arXiv subjects

Curt A. Bronkhorst

Publications and source records attributed to Curt A. Bronkhorst.

12 recordsLinked to original sources

arXiv2026

SPLIT-PINN: Separable Probability Learning Technique via Physics-Informed Neural Networks for High-Dimensional Probabilistic Modeling

We present a probabilistic modeling framework for incorporating small-scale spatial heterogeneity into macroscopic descriptions of material behavior for polycrystalline metallic materials. Spatially heterogeneous material state fields are represented using probability density functions (PDFs), providing a principled statistical description of microstructural variability and state evolution across different computational polycrystalline realizations. The framework is built on the inverse identification of a probabilistic transport model, formulated as a Liouville equation with an unknown drift term. To enable accurate, stable, and interpretable inference of this drift field in high-dimensional, transport-dominated settings, we develop a Separable Probability Learning Technique via Physics-Informed Neural Networks (SPLIT-PINN). This method incorporates a marginal-correction drift decomposition, orthogonality constraints, and residual-based adaptive training to enhance well-posedness, numerical stability, and physical consistency without imposing restrictive parametric assumptions. Using SPLIT-PINN, the drift field governing the temporal evolution of joint state PDFs is inferred directly from data. After benchmark validation, the framework is applied to physical computational datasets describing the evolution of polycrystalline microstructural states, including von Mises stress, dislocation density, and equivalent plastic strain rate. The learned Liouville model, trained on a single dataset, is subsequently used in forward predictions of the temporal evolution of joint and marginal PDFs for multiple unseen polycrystal realizations. Quantitative comparisons with reference PDFs demonstrate that the proposed framework yields accurate and robust probabilistic predictions and generalizes effectively across datasets.

cond-mat.mtrl-sci↗

arXiv2026

Finite-width adiabatic shear banding and dislocation patterning in mesoscale polycrystalline aggregates

Dynamic shear banding under adiabatic conditions in a mesoscale polycrystalline aggregate is studied using a model of mesoscale dislocation mechanics and experiments. The model involves a length scale related to hardening induced by excess/polar/geometrically necessary dislocation (GND) density, and utilizes a simple classical crystal plasticity model with isotropic Voce law hardening. Simulations of statistically representative volume elements of a polycrystal determined from experimental samples are conducted. Studies in 2-d (section) and 3-d capture the experimentally observed finite-width shear bands and the formation of low-angle subgrain boundaries even in the absence of heat conduction in the model, as well as size-dependent strengthening for grain sizes from 1 to 20 $μ$m. The 2-d and large-scale 3-d simulations, the latter involving 1 million finite elements, provide access to the progressive evolution of material strength, stress state, and temperature in the course of large deformations. GND distributions accumulate at grain boundaries and form patterned structures within grain interiors, offering insight into the microstructural changes that precede failure in adiabatic shear bands. Mesh-converged, delocalized and localized plastic flow to very large deformations without softening is observed for a significant range of parameters, reflecting a competition between GND hardening and thermal softening in setting the non-softening steady state in the absence of other ductile damage mechanisms in the model.

cond-mat.mtrl-sci↗

arXiv2026

Decoupling dislocation multiplication and velocity effects in metals at extreme strain rates

The dynamic behavior of metals is governed by collective dislocation motion and interactions that strongly depend on the applied strain rate. Metals exhibit weak strain rate sensitivity (SRS) below a certain threshold, followed by a distinct SRS upturn at higher loading rates. While this upturn is typically attributed to increased glide resistance at high dislocation velocity due to mechanisms such as phonon drag, the role of strain-rate-dependent dislocation multiplication and microstructural evolution under these extreme conditions remains elusive. Here, we decouple these two strengthening effects and show that, while dislocation velocity primarily governs the SRS upturn, the hardening due to microstructure evolution depends strongly on the initial dislocation density. Our investigation of hardness evolution across ten decades of strain rates in a quenched and tempered martensitic low-carbon steel (LCS) using laser-induced projectile impact tests (LIPIT) and nanoindentation reveals SRS upturn around 10^7 1/s. By performing in situ re-indentation of the formed craters, we probe the contribution of dislocations generated during initial deformation at different strain rates. We show that while dislocation multiplication plays a negligible role in fine-grained LCS with high dislocation density, a pronounced dislocation multiplication contributes to the hardness increase in pure iron with lower initial dislocation density. Our results show that, depending on the initial microstructure of metals, dislocation multiplication significantly governs high-strain-rate plasticity, in addition to dislocation velocity effects.

cond-mat.mtrl-sci↗

arXiv2025

A Physics-Informed Variational Inference Framework for Identifying Attributions of Extreme Stress Events in Low-Grain Polycrystals

Polycrystalline metal failure often begins with stress concentration at grain boundaries. Identifying which microstructural features trigger these events is important but challenging because these extreme damage events are rare and the failure mechanisms involve multiple complex processes across scales. Most existing inference methods focus on average behavior rather than rare events, whereas standard sample-based methods are computationally expensive for high-dimensional complex systems. In this paper, we develop a new variational inference framework that integrates a recently developed computationally efficient physics-informed statistical model with extreme value statistics to significantly facilitate the identification of material failure attributions. First, we reformulate the objective to emphasize observed exceedances by incorporating extreme-value theory into the likelihood, thereby highlighting tail behavior. Second, we constrain inference via a physics-informed statistical model that characterizes microstructure-stress relationships, which uniquely provides physically consistent predictions for these rare events. Third, mixture models in a reduced latent space are developed to capture the non-Gaussian characteristics of microstructural features, allowing the identification of multiple underlying mechanisms. In both controlled and realistic experimental tests for the bicrystal configuration, the framework achieves reliable extreme-event prediction and reveals the microstructural features associated with material failure, providing physical insights for material design with uncertainty quantification.

stat.AP↗

arXiv2023

Data-Driven Statistical Reduced-Order Modeling and Quantification of Polycrystal Mechanics Leading to Porosity-Based Ductile Damage

Predicting the process of porosity-based ductile damage in polycrystalline metallic materials is an essential practical topic. Ductile damage and its precursors are represented by extreme values in stress and material state quantities, the spatial PDF of which are highly non-Gaussian with strong fat tails. Traditional deterministic forecasts using physical models often fail to capture the statistics of structural evolution during material deformation. This study proposes a data-driven statistical reduced-order modeling framework to provide a probabilistic forecast of the deformation process leading to porosity-based ductile damage, with uncertainty quantification. The framework starts with computing the time evolution of the leading moments of specific state variables from full-field polycrystal simulations. Then a sparse model identification algorithm based on causation entropy, including essential physical constraints, is used to discover the governing equations of these moments. An approximate solution of the time evolution of the PDF is obtained from the predicted moments exploiting the maximum entropy principle. Numerical experiments based on polycrystal realizations show that the model can characterize the time evolution of the non-Gaussian PDF of the von Mises stress and quantify the probability of extreme events. The learning process also reveals that the mean stress interacts with higher-order moments and extreme events in a strongly nonlinear and multiplicative fashion. In addition, the calibrated moment equations provide a reasonably accurate forecast when applied to the realizations outside the training data set, indicating the robustness of the model and the skill for extrapolation. Finally, an information-based measurement shows that the leading four moments are sufficient to characterize the crucial non-Gaussian features throughout the entire deformation history.

cond-mat.mtrl-sci↗

arXiv2021

Deformation and dislocation evolution in body-centered-cubic single- and polycrystal tantalum

A physically-informed continuum crystal plasticity model is presented to elucidate the deformation mechanisms and dislocation evolution in body-centered-cubic (bcc) tantalum widely used as a key structural material for mechanical and thermal extremes. We show our unified structural modeling framework informed by mesoscopic dislocation dynamics simulations is capable of capturing salient features of the large inelastic behavior of tantalum at quasi-static (10$^{-3}$ s$^{-1}$) to extreme strain rates (5000 s$^{-1}$) and at room temperature and higher (873K) at both single- and polycrystal levels. We also present predictive capabilities of our model for microstructural evolution in the material. To this end, we investigate the effects of dislocation interactions on slip activities, instability and strain-hardening behavior at the single crystal level. Furthermore, ex situ measurements on crystallographic texture evolution and dislocation density growth are carried out for the polycrystal tantalum specimens at increasing strains. Numerical simulation results also support that our modeling framework is capable of capturing the main features of the polycrystal behavior over a wide range of strains, strain rates and temperatures. The theoretical, experimental and numerical results at both single- and polycrystal levels provide critical insight into the underlying physical pictures for micro- and macroscopic responses and their relations in this important class of refractory bcc materials undergoing severe inelastic deformations.

cond-mat.mtrl-sci↗

arXiv2020

Thermomechanical conversion in metals: dislocation plasticity model evaluation of the Taylor-Quinney coefficient

Using a partitioned-energy thermodynamic framework which assigns energy to that of atomic configurational stored energy of cold work and kinetic-vibrational, we derive an important constraint on the Taylor-Quinney coefficient, which quantifies the fraction of plastic work that is converted into heat during plastic deformation. Associated with the two energy contributions are two separate temperatures -- the ordinary temperature for the thermal energy and the effective temperature for the configurational energy. We show that the Taylor-Quinney coefficient is a function of the thermodynamically defined effective temperature that measures the atomic configurational disorder in the material. Finite-element analysis of recently published experiments on the aluminum alloy 6016-T4 \citep{neto_2020}, using the thermodynamic dislocation theory (TDT), shows good agreement between theory and experiment for both stress-strain behavior and temporal evolution of the temperature. The simulations include both conductive and convective thermal energy loss during the experiments, and significant thermal gradients exist within the simulation results. Computed values of the differential Taylor-Quinney coefficient are also presented and suggest a value which differs between materials and increases with increasing strain.

cond-mat.mtrl-sci↗

arXiv2019

Thermodynamic theory of crystal plasticity: formulation and application to polycrystal fcc copper

We present a thermodynamic description of crystal plasticity. Our formulation is based on the Langer-Bouchbinder-Lookman thermodynamic dislocation theory (TDT), which asserts the fundamental importance of an effective temperature that describes the state of configurational disorder and therefore the dislocation density of the crystalline material. We extend the TDT description from isotropic plasticity to crystal plasticity with many slip systems. Finite-element simulations show favourable comparison with experiments on polycrystal fcc copper under uniaxial compression, tension, and simple shear. The thermodynamic theory of crystal plasticity thus provides a thermodynamically consistent and physically rigorous description of dislocation motion in crystals. We also discuss new insights about the interaction of dislocations belonging to different slip systems.

cond-mat.mtrl-sci↗

arXiv2019

Modeling Material Stress Using Integrated Gaussian Markov Random Fields

The equations of a physical constitutive model for material stress within tantalum grains were solved numerically using a tetrahedrally meshed volume. The resulting output included a scalar vonMises stress for each of the more than 94,000 tetrahedra within the finite element discretization. In this paper, we define an intricate statistical model for the spatial field of vonMises stress which uses the given grain geometry in a fundamental way. Our model relates the three-dimensional field to integrals of latent stochastic processes defined on the vertices of the one- and two-dimensional grain boundaries. An intuitive neighborhood structure of said boundary nodes suggested the use of a latent Gaussian Markov random field (GMRF). However, despite the potential for computational gains afforded by GMRFs, the integral nature of our model and the sheer number of data points pose substantial challenges for a full Bayesian analysis. To overcome these problems and encourage efficient exploration of the posterior distribution, a number of techniques are now combined: parallel computing, sparse matrix methods, and a modification of a block update strategy within the sampling routine. In addition, we use an auxiliary variables approach to accommodate the presence of outliers in the data.

stat.AP↗

arXiv2018

Strain localization and dynamic recrystallization in polycrystalline metals: thermodynamic theory and simulation framework

We describe a theoretical and computational framework for adiabatic shear banding (ASB) and dynamic recrystallization (DRX) in polycrystalline materials. The Langer-Bouchbinder-Lookman (LBL) thermodynamic theory of polycrystalline plasticity, which we recently reformulated to describe DRX via the inclusion of the grain boundary density or the grain size as an internal state variable, provides a convenient and self-consistent way to represent the viscoplastic and thermal behavior of the material, with minimal ad-hoc assumptions regarding the initiation of yielding or onset of shear banding. We implement the LBL-DRX theory in conjunction with a finite-element computational framework. Favorable comparison to experimental measurements on a top-hat AISI 316L stainless steel sample compressed with a split-Hopkinson pressure bar suggests the accuracy and usefulness of the LBL-DRX framework, and demonstrates the crucial role of DRX in strain localization.

cond-mat.mtrl-sci↗

arXiv2018

Dynamic recrystallization in adiabatic shear banding: effective-temperature model and comparison to experiments in ultrafine-grained titanium

Dynamic recrystallization (DRX) is often observed in conjunction with adiabatic shear banding (ASB) in polycrystalline materials. The recrystallized nanograins in the shear band have few dislocations compared to the material outside of the shear band. In this paper, we reformulate the recently-developed Langer-Bouchbinder-Lookman (LBL) continuum theory of polycrystalline plasticity and include the creation of grain boundaries. While the shear-banding instability emerges because thermal heating is faster than heat dissipation, recrystallization is interpreted as an entropic effect arising from the competition between dislocation creation and grain boundary formation. We show that our theory closely matches recent results in sheared ultrafine-grained titanium. The theory thus provides a thermodynamically consistent way to systematically describe the formation of shear bands and recrystallized grains therein.

cond-mat.mtrl-sci↗

arXiv2017

Anomalous Plasticity of Body-Centered-Cubic Crystals with Non-Schmid Effect

Plastic deformations in body-centered-cubic (BCC) crystals have been of critical importance in diverse engineering and manufacturing contexts across length scales. Numerous experiments and atomistic simulations on BCC crystals reveal that classical crystal plasticity models with the Schmid law are not adequate to account for abnormal plastic deformations often found in these crystals. In this paper, we address a continuum mechanical treatment of anomalous plasticity in BCC crystals exhibiting non-Schmid effects, inspired from atomistic simulations recently reported. Specifically, anomalous features of plastic flows are addressed in conjunction with a single crystal constitutive model involving two non-Schmid projection tensors widely accepted for representing non-glide components of an applied stress tensor. Further, modeling results on a representative BCC single crystal (tantalum) are presented and compared to experimental data at a range of low temperatures to provide physical insight into deformation mechanisms in these crystals with non-Schmid effects.

cond-mat.mtrl-sci↗