Estimation Of Material Parameters Research Articles

A Computationally Efficient Approach for Estimation of Tissue Material Parameters from Clinical Imaging Data Using a Level Set Method

A Computationally Efficient Approach for Estimation of Tissue Material Parameters from Clinical Imaging Data Using a Level Set Method

Estimation of temperature-dependent piezoelectric material parameters using ring-shaped specimens

Abstract Simulation-driven design processes of piezoelectric actuators and sensors necessitate precise material parameter knowledge. Historically, the IEEE standard on piezoelectricity is used for this purpose, which proposes an analytical method for material parameter identification based on resonance frequency evaluations. This method requires different impedance measurements on differently shaped and processed samples, which yields inconsistent material parameter sets due to processing effects on material properties. Previous studies show that an inverse procedure using a single disc-shaped specimen with some adaptations can be used to identify a full set of parameters. As high-power actuators often use ring-shaped components, this method needs adaptation for this kind of specimen. Furthermore, the dependence of the material parameters on temperature needs to be considered to characterise the temperature effects and the associated non-linear effects of the specimens. For this purpose, samples with different geometrical dimensions at a range of different temperatures are examined in this study. Material parameters are then estimated using an inverse approach utilising the measurement data in conjunction with a numerical FEM simulation model. The observed temperature dependence of the estimated material parameters is examined and presented in this contribution.

Emergent fault friction and supershear in a continuum model of geophysical rupture

Important physical observations in rupture dynamics such as static fault friction, short-slip, self-healing, and the supershear phenomenon in cracks are studied. A continuum model of rupture dynamics is developed using the field dislocation mechanics (FDM) theory. The energy density function in our model encodes accepted and simple physical facts related to rocks and granular materials under compression. We work within a 2-dimensional ansatz of FDM where the rupture front is allowed to move only in a horizontal fault layer sandwiched between elastic blocks. Damage via the degradation of elastic modulus is allowed to occur only in the fault layer, characterized by the amount of plastic slip. The theory dictates the evolution equation of the plastic shear strain to be a Hamilton–Jacobi (H-J) equation, resulting in the representation of a propagating rupture front. A Central-Upwind scheme is used to solve the H-J equation. The rupture propagation is fully coupled to elastodynamics in the whole domain, and our simulations recover static friction laws as emergent features of our continuum model, without putting in by hand any such discontinuous criteria in the formulation. Estimates of material parameters of cohesion and friction angle are deduced. Short-slip and slip-weakening (crack-like) behaviors are also reproduced as a function of the degree of damage behind the rupture front. The long-time behavior of a moving rupture front is probed, and it is deduced that equilibrium profiles under no shear stress are not traveling wave profiles under non-zero shear load in our model. However, it is shown that a traveling wave structure is likely attained in the limit of long times. Finally, a crack-like damage front is driven by an initial impact loading, and it is observed in our numerical simulations that an upper bound to the crack speed is the dilatational wave speed of the material unless the material is put under pre-stressed conditions, in which case supersonic motion can be obtained. Without pre-stress, intersonic (supershear) motion is recovered under appropriate conditions.

Comparison of methods for estimating Young’s moduli of mortar specimens

Precisely estimating material parameters for cement-based materials is crucial for assessing the structural integrity of buildings. Both destructive (e.g., compression test) and non-destructive methods (e.g., ultrasound, computed tomography) are used to estimate Young’s modulus. Since ultrasound estimates the dynamic Young’s modulus, a formula is required to adapt it to the static modulus. For this formulas from the literature are compared. The investigated specimens are cylindrical mortar specimens with four different sand-to-cement mass fractions of 20%, 35%, 50%, and 65%. The ultrasound signals are analyzed in two distinct ways: manual onset picking and full-waveform inversion. Full-waveform inversion involves comparing the measured signal with a simulated one and iteratively adjusting the ultrasound velocities in a numerical model until the measured signal closely matches the simulated one. Using computed tomography measurements, Young’s moduli are semi-analytically determined based on sand distribution in cement images. The reconstructed volume is segmented into sand, cement, and pores. Young’s moduli, as determined by compression tests, were better represented by full-waveform inversions (best RMSE = 0.34 GPa) than by manual onset picking (best RMSE = 0.87 GPa). Moreover, material parameters from full-waveform inversion showed less deviation than those manually picked. The maximal standard deviation of a Young’s modulus determined with FWI was 0.36, while that determined with manual picking was 1.11. Young’s moduli from computed tomography scans match those from compression tests the closest, with an RMSE of 0.13 GPa.

Free-field method for inverse characterization of finite porous acoustic materials using feed forward neural networks.

This paper presents a free-field method for inverse estimation of acoustic porous material parameters from sound pressure measurements above small rectangular samples. The finite sample effect, the spherical propagation of the sound field, and a potential lateral material reaction are considered. Using an extensive series of systematically varied finite element simulations, neural network models are developed to replace computationally expensive simulations as a forward model for the calculation of the complex sound pressure above small samples in the inverse optimization. The method is experimentally validated using various porous material samples. The results show that the influence of the finite sample size is successfully removed and thus, the acoustic properties of the materials can be estimated from the determined porous parameters with high accuracy, even based on a single sound pressure measurement over small samples with pronounced edge diffraction. The poroacoustic parameters hence derived can be used directly, e.g., in simulation applications, or to calculate complex surface impedances or absorption coefficients.

Inverse analysis of granular flows using differentiable graph neural network simulator

Inverse problems in granular flows, such as landslides and debris flows, involve estimating material parameters or boundary conditions based on a target runout profile. Traditional high-fidelity simulators for these inverse problems are computationally expensive, restricting the number of possible simulations. These simulators are also non-differentiable, making efficient gradient-based optimization methods for high-dimensional spaces inapplicable. Machine learning-based surrogate models offer computational efficiency and differentiability. However, they often struggle to generalize beyond their training data due to relying on low-dimensional input–output mappings that fail to capture the complete physics of granular flows. We propose a novel differentiable graph neural network simulator (GNS) that combines reverse mode automatic differentiation of graph neural networks with gradient-based optimization for solving inverse problems. GNS learns the dynamics of granular flow by representing the system as a graph and predicts the evolution of the graph at the next timestep, given the current state. The differentiable GNS demonstrates optimization capabilities beyond the training data. We demonstrate the effectiveness of our method for inverse estimation across single and multi-parameter optimization problems, including evaluating material properties and boundary conditions for a target runout distance and designing baffle locations to limit a landslide runout. Our proposed differentiable GNS framework solves inverse problems with orders of magnitude faster convergence than the conventional gradient-based optimization approach using finite difference.

Macro-indentation testing of soft biological materials and assessment of hyper-elastic material models from inverse finite element analysis

Mechanical characterization of hydrogels and ultra-soft tissues is a challenging task both from an experimental and material parameter estimation perspective because they are much softer than many biological materials, ceramics, or polymers. The elastic modulus of such materials is within the 1 - 100 kPa range, behaving as a hyperelastic solid with strain hardening capability at large strains. In the current study, indentation experiments have been performed on agarose hydrogels, bovine liver, and bovine lymph node specimens. This work reports on the reliable determination of the elastic modulus by indentation experiments carried out at the macro-scale (mm) using a spherical indenter. However, parameter identification of the hyperelastic material properties usually requires an inverse finite element analysis due to the lack of an analytical contact model of the indentation test. Hence a comprehensive study on the spherical indentation of hyperelastic soft materials is carried out through robust computational analysis. Neo-Hookean and first-order Ogden hyperelastic material models were found to be most suitable. A case study on known anisotropic hyperelastic material showed the inability of the inverse finite element method to uniquely identify the whole material parameter set.

Estimation of TbCo composition from local-minimum-energy magnetic images taken by magneto-optical Kerr effect microscope by using machine learning

Recently, the incorporation of machine learning (ML) has heralded significant advancements in materials science. For instance, in spintronics, it has been shown that magnetic parameters, such as the Dzyaloshinskii–Moriya interaction, can be estimated from magnetic domain images using ML. Magnetic materials exhibit hysteresis, leading to numerous magnetic states with locally minimized energy (LME) even within a single sample. However, it remains uncertain whether these parameters can be derived from LME states. In our research, we explored the estimation of material parameters from an LME magnetic state using a convolutional neural network. We introduced a technique to manipulate LME magnetic states, combining the ac demagnetizing method with the magneto-optical Kerr effect. By applying this method, we generated multiple LME magnetic states from a single sample and successfully estimated its material composition. Our findings suggest that ML emphasizes not the global domain structures that are readily perceived by humans but the more subtle local domain structures that are often overlooked. Adopting this approach could potentially facilitate the estimation of magnetic parameters from any state observed in experiments, streamlining experimental processes in spintronics.

Biomechanical characterization of the passive porcine stomach

The complex mechanics of the gastric wall facilitates the main digestive tasks of the stomach. However, the interplay between the mechanical properties of the stomach, its microstructure, and its vital functions is not yet fully understood. Importantly, the pig animal model is widely used in biomedical research for preliminary or ethically prohibited studies of the human digestion system. Therefore, this study aims to thoroughly characterize the mechanical behavior and microstructure of the porcine stomach. For this purpose, multiple quasi-static mechanical tests were carried out with three different loading modes, i.e., planar biaxial extension, radial compression, and simple shear. Stress-relaxation tests complemented the quasi-static experiments to evaluate the deformation and strain-dependent viscoelastic properties. Each experiment was conducted on specimens of the complete stomach wall and two separate layers, mucosa and muscularis, from each of the three gastric regions, i.e., fundus, body, and antrum. The significant preconditioning effects and the considerable regional and layer-specific differences in the tissue response were analyzed. Furthermore, the mechanical experiments were complemented with histology to examine the influence of the microstructural composition on the macrostructural mechanical response and vice versa. Importantly, the shear tests showed lower stresses in the complete wall compared to the single layers which the loose network of submucosal collagen might explain. Also, the stratum arrangement of the muscularis might explain mechanical anisotropy during tensile tests. This study shows that gastric tissue is characterized by a highly heterogeneous microstructure with regional variations in layer composition reflecting not only functional differences but also diverse mechanical behavior. Statement of SignificanceUnfortunately, only few experimental data on gastric tissue are available for an adequate material parameter and model estimation. The present study therefore combines layer- and region-specific stomach wall mechanics obtained under multiple loading conditions with histological insights into the heterogeneous microstructure. On the one hand, the extensive data sets of this study expand our understanding of the interplay between gastric mechanics, motility and functionality, which could help to identify and treat associated pathologies. On the other hand, such data sets are of high relevance for the constitutive modeling of stomach tissue, and its application in the field of medical engineering, e.g., in the development of surgical staplers and the improvement of bariatric surgical interventions.

In Vivo Material Properties of Human Common Carotid Arteries: Trends and Sex Differences.

In vivo estimation of material properties of arterial tissue can provide essential insights into the development and progression of cardiovascular diseases. Furthermore, these properties can be used as an input to finite element simulations of potential medical treatments. This study uses non-invasively measured pressure, diameter and wall thickness of human common carotid arteries (CCAs) acquired in 103 healthy subjects. A non-linear optimization was performed to estimate material parameters of two different constitutive models: a phenomenological, isotropic model and a structural, anisotropic model. The effect of age, sex, body mass index and blood pressure on the parameters was investigated. Although both material models were able to model in vivo arterial behaviour, the structural model provided more realistic results in the supra-physiological domain. The phenomenological model predicted very high deformations for pressures above the systolic level. However, the phenomenological model has fewer parameters that were shown to be more robust. This is an advantage when only the physiological domain is of interest. The effect of stiffening with age, BMI and blood pressure was present for women, but not always for men. In general, sex had the biggest effect on the mechanical properties of CCAs. Stiffening trends with age, BMI and blood pressure were present but not very strong. The intersubject variability was high. Therefore, it can be concluded that finding a representative set of parameters for a certain age or BMI group would be very challenging. Instead, for purposes of patient-specific modelling of surgical procedures, we currently advise the use of patient-specific parameters.

Cohesive Zone Modelling and the Fracture Process of Cement-Based Composites

Computational modelling of quasi-brittle fracture in cement-based composites needs to cover both i) the damage caused by micro-fractured zones, referring to some nonlocal strain-stress relations, respecting quite different behaviour of such composites in tension and compression, and ii) the initiation and propagation of macroscopic cracks, exploiting the cohesive zone model, handled by some modification of the finite element technique, together with the discretization in time. A fundamental issue for such model is the introduction of a traction-separation (stress-displacement) relationship. This contribution pays particular attention to the design, identification and estimation of material parameters for the traction separation law suitable for predicting the deformation behaviour of samples of materials and structures.

Need for transverse strain data for fitting constitutive models of arterial tissue to uniaxial tests

The study deals with the process of estimation of material parameters from uniaxial test data of arterial tissue and focuses on the role of transverse strains. Two fitting strategies are analyzed and their impact on the predictive and descriptive capabilities of the resulting model is evaluated. The standard fitting procedure (strategy A) based on longitudinal stress-strain curves is compared with the enhanced approach (strategy B) taking also the transverse strain test data into account. The study is performed on a large set of material data adopted from literature and for a variety of constitutive models developed for fibrous soft tissues. The standard procedure (A) ignoring the transverse strain test data is found rather hazardous, leading often to unrealistic predictions of the model exhibiting auxetic behaviour. In contrast, the alternative fitting method (B) ensures a realistic strain response of the model and is proved to be superior since it does not require any significant demands of computational effort or additional testing. The results presented in this paper show that even the artificial transverse strain data (i.e., not measured during testing but generated ex post based on assumed Poisson's ratio) are much less hazardous than total disregard of the transverse strain response.

Inverse Model for Simultaneously Estimating Material Parameters and Absorption Coefficient in a Laser-Irradiated Sheet

Inverse Model for Simultaneously Estimating Material Parameters and Absorption Coefficient in a Laser-Irradiated Sheet

DiffXPBD

We present DiffXPBD, a novel and efficient analytical formulation for the differentiable position-based simulation of compliant constrained dynamics (XPBD). Our proposed method allows computation of gradients of numerous parameters with respect to a goal function simultaneously leveraging a performant simulation model. The method is efficient, thus enabling differentiable simulations of high resolution geometries and degrees of freedom (DoFs). Collisions are naturally included in the framework. Our differentiable model allows a user to easily add additional optimization variables. Every control variable gradient requires the computation of only a few partial derivatives which can be computed using automatic differentiation code. We demonstrate the efficacy of the method with examples such as elastic cloth and volumetric material parameter estimation, initial value optimization, optimizing for underlying body shape and pose by only observing the clothing, and optimizing a time-varying external force sequence to match sparse keyframe shapes at specific times. Our approach demonstrates excellent efficiency and we demonstrate this on high resolution meshes with optimizations involving over 26 million degrees of freedom. Making an existing solver differentiable requires only a few modifications and the model is compatible with both modern CPU and GPU multi-core hardware.

Effective data sampling strategies and boundary condition constraints of physics-informed neural networks for identifying material properties in solid mechanics

Material identification is critical for understanding the relationship between mechanical properties and the associated mechanical functions. However, material identification is a challenging task, especially when the characteristic of the material is highly nonlinear in nature, as is common in biological tissue. In this work, we identify unknown material properties in continuum solid mechanics via physics-informed neural networks (PINNs). To improve the accuracy and efficiency of PINNs, we develop efficient strategies to nonuniformly sample observational data. We also investigate different approaches to enforce Dirichlet-type boundary conditions (BCs) as soft or hard constraints. Finally, we apply the proposed methods to a diverse set of time-dependent and time-independent solid mechanic examples that span linear elastic and hyperelastic material space. The estimated material parameters achieve relative errors of less than 1%. As such, this work is relevant to diverse applications, including optimizing structural integrity and developing novel materials.

Determining large-strain metal plasticity parameters using in situ measurements of plastic flow past a wedge

We present a novel approach to determine the constitutive properties of metals under large plastic strains and strain rates that otherwise are difficult to access using conventional materials testing methods. The approach exploits large-strain plastic flow past a sharp wedge, coupled with high-speed photography and image velocimetry to capture the underlying plastic flow dynamics. The inverse problem of estimating material parameters from the flow field is solved using an iterative optimization procedure that minimizes the gap between internal and external plastic work. A major advantage of the method is that it neither makes any assumptions about the flow nor requires computational simulations. To counter the problem of non-unique parameter estimates, we propose a parameterization scheme that takes advantage of the functional form of the constitutive model and reformulates the problem into a more tractable form to identify plasticity parameters uniquely. We present studies to illustrate the principle of the method with two materials with widely different plastic flow characteristics: copper (strain hardening) and a lead-free solder alloy (rate sensitive and deformation history dependent). The results demonstrate the efficacy of the method in reliably determining the material parameters under high strain/strain rate conditions of relevance to a range of practical engineering problems.

Photothermal NDE of UD/Epoxy-Based Carbon Fibre Reinforced Laminates for Quantitative Porosity Analysis

High strength and low density make epoxy-based CFRP a highly interesting construction material for the aerospace manufacturing industry. Porosity represents an unavoidable defect and significantly weakens strength values dominated by the matrix. To evaluate the quality of safety-relevant components, non-destructive evaluation and thus the characterization of porous structures is indispensable. Pulsed thermography represents a fast, large-area and non-contact testing method that enables efficient estimation of material parameters. In this work, the authors demonstrate the quantitative estimation of porosity by pulsed thermography on a multi-axial laminate fabricated from unidirectional Prepregs for the first time. The characteristic, extensive expansion of the pores in fiber direction, is addressed by the 3D microstructure characterization of Cone beam X-ray computed tomography data. Hence, the application of effective medium theories and thus the model based porosity estimation is enabled. After the investigation of the effect of pore expansion on the effective thermal diffusivity in 3D finite element simulations, the quantitative photothermal porosity estimation on a sample with a global volume porosity of Phi =1.51% is demonstrated. The accuracy of this fast and non-contact method for porosity estimation with pulsed thermography (Delta Phi =0.63%) is comparable to the standard ultrasonic method. Consequently, an efficient estimation of porosity for large, complex shaped UD/Epoxy composite components is enabled.

Material Property Characterization and Parameter Estimation of Thermoelectric Generator by Using a Master–Slave Strategy Based on Metaheuristics Techniques

Thermoelectric generators (TEGs) have gained significant interest as a sustainable energy source, due to their ability to convert thermal energy into electrical energy through the Seebeck effect. However, the power output of TEGs is highly dependent on the thermoelectric material properties and operational conditions. Accurate modeling and parameter estimation are essential for optimizing and designing TEGs, as well as for integrating them into smart grids to meet fluctuating energy demands. This work examines the challenges of accurate modeling and parameter estimation of TEGs and explores various optimization metaheuristics techniques to find TEGs parameters in real applications from experimental conditions. The paper stresses the importance of determining the properties of TEGs with precision and using parameter estimation as a technique for determining the optimal values for parameters in a TEG mathematical model that represent the actual behavior of a thermoelectric module. This methodological approach can improve TEG performance and aid in efficient energy supply and demand management, thus reducing the reliance on traditional fossil fuel-based power generation.

Inverse material parameter estimation of patient-specific finite element models at the carotid bifurcation: The impact of excluding the zero-pressure configuration and residual stress.

The carotid bifurcation experiences a complex loading environment due to its anatomical structure. Previous in-vivo material parameter estimation methods often use simplified model geometries, isotropic hyperelastic constitutive equations or neglect key aspects of the vessel, such as the zero-pressure configuration or residual stress, all of which have independently been shown to alter the stress environment of the vessel wall. Characterizing the location of high stress in the vessel wall has often been proposed as a potential indicator of structural weakness. However, excluding the afore-mentioned zero-pressure configuration, residual stress and patient-specific material parameters can lead to an incorrect estimation of the true stress values observed, meaning that stress alone as a risk indicator of rupture is insufficient. In this study, we investigate how the estimated material parameters and overall stress distributions in geometries of carotid bifurcations, extracted from in-vivo MR images, alter with the inclusion of the zero-pressure configuration and residual stress. This approach consists of the following steps: (1) geometry segmentation and hexahedral meshing from in-vivo magnetic resonance images (MRI) at two known phases; (2) computation of the zero-pressure configuration and the associated residual stresses; (3) minimization of an objective function built on the difference between the stress states of an "almost true" stress field at two known phases and a "deformed" stress field by altering the input material parameters to determine patient-specific material properties; and (4) comparison of the stress distributions throughout these carotid bifurcations for all cases with estimated material parameters. This numerical approach provides insights into the need for estimation of both the zero-pressure configuration and residual stress for accurate material property estimation and stress analysis for the carotid bifurcation, establishing the reliability of stress as a rupture risk metric.

Layer-Specific Damage Modeling of Porcine Large Intestine under Biaxial Tension.

The mechanical behavior of the large intestine beyond the ultimate stress has never been investigated. Stretching beyond the ultimate stress may drastically impair the tissue microstructure, which consequently weakens its healthy state functions of absorption, temporary storage, and transportation for defecation. Due to closely similar microstructure and function with humans, biaxial tensile experiments on the porcine large intestine have been performed in this study. In this paper, we report hyperelastic characterization of the large intestine based on experiments in 102 specimens. We also report the theoretical analysis of the experimental results, including an exponential damage evolution function. The fracture energies and the threshold stresses are set as damage material parameters for the longitudinal muscular, the circumferential muscular and the submucosal collagenous layers. A biaxial tensile simulation of a linear brick element has been performed to validate the applicability of the estimated material parameters. The model successfully simulates the biomechanical response of the large intestine under physiological and non-physiological loads.