arXiv subjects

Dennis M. Kochmann

Publications and source records attributed to Dennis M. Kochmann.

At least 19 recordsLinked to original sources

arXiv2026

An electromechanically coupled multiphase-field model with generalized kinetic relations for ferroelectrics

Classical phase-field models typically use the Allen--Cahn evolution law to model interface motion as a consequence of energy-gradient descent. This implies a linear kinetic relation between the velocity of an interface (e.g., a domain wall in a ferroelectric) and its driving force. When nonlinear kinetic relations are to be modeled, as commonly found in ferroelectric ceramics, an alternative evolution law and hence an alternative model is needed. Here, we propose an electromechanically (stress-driven) coupled multiphase-field framework with a general kinetic formulation, which integrates a prescribed kinetic relation directly into the evolution law. We show that this model correctly evolves domain walls with the assigned nonlinear kinetics, e.g., of mixed exponential-power law type, following the so-called Merz--Stadler law. The multiphase formulation further enables distinct kinetic relations and interfacial energies to be assigned to different order-parameter pairs, which reflects the distinguishable properties of the different types of ferroelectric domain walls. The proposed framework is broadly applicable for simulating kinetic relations in materials with applications beyond ferroelectrics.

cond-mat.mtrl-sci↗

arXiv2026

Global DIC-based sample-detector geometry refinement for accurate EBSD indexing

Electron backscatter diffraction is a powerful tool for mapping crystallographic microstructures. However, the primary crux to improving orientation accuracy and applying the technique to challenging materials lies in the correct calibration of the sample-detector geometry. Many approaches have aimed at overcoming this barrier through various pattern center calibration strategies, but the pattern center only defines part of the sample-detector geometry. Here, we present a DIC-based geometry refinement method that obtains a single map-consistent sample-detector geometry, refining both the pattern center and sample/detector angles. We effectively decouple the local orientation changes from the global geometry effects on the Kikuchi patterns by calculating the consistent map-wide simulated-to-experimental pattern shifts associated with global geometry parameter errors. Using single-crystal silicon and barium titanate (a material possessing six pseudosymmetric variants) as model materials, we demonstrate improved map-wide orientation consistency and more robust discrimination of pseudosymmetric variants than the Nelder-Mead and Differential Evolution optimization strategies.

cond-mat.mtrl-sci↗

arXiv2026

Algebraic Language Models for Inverse Design of Metamaterials via Diffusion Transformers

Generative machine learning models have revolutionized material discovery by capturing complex structure-property relationships, yet extending these approaches to the inverse design of three-dimensional metamaterials remains limited by computational complexity and underexplored design spaces due to the lack of expressive representations. Here we present DiffuMeta, a generative framework integrating diffusion transformers with an algebraic language representation, encoding three-dimensional geometries as mathematical sentences. This compact, unified parameterization spans diverse topologies, enabling the direct application of transformers to structural design. DiffuMeta leverages diffusion models to generate new shell structures with precisely targeted stress-strain responses under large deformations, accounting for buckling and contact while addressing the inherent one-to-many mapping by producing diverse solutions. Uniquely, our approach enables simultaneous control over multiple mechanical objectives, including linear and nonlinear responses beyond training domains. Experimental validation of fabricated structures further confirms the efficacy of our approach for accelerated design of metamaterials and structures with tailored properties.

cs.CE↗

arXiv2026

Microscale architected materials for elastic wave guiding: Fabrication and dynamic characterization across length and time scales

We present an experimental protocol for the fabrication and characterization of scalable microarchitected elastic waveguides. Using silicon microfabrication techniques, we develop free-standing 2D truss-based architected waveguides with a maximum diameter of 80 mm, unit cells size of 100 micrometer, and minimum beam width of 5 micrometer, thus achieving scale separation. To characterize elastic wave propagation, we introduce a custom-built scanning optical pump-probe experiment that enables contactless excitation of elastic wave modes and full spatio-temporal reconstruction of wave propagation across hundreds of unit cells with sub-unit cell resolution. Results on periodic architectures show excellent agreement with finite element simulations and equivalent experimental data at larger length scales. Motivated by scalable computational inverse design, we fabricate a specific example of a spatially graded waveguide and demonstrate its ability to guide elastic waves along an arbitrary pre-designed path.

physics.app-ph↗

arXiv2026

Additive Manufacturing-Facilitated Blow Molding for Functional Thin-Walled Polymeric Structures

Thin-walled structures capable of large, reversible deformation are key to multistable structures, origami, kirigami, and soft robotics. However, conventional fabrication techniques, including 3D printing, casting, and laser cutting, suffer from poor surface quality, low durability, complex processing steps, and restricted geometric freedom, hindering the repeatable production of thin-walled, continuous structures. Here, an additive manufacturing-facilitated blow molding (AM-BM) approach is introduced, combining the design flexibility of additive manufacturing with the robustness of blow molding. By replacing metal molds with 3D-printed resin ones, AM-BM enables rapid, low-cost fabrication of thin-walled polymeric components with tunable geometry and controllable wall thickness across diverse thermoplastic materials. The thickness control allows thin-walled components to function either as rigid load-bearing elements or as compliant hinges that permit reversible deformation. The versatility of AM-BM is demonstrated through representative examples: multistable structures with geometry-controlled buckling and rich reconfigurability; origami and kirigami structures with extensive design freedom, scalable complexity, and uniform mechanical properties; and soft actuators and robots with ultrahigh load-to-weight ratios, rapid response, and scalable design. Altogether, AM-BM provides an efficient and versatile method for creating thin-walled structures that combine geometric freedom, mechanical functionality, and scalable production.

cond-mat.soft↗

arXiv2026

Ferroelectric polarization mapping through pseudosymmetry-sensitive EBSD reindexing

Ferroelectric materials exhibit a switchable, spontaneous polarization at the unit cell level--an attractive property utilized in many emerging technologies including, among others, high-density memory storage, low-power transistors, and high-speed fiber optic communication. Understanding the local polarization switching behavior, through domain nucleation and evolution, is critical to advancing these technologies and requires characterization of the local domain microstructure. However, in application-relevant polycrystalline materials exhibiting a distribution of grain orientations, a direct mapping of the polarization direction in three dimensions has remained inaccessible using conventional experimental approaches. Here, taking barium titanate single crystals and lead zirconium titanate polycrystals as our bulk model systems, we map the local polarization directions using a new electron backscatter diffraction indexing technique based on simulated pattern-matching. Through improved pre-processing techniques (including optimized pattern processing, a new pseudosymmetry-sensitive neighbor pattern averaging method, and DIC-based global sample-detector geometry calibration) and a new pseudosymmetry confidence index (which considers not only pattern similarity but pattern dissimilarity trends with other domain variant patterns), we successfully distinguish between the six polarization directions, despite the challengingly small unit cell aspect ratio of the selected materials. The methods developed in this work are not only applicable to ferroelectrics but any material which exhibits close crystallographic pseudosymmetries--extending the current capabilities of EBSD.

cond-mat.mtrl-sci↗

arXiv2025

Deep learning-aided inverse design of porous metamaterials

The ultimate aim of the study is to explore the inverse design of porous metamaterials using a deep learning-based generative framework. Specifically, we develop a property-variational autoencoder (pVAE), a variational autoencoder (VAE) augmented with a regressor, to generate structured metamaterials with tailored hydraulic properties, such as porosity and permeability. While this work uses the lattice Boltzmann method (LBM) to generate intrinsic permeability tensor data for limited porous microstructures, a convolutional neural network (CNN) is trained using a bottom-up approach to predict effective hydraulic properties. This significantly reduces the computational cost compared to direct LBM simulations. The pVAE framework is trained on two datasets: a synthetic dataset of artificial porous microstructures and CT-scan images of volume elements from real open-cell foams. The encoder-decoder architecture of the VAE captures key microstructural features, mapping them into a compact and interpretable latent space for efficient structure-property exploration. The study provides a detailed analysis and interpretation of the latent space, demonstrating its role in structure-property mapping, interpolation, and inverse design. This approach facilitates the generation of new metamaterials with desired properties. The datasets and codes used in this study will be made open-access to support further research.

cs.LG↗

arXiv2025

Predicting temperature-dependent failure and transformation zones in 2D silica glass through quasistatic Gaussian Phase Packets

The athermal quasistatic (AQS) method is a powerful technique to study the mechanical behavior of disordered systems. However, its applicability is limited to temperatures near zero, where thermal activation is unlikely. In this work, we extend the AQS method to finite temperatures, based on a formulation that describes atoms as temperature-dependent Gaussian packets (GPPs) in phase space under quasistatic conditions, thus equivalent to minimum free energy conditions. This framework is used to study the effect of temperature on the onset of inelasticity and fracture in amorphous two-dimensional silica glass approaching quasistatic conditions under uniaxial tensile loading. An important characteristic of this formulation is the directional dependence of the variance of each Gaussian packet in configuration space, making this formulation an inexpensive and accurate predictor of zones prone to atomic-scale rearrangements, both in the undeformed state and (with increasing accuracy) as the deformation progresses. This method is also shown to accurately capture the thermal expansion of the disordered material. Furthermore, combining the GPP description with Metropolis sampling predicts the effect of temperature on the onset of fracture of the material, which is validated through MD simulations at strain rates as low as $10^{4}$s$^{-1}$. The presented framework therefore provides a valuable technique for studying the nonlinear mechanics of disordered materials at finite temperature and for predicting local rearrangement zones in disordered solids efficiently without the need for expensive MD simulations.

cond-mat.dis-nn↗

arXiv2025

Graded phononic metamaterials: Scalable design meets scalable microfabrication

Metamaterials are a new generation of advanced materials, exhibiting engineered microstructures that enable customized material properties not found in nature. The dynamics of metamaterials are particularly fascinating, promising the capability to guide, attenuate, and focus waves at will. Phononic metamaterials aim to manipulate mechanical waves with broad applications in acoustics, elastodynamics, and structural vibrations. A key bottleneck in the advancement of phononic metamaterials is scalability -- in design, simulation, and especially fabrication (e.g., beyond tens of unit cells per spatial dimension). We present a framework for scalable inverse design of spatially graded metamaterials for elastic wave guiding, together with a scalable microfabrication method. This framework enables the design and realization of complex waveguides including hundreds of thousands of unit cells, with the potential to extend to millions with no change in protocol. Scalable design is achieved via optimization with a ray tracing model for waves in spatially graded beam lattices. Designs are fabricated by photolithography and etching of silicon wafers to create free-standing microarchitected films. Wave guiding is demonstrated experimentally, using pulsed laser excitation and an interferometer for displacement measurements. Broadband wave guiding is demonstrated, indicating the promise of our scalable design and fabrication methods for on-chip elastic wave manipulation.

physics.app-ph↗

arXiv2025

Long-term atomistic finite-temperature substitutional diffusion

Simulating long-term mass diffusion kinetics with atomic precision is important to predict chemical and mechanical properties of alloys over time scales of engineering interest in applications, including (but not limited to) alloy heat treatment, corrosion resistance, and hydrogen embrittlement. We present a new strategy to bridge from the time scale of atomic vibrations to that of vacancy-mediated atomic hops by a combination of statistical mechanics-based Gaussian phase packets (GPP) relaxation and a nudged elastic band (NEB)-facilitated harmonic transition state theory (H-TST) time update. We validate the approach by simulating bulk self-diffusion in copper and the segregation of vacancies and magnesium to a stacking fault and a symmetric tilt grain boundary in aluminum, modeled with an embedded atom method (EAM) potential. The method correctly predicts the kinetics in bulk copper and equilibrium impurity concentrations in aluminum, in agreement with the Langmuir-Mclean solution in the dilute limit. Notably, this technique can reach realistic diffusion time scales of days, weeks, and even years in a computational time of hours, demonstrating its capability to study the long-term chemo-thermo-mechanically coupled behavior of atomic ensembles.

cond-mat.mtrl-sci↗

arXiv2025

Physics-Informed Diffusion Models

Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied data distribution are expected to adhere to specific governing equations. We present a framework that unifies generative modeling and partial differential equation fulfillment by introducing a first-principle-based loss term that enforces generated samples to fulfill the underlying physical constraints. Our approach reduces the residual error by up to two orders of magnitude compared to previous work in a fluid flow case study and outperforms task-specific frameworks in relevant metrics for structural topology optimization. We also present numerical evidence that our extended training objective acts as a natural regularization mechanism against overfitting. Our framework is simple to implement and versatile in its applicability for imposing equality and inequality constraints as well as auxiliary optimization objectives.

cs.LG↗

arXiv2024

HyperCAN: Hypernetwork-Driven Deep Parameterized Constitutive Models for Metamaterials

We introduce HyperCAN, a machine learning framework that utilizes hypernetworks to construct adaptable constitutive artificial neural networks for a wide range of beam-based metamaterials exhibiting diverse mechanical behavior under finite deformations. HyperCAN integrates an input convex network that models the nonlinear stress-strain map of a truss lattice, while ensuring adherence to fundamental mechanics principles, along with a hypernetwork that dynamically adjusts the parameters of the convex network as a function of the lattice topology and geometry. This unified framework demonstrates robust generalization in predicting the mechanical behavior of previously unseen metamaterial designs and loading scenarios well beyond the training domain. We show how HyperCAN can be integrated into multiscale simulations to accurately capture the highly nonlinear responses of large-scale truss metamaterials, closely matching fully resolved simulations while significantly reducing computational costs. This offers new efficient opportunities for the multiscale design and optimization of truss metamaterials.

cs.CE↗

arXiv2024

Stiff and Deformable Quasicrystalline Architected Materials

Architected materials achieve unique mechanical properties through precisely engineered microstructures that minimize material usage. However, a key challenge of low-density materials is balancing high stiffness with stable deformability up to large strains. Current microstructures, which employ slender elements such as thin beams and plates arranged in periodic patterns to optimize stiffness, are largely prone to instabilities, including buckling and brittle collapse at low strains. This challenge is here addressed by introducing a new class of aperiodic architected materials inspired by quasicrystalline lattices. Beam networks derived from canonical quasicrystalline patterns, such as the Penrose tiling in 2D and icosahedral quasicrystals in 3D, are shown to create stiff, stretching-dominated topologies with non-uniform force chain distributions, effectively mitigating the global instabilities observed in periodic designs. Numerical and experimental results confirm the effectiveness of these designs in combining stiffness and stable deformability at large strains, representing a significant advancement in the development of low-density metamaterials for applications requiring high impact resistance and energy absorption. Our results demonstrate the potential of deterministic quasi-periodic topologies to bridge the gap between periodic and random structures, while branching towards uncharted territory in the property space of architected materials.

cond-mat.mtrl-sci↗

arXiv2024

Atomistic-informed phase field modeling of magnesium twin growth by disconnections

The nucleation and propagation of disconnections play an essential role during twin growth. Atomistic methods can reveal such small structural features on twin facets and model their motion, yet are limited by the simulation length and time scales. Alternatively, mesoscale modeling approaches (such as the phase field method) address these constraints of atomistic simulations and can maintain atomic-level accuracy when integrated with atomic-level information. In this work, a phase field model is used to simulate the disconnection-mediated twinning, informed by molecular dynamics (MD) simulations. This work considers the specific case of the growth of $\{10\bar{1}2\}$ twin in magnesium. MD simulations are first conducted to obtain the orientation-dependent interface mobility and motion threshold, and to simulate twin embryo growth and collect facet velocities, which can be used for calibrating the continuum model. The phase field disconnections model, based on the principle of minimum dissipation potential, provides the theoretical framework. This model incorporates a nonconvex grain boundary energy, elasticity and shear coupling, and simulates disconnections as a natural emergence under the elastic driving force. The phase field model is further optimized by including the anisotropic interface mobility and motion threshold suggested by MD simulations. Results agree with MD simulations of twin embryo growth in the aspects of final twin thickness, twin shape, and twin size, as well as the kinetic behavior of twin boundaries and twin tips. The simulated twin microstructure is also consistent with experimental observations, demonstrating the fidelity of the model.

cond-mat.mtrl-sci↗

arXiv2024

Unifying the design space and optimizing linear and nonlinear truss metamaterials by generative modeling

The rise of machine learning has fueled the discovery of new materials and, especially, metamaterials--truss lattices being their most prominent class. While their tailorable properties have been explored extensively, the design of truss-based metamaterials has remained highly limited and often heuristic, due to the vast, discrete design space and the lack of a comprehensive parameterization. We here present a graph-based deep learning generative framework, which combines a variational autoencoder and a property predictor, to construct a reduced, continuous latent representation covering an enormous range of trusses. This unified latent space allows for the fast generation of new designs through simple operations (e.g., traversing the latent space or interpolating between structures). We further demonstrate an optimization framework for the inverse design of trusses with customized mechanical properties in both the linear and nonlinear regimes, including designs exhibiting exceptionally stiff, auxetic, pentamode-like, and tailored nonlinear behaviors. This generative model can predict manufacturable (and counter-intuitive) designs with extreme target properties beyond the training domain.

cs.CE↗

arXiv2024

A mixed-order quasicontinuum approach for beam-based architected materials with application to fracture

Predicting the mechanics of large structural networks, such as beam-based architected materials, requires a multiscale computational strategy that preserves information about the discrete structure while being applicable to large assemblies of struts. Especially the fracture properties of such beam lattices necessitate a two-scale modeling strategy, since the fracture toughness depends on discrete beam failure events, while the application of remote loads requires large simulation domains. As classical homogenization techniques fail in the absence of a separation of scales at the crack tip, we present a concurrent multiscale technique: a fully-nonlocal quasicontinuum (QC) multi-lattice formulation for beam networks, based on a conforming mesh. Like the original atomistic QC formulation, we maintain discrete resolution where needed (such as around a crack tip) while efficiently coarse-graining in the remaining simulation domain. A key challenge is a suitable model in the coarse-grained domain, where classical QC uses affine interpolations. This formulation fails in bending-dominated lattices, as it overconstrains the lattice by preventing bending without stretching of beams. Therefore, we here present a beam QC formulation based on mixed-order interpolation in the coarse-grained region -- combining the efficiency of linear interpolation where possible with the accuracy advantages of quadratic interpolation where needed. This results in a powerful computational framework, which, as we demonstrate through our validation and benchmark examples, overcomes the deficiencies of previous QC formulations and enables, e.g., the prediction of the fracture toughness and the diverse nature of stress distributions of stretching- and bending-dominated beam lattices in two and three dimensions.

cs.CE↗

arXiv2024

Finite-temperature grain boundary properties from quasistatic atomistics

Grain boundary (GB) properties greatly influence the mechanical, electrical, and thermal response of polycrystalline materials. Most computational studies of GB properties at finite temperatures use molecular dynamics (MD), which is computationally expensive, limited in the range of accessible timescales, and requires cumbersome techniques like thermodynamic integration to estimate free energies. This restricts the reasonable computation (without incurring excessive computational expense) of GB properties to regimes that are often unrealistic, such as zero temperature or extremely high strain rates. Consequently, there is a need for simulation methodology that avoids the timescale limitations of MD, while providing reliable estimates of GB properties. The Gaussian Phase-Packet (GPP) method is a temporal coarse-graining technique that can predict relaxed atomic structures at finite temperature in the quasistatic limit. This work applies GPP, combined with the quasiharmonic approximation for computing the free energy, to the problem of determining the free energy and shear coupling factor of grain boundaries in metals over a range of realistic temperatures. Validation is achieved by comparison to thermodynamic integration, which confirms that the presented approach captures relaxed-energy GB structures and shear coupling factors at finite temperature with a high degree of accuracy.

cond-mat.mtrl-sci↗

arXiv2023

Conformally Graded Metamaterials for Elastic Wave Guidance

Although metamaterials have been widely used for controlling elastic waves through bandgap engineering, the directed guidance of stress waves in non-periodic structures has remained a challenge. This work demonstrates that spatially graded metamaterials based on conformal mappings present a rich design space for controlling and attenuating wave motion - without the need for bandgaps. Conformal mappings transform an elementary unit cell by scaling and rotation into graded lattices with approximately geometrically similar unit cells. This self-similarity allows for control over the local wave dispersion throughout the metamaterial. As a key mechanism, it is shown that elastic waves cannot propagate through graded unit cells with significant size differences, except at low frequencies. This is exploited to create low-pass elastic wave guides, extending beyond classical bandgap engineering, since bandgaps are not required to achieve wave guiding and attenuation. Experiments confirm the low-pass elastic wave filtering capability of a planar truss metamaterial with conformal grading. Finally, a systematic design of curved metamaterial surfaces is presented, providing a flexible framework for programming low-pass attenuation and wave guiding in three dimensions.

physics.app-ph↗