arXiv subjects

Fatemeh Pourahmadian

Publications and source records attributed to Fatemeh Pourahmadian.

18 recordsLinked to original sources

arXiv2025

Calibrating a Finite-strain Phase-field Model of Fracture for Bonded Granular Materials with Uncertainty Quantification

To study the mechanical behavior of mock high explosives, an experimental and simulation program was developed to calibrate, with quantified uncertainty, a material model of the bonded granular material Idoxuridine and nitroplasticized Estane-5703. This paper reports on the efficacy of such a framework as a generalizable methodology for calibrating material models against experimental data with uncertainty quantification. Additionally, this paper studies the effect of two manufacturing temperatures and three initial granular configurations on the unconfined compressive behavior of the resulting bonded granular materials. In each of these cases, the same calibration framework was used; in that, hundreds of high-fidelity direct numerical simulations using a new, GPU-enabled, high-performance finite element method software, Ratel, were run to calibrate a finite-strain phase-field fracture model against experimental data. It was found that manufacturing temperature influenced the elastic response of the mock high explosives, with higher temperatures yielding a stiffer response. By contrast, it was found that the initial configuration of the grains had a negligible impact on the overall behavior of the mock high explosives, though it remains possible that local damage accumulation within the specimens could be altered by the initial configurations. Overall, the calibration framework was successful at creating well-calibrated models, showing its usefulness as an engineering and scientific tool.

physics.comp-ph↗

arXiv2025

Deep regularization networks for inverse problems with noisy operators

A supervised learning approach is proposed for regularization of large inverse problems where the main operator is built from noisy data. This is germane to superresolution imaging via the sampling indicators of the inverse scattering theory. We aim to accelerate the spatiotemporal regularization process for this class of inverse problems to enable real-time imaging. In this approach, a neural operator maps each pattern on the right-hand side of the scattering equation to its affiliated regularization parameter. The network is trained in two steps which entails: (1) training on low-resolution regularization maps furnished by the Morozov discrepancy principle with nonoptimal thresholds, and (2) optimizing network predictions through minimization of the Tikhonov loss function regulated by the validation loss. Step 2 allows for tailoring of the approximate maps of Step 1 toward construction of higher quality images. This approach enables direct learning from test data and dispenses with the need for a-priori knowledge of the optimal regularization maps. The network, trained on low-resolution data, quickly generates dense regularization maps for high-resolution imaging. We highlight the importance of the training loss function on the network's generalizability. In particular, we demonstrate that networks informed by the logic of discrepancy principle lead to images of higher contrast. In this case, the training process involves many-objective optimization. We propose a new method to adaptively select the appropriate loss weights during training without requiring an additional optimization process. The proposed approach is synthetically examined for imaging damage evolution in an elastic plate. The results indicate that the discrepancy-informed regularization networks not only accelerate the imaging process, but also remarkably enhance the image quality in complex environments.

math.NA↗

arXiv2025

Micropolar elastoplasticity using a fast Fourier transform-based solver

This work presents a micromechanical spectral formulation for obtaining the full-field and homogenized response of elastoplastic micropolar composites. A closed-form radial-return mapping is derived from thermodynamics-based micropolar elastoplastic constitutive equations to determine the increment of plastic strain necessary to return the generalized stress state to the yield surface, and the algorithm implementation is verified using the method of numerically manufactured solutions. Then, size-dependent material response and micro-plasticity are shown as features that may be efficiently simulated in this micropolar elastoplastic framework. The computational efficiency of the formulation enables the generation of large datasets in reasonable computing times.

cs.CE↗

arXiv2024

Laser Ultrasonic Imaging via the Time Domain Linear Sampling Method

This study investigates the imaging ability of the time-domain linear sampling method (TLSM) when applied to laser ultrasonic (LU) tomography of subsurface defects from limited-aperture measurements. In this vein, the TLSM indicator and it spectral counterpart known as the multifrequency LSM are formulated within the context of LU testing. The affiliated imaging functionals are then computed using synthetic and experimental data germane to LU inspection of aluminum alloy specimens with manufactured defects. Hyperparameters of inversion are computationally analyzed. We demonstrate using synthetic data that the TLSM indicator has the unique ability to recover weak (or hard-to-reach) scatterers and has the potential to generate higher quality images compared to LSM. Provided high-SNR measurements, this advantage may be preserved in reconstructions from LU test data.

eess.SP↗

arXiv2024

Network scaling and scale-driven loss balancing for intelligent poroelastography

A deep learning framework is developed for multiscale characterization of poroelastic media from full waveform data which is known as poroelastography. Special attention is paid to heterogeneous environments whose multiphase properties may drastically change across several scales. Described in space-frequency, the data takes the form of focal solid displacement and pore pressure fields in various neighborhoods furnished either by reconstruction from remote data or direct measurements depending on the application. The objective is to simultaneously recover the six hydromechanical properties germane to Biot equations and their spatial distribution in a robust and efficient manner. Two major challenges impede direct application of existing state-of-the-art techniques for this purpose: (i) the sought-for properties belong to vastly different and potentially uncertain scales, and~(ii) the loss function is multi-objective and multi-scale (both in terms of its individual components and the total loss). To help bridge the gap, we propose the idea of \emph{network scaling} where the neural property maps are constructed by unit shape functions composed into a scaling layer. In this model, the unknown network parameters (weights and biases) remain of O(1) during training. This forms the basis for explicit scaling of the loss components and their derivatives with respect to the network parameters. Thereby, we propose the physics-based \emph{dynamic scaling} approach for adaptive loss balancing. The idea is first presented in a generic form for multi-physics and multi-scale PDE systems, and then applied through a set of numerical experiments to poroelastography. The results are presented along with reconstructions by way of gradient normalization (GradNorm) and Softmax adaptive weights (SoftAdapt) for loss balancing. A comparative analysis of the methods and corresponding results is provided.

eess.SP↗

arXiv2024

Ensemble WSINDy for Data Driven Discovery of Governing Equations from Laser-based Full-field Measurements

This work leverages laser vibrometry and the weak form of the sparse identification of nonlinear dynamics (WSINDy) for partial differential equations to learn macroscale governing equations from full-field experimental data. In the experiments, two beam-like specimens, one aluminum and one IDOX/Estane composite, are subjected to shear wave excitation in the low frequency regime and the response is measured in the form of particle velocity on the specimen surface. The WSINDy for PDEs algorithm is applied to the resulting spatio-temporal data to discover the effective dynamics of the specimens from a family of potential PDEs. The discovered PDE is of the recognizable Euler-Bernoulli beam model form, from which the Young's modulus for the two materials are estimated. An ensemble version of the WSINDy algorithm is also used which results in information about the uncertainty in the PDE coefficients and Young's moduli. The discovered PDEs are also simulated with a finite element code to compare against the experimental data with reasonable accuracy. Using full-field experimental data and WSINDy together is a powerful non-destructive approach for learning unknown governing equations and gaining insights about mechanical systems in the dynamic regime.

math.NA↗

arXiv2023

Ultrasonic imaging in highly heterogeneous backgrounds

This work formally investigates the differential evolution indicators as a tool for ultrasonic tracking of elastic transformation and fracturing in randomly heterogeneous solids. Within the framework of periodic sensing, it is assumed that the background contains (i) a multiply connected set of viscoelastic, anisotropic, and piecewise homogeneous inclusions, and (ii) a union of possibly disjoint fractures and pores. The support, material properties, and interfacial condition of scatterers in (i) and (ii) are unknown, while elastic constants of the matrix are provided. The domain undergoes progressive variations of arbitrary chemo-mechanical origins such that its geometric configuration and elastic properties at future times are distinct. At every sensing step $t_\circ, t_1, \ldots,$ multi-modal incidents are generated by a set of boundary excitations, and the resulting scattered fields are captured over the observation surface. The test data are then used to construct a sequence of wavefront densities by solving the spectral scattering equation. The incident fields affiliated with distinct pairs of obtained wavefronts are analyzed over the stationary and evolving scatterers for a suit of geometric and elastic evolution scenarios entailing both interfacial and volumetric transformations. The main theorem establishes the invariance of pertinent incident fields at the loci of static fractures and inclusions between a given pair of time steps, while certifying variation of the same fields over the modified regions. These results furnish a basis for theoretical justification of differential evolution indicators for imaging in complex composites which, in turn, enable the exclusive tomography of evolution in a background endowed with many unknown features.

math.AP↗

arXiv2023

Deep learning for full-field ultrasonic characterization

This study takes advantage of recent advances in machine learning to establish a physics-based data analytic platform for distributed reconstruction of mechanical properties in layered components from full waveform data. In this vein, two logics, namely the direct inversion and physics-informed neural networks (PINNs), are explored. The direct inversion entails three steps: (i) spectral denoising and differentiation of the full-field data, (ii) building appropriate neural maps to approximate the profile of unknown physical and regularization parameters on their respective domains, and (iii) simultaneous training of the neural networks by minimizing the Tikhonov-regularized PDE loss using data from (i). PINNs furnish efficient surrogate models of complex systems with predictive capabilities via multitask learning where the field variables are modeled by neural maps endowed with (scaler or distributed) auxiliary parameters such as physical unknowns and loss function weights. PINNs are then trained by minimizing a measure of data misfit subject to the underlying physical laws as constraints. In this study, to facilitate learning from ultrasonic data, the PINNs loss adopts (a) wavenumber-dependent Sobolev norms to compute the data misfit, and (b) non-adaptive weights in a specific scaling framework to naturally balance the loss objectives by leveraging the form of PDEs germane to elastic-wave propagation. Both paradigms are examined via synthetic and laboratory test data. In the latter case, the reconstructions are performed at multiple frequencies and the results are verified by a set of complementary experiments highlighting the importance of verification and validation in data-driven modeling.

math.NA↗

arXiv2022

Time- vs. frequency- domain inverse elastic scattering: Theory and experiment

This study formally adapts the time-domain linear sampling method (TLSM) for ultrasonic imaging of stationary and evolving fractures in safety-critical components. The TLSM indicator is then applied to the laboratory test data of [22, 18] and the obtained reconstructions are compared to their frequency-domain counterparts. The results highlight the unique capability of the time-domain imaging functional for high-fidelity tracking of evolving damage, and its relative robustness to sparse and reduced aperture data at moderate noise levels. A comparative analysis of the TLSM images against the multifrequency LSM maps of [22] further reveals that thanks to the full-waveform inversion in time and space, the TLSM generates images of remarkably higher quality with the same dataset.

math.NA↗

arXiv2021

Poroelastic near-field inverse scattering

A multiphysics data analytic platform is established for imaging poroelastic interfaces of finite permeability (e.g., hydraulic fractures) from elastic waveforms and/or acoustic pore pressure measurements. This is accomplished through recent advances in design of non-iterative sampling methods to inverse scattering. The direct problem is formulated via the Biot equations in the frequency domain where a network of discontinuities is illuminated by a set of total body forces and fluid volumetric sources, while monitoring the induced (acoustic and elastic) scattered waves in an arbitrary near-field configuration. A thin-layer approximation is deployed to capture the rough and multiphase nature of interfaces whose spatially varying hydro-mechanical properties are a priori unknown. In this setting, the well-posedness analysis of the forward problem yields the admissibility conditions for the contact parameters. In light of which, the poroelastic scattering operator and its first and second factorizations are introduced and their mathematical properties are carefully examined. It is shown that the non-selfadjoint nature of the Biot system leads to an intrinsically asymmetric factorization of the scattering operator which may be symmetrized at certain limits. These results furnish a robust framework for systematic design of regularized and convex cost functionals whose minimizers underpin the multiphysics imaging indicators. The proposed solution is synthetically implemented with application to spatiotemporal reconstruction of hydraulic fracture networks via deep-well measurements.

math.NA↗

arXiv2020

Laboratory application of sampling approaches to inverse scattering

This study presents an experimental investigation of the recently established generalized linear sampling method (GLSM) for non-destructive evaluation of damage in elastic materials. To this end, ultrasonic shear waves are generated in a prismatic slab of charcoal granite featuring a discontinuity interface induced by the three-point bending (3PB). The interaction of probing waves with the 3PB-induced damage gives rise to transient velocity responses measured on the sample's boundary by a 3D scanning laser Doppler vibrometer. Thus obtained waveform data are then carefully processed to retrieve the associated spectra of scattered displacement fields. On deploying multifrequency sensory data, the GLSM indicators are computed and their counterparts associated with the classical linear sampling method (LSM) for comparative analysis. Verified with in-situ observations, the GLSM map successfully exposes the support of hidden scatterers in the specimen with a remarkable clarity and resolution compared to its predecessor LSM. It is further shown that the GLSM remains robust for sparse and partial-aperture data inversion, thanks to its rigorous formulation. For completeness, the one-sided reconstruction by both indicators is investigated.

physics.app-ph↗

arXiv2020

Experimental validation of differential evolution indicators for ultrasonic imaging in unknown backgrounds

The differential evolution indicators, recently introduced for imaging mechanical evolution in highly scattering solids, is examined in a laboratory setting with the focus on spatiotemporal tracking of an advancing damage zone in an elastic specimen. To this end, a prismatic slab of charcoal granite is quasi-statically fractured in the three-point-bending (3PB) configuration, while ultrasonic shear waves are periodically generated in the sample at certain time steps $t_κ$, $κ= \circ, 1, 2, ..., 4$. The interaction of probing waves with the propagating damage give rise to transient velocity responses measured on the plate's boundary by a 3D scanning laser Doppler vibrometer. Thus obtained sensory data are then carefully processed to retrieve the associated spectra of scattered displacement fields $v^κ$ at every $t_κ$. On deploying consecutive pairs of multi-frequency data $(v^κ, v^{κ+1})$, the differential indicators are computed exposing the progress of 3PB-induced damage in the specimen. Verified with in-situ observations, each indicator map successfully reconstructs (a) the support of newborn fractures, and (b) the loci of discontinuities in the process zone that undergo interfacial evolution in the designated timeframe $[t_κ\,\,\, t_{κ+1}]$. Further, it is shown that the evolution indicators help better understand the damage mechanism e.g., by shining light on the fragmented nature of induced cracks and their coalescence. For completeness, data inversion via reduced and partial-aperture data is investigated, including the one-sided reconstruction.

physics.app-ph↗

arXiv2019

Differential tomography of micromechanical evolution in elastic materials of unknown micro/macrostructure

Differential evolution indicators are introduced for 3D spatiotemporal imaging of micromechanical processes in complex materials where progressive variations due to manufacturing and/or aging are housed in a highly scattering background of a-priori unknown or uncertain structure. In this vein, a three-tier imaging platform is established where: (1) the domain is periodically (or continuously) subject to illumination and sensing in an arbitrary configuration; (2) sequential sets of measured data are deployed to distill segment-wise scattering signatures of the domain's internal structure through carefully constructed, non-iterative solutions to the scattering equation; and (3) the resulting solution sequence is then used to rigorously construct an imaging functional carrying appropriate invariance with respect to the unknown stationary components of the background e.g., pre-existing interstitial boundaries and bubbles. This gives birth to differential indicators that specifically recover the 3D support of micromechanical evolution within a network of unknown scatterers. The direct scattering problem is formulated in the frequency domain where the background is comprised of a random distribution of monolithic fragments. The constituents are connected via highly heterogeneous interfaces of unknown elasticity and dissipation which are subject to spatiotemporal evolution. The support of internal boundaries are sequentially illuminated by a set of incident waves and thus-induced scattered fields are captured over a generic observation surface. The performance of the proposed imaging indicator is illustrated through a set of numerical experiments for spatiotemporal reconstruction of progressive damage zones featuring randomly distributed cracks and bubbles.

math.NA↗

arXiv2018

Real-time imaging of interfacial damage in layered composites

A theoretical platform is developed for active elastic-wave sensing of (stationary and advancing) fractures along bi-material interfaces in layered composites. Damaged contact surfaces are characterized by a heterogeneous distribution of (elastic) stiffness $\boldsymbol{K}$ which is a-priori unknown. The proposed imaging functional takes advantage of sequential wavefield measurements for non-iterative and concurrent reconstruction of multiple fractures in heterogeneous domains, with an exceptional spatial resolution and with minimal sensitivity to measurement errors and uncertain elasticity of damage zones. This is accomplished through adaptation of the $F_\sharp$-factorization method (FM) applied to elastodynamic wavefields in a sensing sequence i.e. a measurement campaign performed before and after the formation (or evolution) of interfacial fractures. The direct scattering problem is formulated in the frequency domain where the damage support is illuminated by a set of incident P- and S-waves, and thus-induced scattered waves are monitored at the far field. In this setting, the germane mixed reciprocity principle is introduced, and $F_\sharp$-factorization of the differential scattering operator is rigorously established for composite backgrounds. These results lead to the development of an FM-based fracture indicator whose affiliated cost functional is inherently convex, thus, its minimizer can be computed without iterations. This attribute coupled with the reduced sampling space, proposed in this work, remarkably expedite the data inversion process. The performance of proposed imaging functional is demonstrated by a set of numerical experiments.

math.NA↗

arXiv2017

On the elastic anatomy of heterogeneous fractures in rock

This study examines the feasibility of the full-field ultrasonic characterization of fractures in rock. To this end, a slab-like specimen of granite is subjected to in-plane, O(10$^4$Hz) excitation while monitoring the induced 2D wavefield by a Scanning Laser Doppler Vibrometer (SLDV) with sub-centimeter spatial resolution. Upon suitable filtering and interpolation, the observed wavefield is verified to conform with the plane-stress approximation and used to: (i) compute the maps of elastic modulus in the specimen (before and after fracturing) via a rudimentary application of the principle of elastography; (ii) reconstruct the fracture geometry; (iii) expose the fracture's primal (traction-displacement jump) contact behavior, and (iv) identify its profiles of shear and normal specific stiffness. Through the use of full-field ultrasonic data, the approach provides an unobscured, high-resolution insight into the fracture's contact behavior, foreshadowing in-depth laboratory exploration of interdependencies between the fracture geometry, aperture, interphase properties, and its seismic characteristics.

physics.geo-ph↗

arXiv2016

A synoptic approach to the seismic sensing of heterogeneous fractures: from geometric reconstruction to interfacial characterization

A non-iterative waveform sensing approach is proposed toward (i) geometric reconstruction of penetrable fractures, and (ii) quantitative identification of their heterogeneous contact condition by seismic i.e. elastic waves. To this end, the fracture support $Γ$ (which may be non-planar and unconnected) is first recovered without prior knowledge of the interfacial condition by way of the recently established approaches to non-iterative waveform tomography of heterogeneous fractures, e.g. the methods of generalized linear sampling and topological sensitivity. Given suitable approximation $\breveΓ$ of the fracture geometry, the jump in the displacement field across $\breveΓ$ i.e. the fracture opening displacement (FOD) profile is computed from remote sensory data via a regularized inversion of the boundary integral representation mapping the FOD to remote observations of the scattered field. Thus obtained FOD is then used as input for solving the traction boundary integral equation on $\breveΓ$ for the unknown (linearized) contact parameters. In this study, linear and possibly dissipative interactions between the two faces of a fracture are parameterized in terms of a symmetric, complex-valued matrix $\boldsymbol{K}(\boldsymbolξ)$ collecting the normal, shear, and mixed-mode coefficients of specific stiffness. To facilitate the high-fidelity inversion for $\boldsymbol{K}(\boldsymbolξ)$, a 3-step regularization algorithm is devised to minimize the errors stemming from the inexact geometric reconstruction and FOD recovery. The performance of the inverse solution is illustrated by a set of numerical experiments where a cylindrical fracture, endowed with two example patterns of specific stiffness coefficients, is illuminated by plane waves and reconstructed in terms of its geometry and heterogeneous (dissipative) contact condition.

math.NA↗

arXiv2016

Generalized linear sampling method for elastic-wave sensing of heterogeneous fractures

A theoretical foundation is developed for active seismic reconstruction of fractures endowed with spatially-varying interfacial condition (e.g.~partially-closed fractures, hydraulic fractures). The proposed indicator functional carries a superior localization property with no significant sensitivity to the fracture's contact condition, measurement errors, and illumination frequency. This is accomplished through the paradigm of the $F_\sharp$-factorization technique and the recently developed Generalized Linear Sampling Method (GLSM) applied to elastodynamics. The direct scattering problem is formulated in the frequency domain where the fracture surface is illuminated by a set of incident plane waves, while monitoring the induced scattered field in the form of (elastic) far-field patterns. The analysis of the well-posedness of the forward problem leads to an admissibility condition on the fracture's (linearized) contact parameters. This in turn contributes toward establishing the applicability of the $F_\sharp$-factorization method, and consequently aids the formulation of a convex GLSM cost functional whose minimizer can be computed without iterations. Such minimizer is then used to construct a robust fracture indicator function, whose performance is illustrated through a set of numerical experiments. For completeness, the results of the GLSM reconstruction are compared to those obtained by the classical linear sampling method (LSM).

physics.geo-ph↗

arXiv2015

On the elastic-wave imaging and characterization of fractures with specific stiffness

The concept of topological sensitivity (TS) is extended to enable simultaneous 3D reconstruction of fractures with unknown boundary condition and characterization of their interface by way of elastic waves. Interactions between the two surfaces of a fracture, due to e.g. presence of asperities, fluid, or proppant, are described via the Schoenberg's linear slip model. The proposed TS sensing platform is formulated in the frequency domain, and entails point-wise interrogation of the subsurface volume by infinitesimal fissures endowed with interfacial stiffness. For completeness, the featured elastic polarization tensor - central to the TS formula - is mathematically described in terms of the shear and normal specific stiffness (ks,kn) of a vanishing fracture. Simulations demonstrate that, irrespective of the contact condition between the faces of a hidden fracture, the TS (used as a waveform imaging tool) is capable of reconstructing its geometry and identifying the normal vector to the fracture surface without iterations. On the basis of such geometrical information, it is further shown via asymptotic analysis -- assuming "low frequency" elastic-wave illumination, that by certain choices of (ks,kn) characterizing the trial (infinitesimal) fracture, the ratio between the shear and normal specific stiffness along the surface of a nearly-panar (finite) fracture can be qualitatively identified. This, in turn, provides a valuable insight into the interfacial condition of a fracture at virtually no surcharge -- beyond the computational effort required for its imaging. The proposed developments are integrated into a computational platform based on a regularized boundary integral equation (BIE) method for 3D elastodynamics, and illustrated via a set of numerical experiments.

cond-mat.mtrl-sci↗