David L. McDowell

• The description of dislocation avalanching is described in the context of a Gibbs thermodynamic description of the constrained local equilibrium state of each subsystem forming the basis of the precursor dislocation-barrier reaction probability. • Avalanching is triggered by precursor dislocation segment reactions, with the power-law regime of avalanching corresponding to a plateau of degree-of-correlation of dislocation-barrier reactions that reflects a second order phase transition, first a jamming transition followed by a depinning transition. The degree-of-correlation of reactions is an important novel aspect of this framework. • Scale-free intermittent flow with universal scaling up to some maximum avalanche size is realized only in the depinning transition, with the jamming transition expressing dislocation and subsystem configuration dependent scaling exponents. • Decorrelated reactions invite spatio-temporal overlap of avalanches, delaying early stage jamming transition and leading to strain rate dependent behavior of the stress-integrated cumulative size distribution of avalanches and transient behavior often observed in small laboratory specimens. • Statistical inhomogeneity of heterogenous obstacles and dislocation sources confer more pronounced wild avalanche strain bursts to behavior of micron scale specimens. • Specific identification and linkage of the avalanche power-law scaling characteristics to kinetics of thermally activated precursor reactions are discussed for FCC, BCC and HCP crystals along with the role of decorrelated reactions, including multiplication and cross-slip. Representative experimental findings are reviewed regarding the distribution of avalanche sizes in crystals. Insight gained from mean field theory regarding universal scaling relations in the depinning transition and the influence of the dislocation jamming transition on extended criticality are addressed within a framework for nonequilibrium thermodynamics for a sequence of constrained local equilibrium states introduced by ( McDowell 2024a , b , c ) and McDowell and Liu (2025) . The concept of the degree-of-correlation of dislocation-barrier reactions plays a central role. Early-stage decorrelated dislocation multiplication processes along with cross-slip and other weak barrier reactions are argued to diminish in the jamming transition as internal stress fields develop in an extended critical state towards the depinning transition. Under depinning dominance universal scaling is realized. The progression towards increasingly correlated reactions is argued to maximize the entropy of pending reactions at each step along the nonequilibrium trajectory as a proxy assertion for maximal intrinsic entropy production associated with state transitions. In the depinning transition, dislocation avalanches of all sizes up to the maximum avalanche size established by the dissipation-weighted effective enthalpy barrier contribute to slip system shearing. Size effects and “wild to mild” transitions from submicron specimen responses up to polycrystals are interpreted in terms of scale-appropriate dislocation precursor reactions and averaging of distributed avalanching processes. Dominant effects of free surface interactions and dislocation source limitations are exerted for specimens with size below 1 μm, with jerky avalanching owing to statistical inhomogeneity and elevated stress. Increasing specimen size leads to progressive smoothing of overall stress-strain response.

This work presents a multiscale study of the uniaxial compression of Si pillars, with diameters ranging from 50 nm to 360 nm, using the Concurrent Atomistic-Continuum (CAC) method. The simulations reproduce the brittle and ductile deformation behaviors of Si pillars observed in experiments. For defect-free Si pillars compressed by a perfectly smooth flat punch with a repulsive force field to reflect an assumed rigid indenter, dislocations are nucleated from the corner of the bottom surface for pillars with diameters of 100 nm and below, while for pillars with diameters of 220 nm and above, dislocations nucleate from the top surface; multiple slip systems are activated in all pillars except for the pillar with a diameter of 50 nm. A strong size effect is thus demonstrated with regard to the nucleation of dislocations. Another key finding is the critical role of defects on the indenter surface. For a perfectly flat indenter, all the defect-free Si pillars with diameters ranging from 50 nm to 360 nm exhibit ductile deformation. By contrast, for an indenter with surface steps, all pillars with diameters of 100 nm and above deform in a brittle manner. These surface steps cause sequential nucleation of dislocations and activation of two slip systems, leading to dislocation intersection and formation of a sessile Lomer lock. Continued pileups of dislocations against the Lomer lock lead to the initiation of a crack at the intersection. The deformation mechanism underlying the crack formation is thus demonstrated. Conclusion: This study demonstrates the critical role of surface steps and pillar size in the ductile and brittle deformation in Si micropillars under uniaxial compression. Results show that surface steps promote dislocation pileup and crack initiation, leading to brittle failure. In contrast, when compressed by a flat punch, pillars exhibit ductile behavior, with dislocations nucleating and propagating without reaction or pileup.

Materials can now be designed and architectured like structural components for targeted mechanical and physical properties. Structures and microstructures should not be studied independently and their design will benefit from a multiscale approach combining nonlinear continuum mechanics approaches and physical descriptions of elasticity, viscoplasticity, phase transformations and damage of microstructures, at various scales. The aim of the workshop was to gather outstanding junior and senior researchers in the various branches of mathematics, physics and engineering sciences suited to address the question of design of materials and structures by means of multiscale discrete and continuum approaches to their constitutive behavior. Examples include atomic or macroscopic lattices, random or periodic cellular materials, smart materials like shape memory alloys, 3D woven composites, acoustic and electromagnetic metamaterials, etc. Modern continuum mechanics relies on sophisticated constitutive laws for anisotropic materials exhibiting elastoviscoplastic behavior, still a field of intense research with new mathematical concepts. In particular size-dependent properties are addressed by resorting to generalized continua such as gradient or micromorphic and phase field models. The latter are attractive for the simulation of microstructure evolution coupled with mechanics, due to thermodynamic and metallurgical processes and damage. Scale transition and homogenization methods for continuous and discrete systems are required for the determination of effective material and structural behavior. Metamaterials are architectured materials specifically designed to achieve certain propagation and dispersion properties of elastic and plastic waves. Optimization strategies for the design of optimal architectures are involved in the design process. Target functions for optimization are now based on multicriteria (stiffness, strength, thermal expansion, transport properties, anisotropy etc.).

This case study paper presents the origins, philosophy, organization, development, and contributions of the joint Penn State-Georgia Tech Center for Computational Materials Design (CCMD), a NSF Industry/University Cooperative Research Center (I/UCRC) founded in 2005. As a predecessor of and catalyst for Integrated Computational Materials Engineering (ICME), the CCMD served as a basis for coupling industry, academia, and government in advancing the state of computational materials science and mechanics across a portfolio of process-structure-property-performance relations, with emphasis on education and training of the future workforce in computational materials design.

Defects in crystals influence and control many relevant material properties. It is essential to employ multiscale modeling to understand structure and evolution of crystal defects. Most multiscale modeling schemes are hierarchical in nature, typically passing results from modeling conducted at each successive length/time scale to the next higher scale(s), with the intent to inform model parameters or instruct the form of reduced-order models. Here, we briefly review some pertinent hierarchical multiscale modeling advances for fundamentals of crystal defects.

The Peierls barrier measures the lattice resistance to dislocation glide in crystalline solids. We use the nudged elastic band (NEB) method to calculate the Peierls barriers for screw and edge dislocation glide in a face-centered cubic (FCC) metal of Ni. The minimum energy paths (MEPs) across single or sequential Peierls barriers are determined under shear loading. The NEB results show the decreasing Peierls barrier with increasing shear stress, giving the Peierls stress at which the Peierls barrier vanishes. The effects of boundary condition and system size on Peierls barriers are studied by comparing strain-and stress-controlled NEB results. Furthermore, the free-end NEB methods are applied to determine MEPs with improved computational efficiency. The NEB results are also used to evaluate the energetic driving force of dislocation glide, which is consistent with that determined from the Peach-Koehler force. The accuracy of the present NEB results based on an empirical interatomic potential is assessed by comparison with a machine-learning potential. This work demonstrates the robust and efficient quantification of Peierls barriers to dislocation glide in an FCC metal, and it lays a solid foundation for the atomistic determination of Peierls barriers in compositionally complex alloys with the FCC structure in future studies.

Abstract This paper presents a novel framework for assessing the relative accuracy of the different slip transfer criterion in modeling the constitutive response of the lamellar morphology grains in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>α</mml:mi> <mml:mo>−</mml:mo> <mml:mi>β</mml:mi> </mml:math> Titanium alloys. The main steps involved in the proposed framework include: (i) rigorous statistical evaluation of the salient morphological characteristics of the lamellar grains using image processing techniques, (ii) modeling the effects of dislocation slip transfer as additive penalties to the critical resolved shear strengths of the different slip systems in each phase, (iii) consideration of multiple geometric slip transfer criteria for the numerical evaluation of the different penalty terms, and (iv) the Bayesian calibration of the material parameters in the constitutive descriptions using spherical nanoindentation experimental data on a polycrystalline Ti-6Al-4V sample. Step (iv) described above involves the construction and refinement of a Gaussian process (GP) surrogate model for the indentation measurements, which is trained on crystal plasticity finite element simulations incorporating the constitutive descriptions selected in Steps (ii) and (iii). The GP surrogates are then combined with Markov Chain Monte Carlo sampling techniques to calibrate the parameters in the various constitutive models studied in this work. Additionally, we have computed the posterior model probabilities for all the constitutive models considered and identified the most plausible slip transfer criterion. This specific constitutive model is then utilized to present a homogenized crystal plasticity model for the lamellar morphology. The proposed framework presents a robust scale-bridging protocol for incorporating the uncertain information obtained from lower scales.

This work presents an open source, dislocation density based crystal plasticity modeling framework, $\rho$-CP. A Kocks-type thermally activated flow is used for accounting for the temperature and strain rate effects on the crystallographic shearing rate. Slip system-level mobile and immobile dislocation densities, as well slip system-level backstress, are used as internal state variables for representing the substructure evolution during plastic deformation. A fully implicit numerical integration scheme is presented for the time integration of the finite deformation plasticity model. The framework is implemented and integrated with the open source finite element solver, Multiphysics Object-Oriented Simulation Environment (MOOSE). Example applications of the model are demonstrated for predicting the anisotropic mechanical response of single and polycrystalline hcp magnesium, strain rate effects and cyclic deformation of polycrystalline fcc OFHC copper, and temperature and strain rate effects on the thermo-mechanical deformation of polycrystalline bcc tantanlum. Simulations of realistic Voronoi-tessellated microstructures as well as Electron Back Scatter Diffraction (EBSD) microstructures are demonstrated to highlight the model's ability to predict large deformation and misorientation development during plastic deformation.

This work presents an open source, dislocation density based crystal plasticity modeling framework, $ρ$-CP. A Kocks-type thermally activated flow is used for accounting for the temperature and strain rate effects on the crystallographic shearing rate. Slip system-level mobile and immobile dislocation densities, as well slip system-level backstress, are used as internal state variables for representing the substructure evolution during plastic deformation. A fully implicit numerical integration scheme is presented for the time integration of the finite deformation plasticity model. The framework is implemented and integrated with the open source finite element solver, Multiphysics Object-Oriented Simulation Environment (MOOSE). Example applications of the model are demonstrated for predicting the anisotropic mechanical response of single and polycrystalline hcp magnesium, strain rate effects and cyclic deformation of polycrystalline fcc OFHC copper, and temperature and strain rate effects on the thermo-mechanical deformation of polycrystalline bcc tantanlum. Simulations of realistic Voronoi-tessellated microstructures as well as Electron Back Scatter Diffraction (EBSD) microstructures are demonstrated to highlight the model's ability to predict large deformation and misorientation development during plastic deformation.

Pilomyxoid astrocytoma (PMA) is a rare variant of astrocytoma that is usually present in the hypothalamic and chiasmatic areas in the paediatric population. PMA shares many similar histopathological features to Pilocytic astrocytoma (PA), with some notable differences in its radiological and histopathological findings. On the contrary, PMA has been reported to behave more aggressively in its clinical progression than PA. Here, we describe a rare case of PMA in a 25-year-old female involving the temporal lobe, presenting with recurrent partial seizures. To our knowledge, this is the first reported case of PMA presenting in the temporal lobe in an adult female with an atypical location of the tumour, uncommon age group, and unusual radiological features being unique in this case report.