Materials Theory最新文献

A constrained Variational Crack Element Method (VCEM) for interacting crack networks in two-dimensional isotropic elasticity is formulated. The method is variational at the level of crack equilibrium for fixed geometry, while crack advance is treated separately using near-tip propagation criteria. Cracks are represented by distributed Burgers-density fields, preserving the exact crack-tip singular structure within a unified energy-minimization framework. The governing equations follow from a constrained variational problem in which equality constraints enforce Burgers-vector closure and displacement single-valuedness at junctions, while inequality constraints enforce crack-face non-penetration. The resulting system has a Karush–Kuhn–Tucker (KKT) saddle-point structure. Crack geometry is represented by graph-based polylines composed of polarity-carrying half-crack elements, allowing the treatment of tips, kinks, branching, and multi-degree junctions. Elastostatic interactions are expressed through tensor kernels derived from Kelvin’s fundamental solutions, and both strong (collocation) and weak (Galerkin/least-squares) traction enforcement are implemented. The framework provides a sharp-interface, computationally scalable approach for equilibrium and criterion-based evolution of complex crack networks in finite or infinite domains.

This study introduces a novel three-dimensional graph neural network (GNN) based finite element (FE) surrogate model designed to emulate full-field tensile simulations of aluminum alloy 6DR1. The proposed model captures the spatial and temporal evolution of mechanical fields while drastically reducing computational cost. Compared with conventional Abaqus simulations, the GNN achieves a speed-up of nearly four orders of magnitude (≈10,000 × faster), enabling real-time parameter identification essential for digital twin applications in manufacturing. The surrogate accurately reproduces both local and global mechanical responses, including stress, strain, and force–displacement behavior, across the entire deformation history. Sensitivity analyses reveal the most influential material parameters governing the model’s predictive behavior, while uncertainty quantification defines the parameter space in which GNN predictions remain reliable. The presented framework establishes an efficient and physically consistent approach for accelerated parameter calibration and opens a pathway toward the integration of GNN-based surrogates into real-time digital twins for process monitoring and optimization.

Over the past twenty-five years, I have explored the application of molecular dynamics simulations and lattice dynamics calculations for determining phonon properties and thermal conductivity. Motivated by conversations with my group members and colleagues, I share insights about aspects of these methods that can be overlooked or misunderstood. For molecular dynamics, I focus on how to set up the simulations and apply the Green-Kubo method. For lattice dynamics, I outline the calculation workflow and highlight key decisions. I offer thoughts about the benefits of calculations and how they can be compared to experiments. I share highlights, mistakes, and missteps from my group’s work. I conclude with reflections on the past, present, and future of nanoscale thermal transport modeling.

Machine learning (ML) is transforming fracture mechanics research by offering unprecedented capabilities for analyzing high-throughput, multi-modal, and multi-fidelity data. Recent work has generated large amounts of new fracture data through experiments and simulations and extracted useful insights from them. However, the vast body of fracture data accumulated over the past century remains largely untapped, primarily because it is scattered throughout the literature without systematic organization. Our central hypothesis is that these historical data contain valuable insights that can be unlocked using ML. To test this hypothesis, we present a case study on crack arrest fracture toughness, a critical yet poorly understood property in fracture mechanics. We compiled a comprehensive dataset of crack arrest toughness for a wide range of structural steels through a thorough literature review and analyzed it using neural network (NN)-based methods, including feature-importance assessment and high-dimensional regression. Our analysis shows that elements such as carbon and manganese exert a stronger influence on crack arrest toughness than others such as copper, and that temperature also plays a critical role. We further developed an NN-based model capable of predicting crack arrest toughness from these factors with an error of 11.8%. This study demonstrates the substantial opportunities for advancing fracture mechanics by mining the vast body of historical literature data, while also highlighting the challenges associated with their fragmented and multi-fidelity nature.

Void growth plays a central role in ductile fracture, yet the specific mechanisms that control this remain obscure. Classical models, such as those proposed by Rice and Tracey in 1969, are able to capture average rates of void growth, but cannot capture the heterogeneity of individual void growth. Building on recent work, the present study employs laboratory-based diffraction contrast tomography and in-situ x-ray computed tomography to investigate the effect of grain structure and other microstructural factors on void growth in an Al-2219 alloy. Crystal plasticity finite element (CP-FE) modeling is used alongside experimental data to evaluate the contributions of local mechanical states, grain orientation, grain size, and neighboring microstructural features. No strong linear relationships are found with any of the considered descriptors and void growth rate. Potential complex nonlinear relationships are explored with the use of a random forest regression model, which identifies initial void volume, void aspect ratio, local normal stress state, local shear stress state, and local equivalent plastic strain (EQPS) as features that most improve void growth rate predictions. The combination of these analyses suggests that these features should be prioritized to improve models of void growth.

Crystal plasticity primarily arises from the motion and interactions of dislocations. Consequently, one may expect a continuum theory of plasticity to emerge as a statistical continuum theory of interacting ‘particles’ – where these particles are, in fact, dislocations, i.e., extended and flexible moving curves. Due to the long range elastic interactions between dislocations, pair correlations play an important role for the emerging plastic characteristics of crystals. For these systems correlations arise not only from the relative positions of different dislocations (pair correlations) but also from non-trivial self correlations that reflect the geometry of individual dislocations as connected lines. The self correlations reflect interactions between segments of the same dislocation, which, for example, yield a tendency for dislocations to be straight. These self correlations need to be understood because they usually dominate numerically obtained correlation data from dislocation distributions.

In this paper, we derive analytical expressions for self correlations in various hypothetical dislocation configurations which can serve as approximations for more general dislocation systems. The most general configurations we analyse are uncorrelated dislocations that form circular loops with a given distribution of radii. Additionally, we also derive pair correlations in various dipole-like configurations of dislocation pairs.

Furthermore, we examine the radius distribution obtained from discrete dislocation dynamics simulations and show that these match radius distributions obtained from a maximum information entropy ansatz considering dislocation curvature. Our results suggest that to obtain a physically meaningful radius distribution within this maximum information entropy framework, an additional curvature-related variable must be introduced – one that has not yet been considered in continuum dislocation dynamics.

Existing phase field (diffuse interface) models for void evolution in solids are not quantitative, in the sense that they do not capture the physics of the sharp interface counterpart. In this work, we introduce a thermodynamically consistent, quantitative phase field model for void evolution in crystalline solids under irradiation. This model considers both vacancies and self-interstitials in the description of void evolution. Unique to this model is fixing the evolution of the non-conserved order parameter describing void surface dynamics by two contributions associated with the interactions of vacancies and interstitials with the void surface by incorporating two mobility parameters in the corresponding Allen–Cahn equation. Asymptotic matching of the phase field model with the sharp-interface theory fixed the two Allen–Cahn mobility parameters in terms of the kinetics of the point defect-surface reactions. The Landau and the gradient coefficients in the free energy construction of the system in its diffuse-interface description are fixed using thermodynamic arguments in terms of the interfacial energy and diffuse interface width. With all the parameters in the phase model clearly expressed in terms of the sharp interface counterparts, we have a novel, quantitative phase field formalism for void evolution in the presence of point defects. To validate this new formalism, several simple test cases were carried out showing the void evolution under simple defect supersaturation scenarios.

The mean nearest-neighbor distance is an important clustering/ordering metric in quantitative spatial analysis of microstructures; especially for materials containing particles or voids. Nearest-neighbor distance (d_NN) distributions in three-dimensional (3D), random-sequential-addition, uniform, hard-sphere, computer-generated patterns have been studied for volume fractions from 0.0001 to 0.35. Normal distributions can well fit these d_NN distributions and they provide insight into the study of nearest-neighbor (NN) metrics such as means, medians, and modes. Furthermore, we report on the development of an estimator for the 3D mean d_NN (μ_NN) based upon stochastic tiling. Stochastic tiling models involve random rotations of polyhedral space-filling tiles which allows the calculation of the probabilities for d_NN distributions. Solutions are presented for volume fractions ≈0.10 to the cubic theoretical maximum of ≈0.52. Extrapolating solutions to lower volume fractions also provides reasonable estimates. There is good agreement between the μ_NN estimates compared to the computer-generated random patterns. In the volume fraction region where deviations from these estimates exist, there is an apparent transition in the relationship between the fitted normal distribution means and the NN distance means at a volume fraction ≈0.25. Suggestions for areas of future research are highlighted.

Graphical Abstract

A personal, but quite general viewpoint on current morphogenic plasticity developments is given by elaborating on dislocation patterning and deformation bands with an eye on Nasr Ghoniem’s pioneering contributions to material instabilities. It is based on the gradient approach advocated by the author in the early 1980s and subsequently pursued by him and his co-workers, as well as other leading scientists, including Ghoniem himself. Since the physical origin of plastic flow in metals is due to the existence of dislocations, a brief discussion on the removal of classical elasticity singularities for this type of line defects is provided based on a gradient modification of Hooke’s law and its extension to also include fractional and fractal effects. The article will thus first briefly revisit early efforts on pattern-forming instabilities in plasticity and then discuss the need for combined gradient-stochastic models to capture plastic heterogeneity phenomena at small scales. It will continue with listing easy-to-use fractional/fractal dislocation solutions for potential implementation to respective dislocation-based computer simulations and conclude with a few remarks on possible extensions of the Laplacian-based gradient approach described herein to other multiscale/multiphysics phenomena. The last topic is an open issue that has not been pursued as yet in the material physics and mechanics community. Even though some of our new unpublished results are preliminary and sporadically shared with the community in conference presentations available at the internet, it is hoped that they can still inspire a much-needed collective collaboration and more elaborate interdisciplinary studies in the near future.

The investigation of strain hardening in metals is complex, with the outcome depending on experimental conditions, that may involve microstructural history, temperature and loading rate. Hardening is commonly measured, after mechanical processing, through controlled mechanical testing, in ways that either distinguish elastic (stress) from total deformation measurements, or by identifying plastic slip contributions. In this paper, we conjecture that hardening effects can be unraveled through statistical analysis of total strain fluctuations during the evolution sequence of profiles, measured in-situ, through digital image correlation. In particular, we hypothesize that the work hardening exponent is related, through a power-law relationship, to a particular exponent arising from principal component analysis. We demonstrate a scaling analysis for synthetic data produced by widely applicable crystal plasticity models for polycrystalline solids.

Graphical Abstract