures. In addition, the effect of the design space and the number of design variables is studied and several combinations of optimization objectives and constraints are tested.

Topology optimization approach for functionally graded metamaterial components based on homogenization of mechanical variables

The micron resolutions that 3D printers are reaching allow for a change of paradigm in the design of components, optimizing not only the topology of the component, but also the microstructure of the material, which can adopt different objectives at different locations in the component, reaching different mechanical properties and different optimal microstructures at those locations. This constitutes a flip in the design objectives to focus on tailored material work, aimed either at local objectives or at component-wide ones, instead of pursuing homogeneous material properties for global objectives. For this new concurrent structure-material design leading to optimized components made of functionally graded (FG) metamaterials, new topology optimization (TO) procedures are needed in which the objective is to obtain component-wise mechanical variables or distributions of these variables, rather than global component objectives as compliance, which is a typical objective of classical TO approaches.In this work we present a new TO approach aimed at FG metamaterial design pursuing homogeneous mechanical variables. We focus on homogenization of deformation level along the component by minimizing its standard deviation across the domain. The proposed formulation can be naturally generalized to anisotropy, nonlinear behavior, and other optimization objectives. Convergence to a suitable optimized solution, with a distribution of material properties resulting in a homogeneously deformed component, is obtained. These FG material properties may be obtained from local metamaterial design. Classical material/void configurations may also be obtained following our procedure, and results for such cases can be compared qualitatively to the Solid Isotropic Material with Penalization (SIMP) approach.

Quantification of inhomogeneity and anisotropy of bituminous mixtures using biaxial experimental data

Most of the existing mechanical characterization test methods and the analytical models for bituminous mixtures are developed based on the assumption of homogenous and isotropic material properties. However, the extent to which such assumptions hold good for bituminous mixtures is not very clear. A biaxial testing scheme in indirect tension mode can come in handy to collect the experimental data at different test temperature regimes. In this study, a bituminous mixture with a nominal maximum aggregate size (NMAS) of 13.2 mm is used to fabricate cylindrical test specimens with 150 mm diameter and 63.5 mm thickness for conducting the repeated load indirect tension (IDT) test. The input load level is selected as 5 to 13 % of the indirect tensile (ITS) failure load in the form of a haversine pulse of 0.1 s loading and 0.9 s rest period. Such loading is applied on zero-degree and ninety-degree orientations of the specimen. The resulting deformations in different directions are measured using linear variable differential transducers (LVDT) attached to both diametral faces of the specimen. The response of the bituminous mixture specimen is captured at three different temperatures of 20, 25, and 30 °C using two different gauge length (half and quarter gauge of the total diameter). A new framework is introduced in this study to evaluate the extent of inhomogeneity and anisotropy of bituminous mixtures. The deformation response of the test specimen captured in the same orientation at different diametral faces is compared to evaluate the extent of inhomogeneity. The extent of anisotropy is evaluated by comparing the deformation response of the test specimen captured at different orientations within the same diametral face. A 15 % variation in the average peak deformation is chosen as the demarcation for determining the extent of inhomogeneity and anisotropy. From this investigation, it is observed that half gauge length experimental data exhibits homogenous and isotropic behavior for all three test temperatures. The quarter gauge length data exhibit similar behavior at 30 °C, whereas it is observed as homogenous and anisotropic at the other two test temperatures.

DL-MSTO+: A deep learning-based multi-scale topology optimization framework via positive definiteness ensured material representation network

A multi-scale approach to topology optimization has recently emerged due to its lightweight, robust, and multi-functional characteristics. Considering material diversity, an increasing number of materials leads to a computational burden due to numerous design variables and homogenization equations. This study proposes DL-MSTO+, a deep learning-based multi-scale topology optimization framework. The framework consists of two distinct deep neural networks for multi-scale topology optimization problems to reduce the dimensionality of design variables and predict homogenized material properties. First, a generator network learns the low-dimensional representation of a material microstructure in an unsupervised manner. Thus, the trained generator produces a micro-structural image from a low-dimensional vector. Second, a predictor network is trained in a supervised manner to predict the homogenized elasticity matrix for a given micro-structural image. Additionally, the predictor is specifically designed to ensure the positive definiteness of the predicted elasticity matrix. Lastly, the networks are integrated into the algorithm to improve the efficiency of multi-scale topology optimization. The numerical experiments demonstrate higher efficiency for the proposed algorithm than the conventional multi-scale approach. Moreover, the proposed method provides connectable multi-scale designs, and the low-dimensional latent representation enables semantic interpolation between solutions.

Derivation of heterogeneous material distributions and their sensitivity to HM-coupled two-phase flow models exemplified with the LASGIT experiment

Advective gas transport in bentonite, a possible buffer material in repositories for radioactive materials, is difficult to simulate in numerical continuum models, partly due to the complicated microstructure of bentonite. To generate reliable models of repositories nevertheless, spatially distributed heterogeneous material properties can be used to allow localization of gas flow. In this study, a pore-size-dependent stochastic approach of the gas entry pressure is derived from Mercury Intrusion Porosimetry, which is used to replicate measurements from the LASGIT experiment. In addition, three benchmark tests are simulated to investigate the dependence of heterogeneous distributions of material properties on the mesh discretization, the temporal dependence, and the coupling between the processes influenced by the heterogeneous parameters. The numerical modeling results of the LASGIT experiment show that the onset of gas flow into the system and the subsequent increase in pressure and stress can be well reproduced using heterogeneous distributions. Compared to a model with homogeneous material properties, heterogeneous distributions may allow the generation of dilatancy-controlled microfractures—an important feature with regard to the advective gas flow in bentonites. However, it can be observed that the heterogeneous distributions in LASGIT are less significant, as technical gaps or differences in material types could have a greater impact.

A Variational Formulation of Physics-Informed Neural Network for the Applications of Homogeneous and Heterogeneous Material Properties Identification

A new approach for solving computational mechanics problems using physics-informed neural networks (PINNs) is proposed. Variational forms of residuals for the governing equations of solid mechanics are utilized, and the residual is evaluated over the entire computational domain by employing domain decomposition and polynomials test functions. A parameter network is introduced and initial and boundary conditions, as well as data mismatch, are incorporated into a total loss function using a weighted summation. The accuracy of the model in solving forward problems of solid mechanics is demonstrated to be higher than that of the finite element method (FEM). Furthermore, homogeneous and heterogeneous material distributions can be effectively captured by the model using limited observations, such as strain components. This contribution is significant for potential applications in non-destructive evaluation, where obtaining detailed information about the material properties is difficult.

A novel homogenization method for periodic piezoelectric composites via diffused material interface

In this article, we propose a novel homogenization method for piezoelectric composites with periodic microstructures. In the proposed homogenization method, one can find the analytical expressions for the material properties of the composites in the representative volume element (RVE) via diffused material interface method. The availability of analytical expressions for the material properties in the entire domain of the RVE enables one to determine the effective homogenized material properties with the standard finite element method. As the proposed homogenization method regularizes the discontinuity in material properties across the interfaces, there is no need to explicitly track the material interfaces while implementing the finite element method for determining the effective material properties. Hence, one can implement the proposed homogenized method for any piezoelectric composites with complicated material interfaces and determine the effective material properties. In this study, we have considered the piezoelectric composites to be comprised of periodic microstructures where the RVE constitutes a matrix with an inclusion of a specific shape. We have carried out a study on the effect of the shape of inclusion viz. square-shaped, I-shaped, T-shaped, and plus-shaped, and the size of inclusion on the effective piezoelectric material properties. We have also studied the influence of shape and size of inclusion on the electro-mechanical response of a homogenized piezoelectric continuum. To implement the proposed homogenization method, we have used Gridap, an open-source finite element toolbox in Julia that provides very compact codes freely available to all the researchers and makes a third-party verification of the proposed method straightforward.

Application of Chebyshev collocation element method to Green-Naghdi thermoelasticity of a bi-layered media consists of FGM and viscoelastic domains

In this study, the generalized coupled thermoelastic wave propagation and temporal evolution in a bi-layered system are analyzed. The main layer is made of functionally graded materials (FGM), while the holder layer is viscoelastic. The constituent volume fractions in the FGM layer are calculated by a power law function. Moreover, the Voigt rule of mixtures is employed to obtain the homogenized material properties. On the other hand, the constitutive law for the viscoelastic environment is considered based on the Kelvin-Voigt model. The heat conduction equation for each layer is represented based on the general form of the Green-Naghdi theory. First, for each layer, two motion and heat conduction coupled equations are derived, as well as the boundary and appropriate continuity conditions. The Chebyshev collocation element (CCE) method is used to solve the spatial-dependent parts of equations and also assemble the governing matrices into a global system. Finally, the Newmark numerical integration method is implemented to solve the ODEs and calculate the system response. The achieved response is verified with limited articles in the literature. Some parametric results are shown to evaluate the performance of FG and viscoelastic characteristics on the FGM layer response which is subjected to a thermal shock.

Bulk Tungsten Fiber-Reinforced Tungsten (Wf/W) Composites Using Yarn-Based Textile Preforms

The use of tungsten fiber-reinforced tungsten composites (Wf/W) has been demonstrated to significantly enhance the mechanical properties of tungsten (W) by incorporating W-fibers into the W-matrix. However, prior research has been restricted by the usage of single fiber-based textile fabrics, consisting of 150 µm warp and 50 µm weft filaments, with limited homogeneity, reproducibility, and mechanical properties in bulk structures due to the rigidity of the 150 µm W-fibers. To overcome this limitation, two novel textile preforms were developed utilizing radial braided W-yarns with 7 core and 16 sleeve filaments (R.B. 16 + 7), with a diameter of 25 µm each, as the warp material. In this study, bulk composites of two different fabric types were produced via a layer-by-layer CVD process, utilizing single 50 µm filaments (type 1) and R.B. 16 + 7 yarns (type 2) as weft materials. The produced composites were sectioned into KLST-type specimens based on DIN EN ISO 179-1:2000 using electrical discharge machining (EDM) and subjected to three-point bending tests. Both composites demonstrated enhanced mechanical properties with pseudo-ductile behavior at room temperature and withstood over 10,000 load cycles between 50–90% of their respective maximum load without sample fracture in three-point cyclic loading tests. Furthermore, a novel approach to predict the fatigue behavior of the material under cyclic loading was developed based on the high reproducibility of the composites produced, especially for the composite based on type 1. This approach provides a new benchmark for upscaling endeavors and may enable a better prediction of the service life of the produced components made of Wf/W in the future. In comparison, the composite based on fabric type 1 demonstrated superior results in manufacturing performance and mechanical properties. With a high relative average density (>97%), a high fiber volume fraction (14–17%), and a very homogeneous fiber distribution in the CVD-W matrix, type 1 shows a promising option to be further tested in high heat flux tests and to be potentially used as an alternative to currently used materials for the most stressed components of nuclear fusion reactors or other potential application fields such as concentrated solar power (CSP), aircraft turbines, the steel industry, quantum computing, or welding tools. Type 2 composites have a higher layer spacing compared to type 1, resulting in gaps within the matrix and less homogeneous material properties. While type 2 composites have demonstrated a notable enhancement over 150 µm fiber-based composites, they are not viable for industrial scale-up unlike type 1 composites.

Mechanical and Thermal Properties of the High Thermal Conductivity Steel (HTCS) Additively Manufactured via Powder-Fed Direct Energy Deposition

High thermal conductivity steel (HTCS-150) is deposited onto non-heat-treated AISI H13 (N-H13) via powder-fed direct energy deposition (DED) based on the response surface methodology (RSM) to enhance the mechanical properties and thermal conductivity of N-H13, which is generally used as a hot-work tool steel. The main process parameters of the powder-fed DED are priorly optimized to minimize defects in the deposited regions and, therefore, to obtain homogeneous material properties. The deposited HTCS-150 is comprehensively evaluated through hardness, tensile, and wear tests at the different temperatures of 25, 200, 400, 600, and 800 °C. Compared to conventionally heat-treated (quenched and tempered) H13 (HT-H13), the hardness of the additively manufactured HTCS-150 slightly increases at 25 °C, whereas it does not show any significant difference above 200 °C. However, the HTCS-150 deposited on N-H13 shows a lower ultimate tensile strength and elongation than HT-H13 at all tested temperatures, and the deposition of the HTCS-150 on N-H13 enhances the ultimate tensile strength of N-H13. While the HTCS-150 does not show a significant difference in the wear rate below 400 °C compared to HT-H13, it shows a lower wear rate above 600 °C. The HTCS-150 reveals a higher thermal conductivity than the HT-H13 below 600 °C, whereas the behavior is reversed at 800 °C. The results suggest that the HTCS-150 additively manufactured via powder-fed direct energy deposition can enhance the mechanical and thermal properties of N-H13, including hardness, tensile strength, wear resistance, and thermal conductivity in a wide range of temperatures, often superior to those of HT-H13.

Mechanostat parameters estimated from time-lapsed in vivo micro-computed tomography data of mechanically driven bone adaptation are logarithmically dependent on loading frequency.

Mechanical loading is a key factor governing bone adaptation. Both preclinical and clinical studies have demonstrated its effects on bone tissue, which were also notably predicted in the mechanostat theory. Indeed, existing methods to quantify bone mechanoregulation have successfully associated the frequency of (re)modeling events with local mechanical signals, combining time-lapsed in vivo micro-computed tomography (micro-CT) imaging and micro-finite element (micro-FE) analysis. However, a correlation between the local surface velocity of (re)modeling events and mechanical signals has not been shown. As many degenerative bone diseases have also been linked to impaired bone (re)modeling, this relationship could provide an advantage in detecting the effects of such conditions and advance our understanding of the underlying mechanisms. Therefore, in this study, we introduce a novel method to estimate (re)modeling velocity curves from time-lapsed in vivo mouse caudal vertebrae data under static and cyclic mechanical loading. These curves can be fitted with piecewise linear functions as proposed in the mechanostat theory. Accordingly, new (re)modeling parameters can be derived from such data, including formation saturation levels, resorption velocity moduli, and (re)modeling thresholds. Our results revealed that the norm of the gradient of strain energy density yielded the highest accuracy in quantifying mechanoregulation data using micro-finite element analysis with homogeneous material properties, while effective strain was the best predictor for micro-finite element analysis with heterogeneous material properties. Furthermore, (re)modeling velocity curves could be accurately described with piecewise linear and hyperbola functions (root mean square error below 0.2µm/day for weekly analysis), and several (re)modeling parameters determined from these curves followed a logarithmic relationship with loading frequency. Crucially, (re)modeling velocity curves and derived parameters could detect differences in mechanically driven bone adaptation, which complemented previous results showing a logarithmic relationship between loading frequency and net change in bone volume fraction over 4weeks. Together, we expect this data to support the calibration of in silico models of bone adaptation and the characterization of the effects of mechanical loading and pharmaceutical treatment interventions in vivo.