arXiv subjects

David S. Kammer

Publications and source records attributed to David S. Kammer.

At least 19 recordsLinked to original sources

arXiv2026

Crack-Tip Opening as a Probe for Length-Scale Separation in Geometrically Nonlinear Solids

Soft elastic solids are highly deformable materials where fracture is driven by the complex coupling of geometric and material nonlinearities. While geometric nonlinearity (GNL) arises kinematically from the intrinsic capacity of solids to undergo large deformations, material nonlinearity stems from the constitutive behavior unique to each class of materials. Because GNL is a universal feature of all highly deformable solids, establishing its standalone impact is a prerequisite for understanding nonlinear fracture. Here, we focus on brittle soft solids to study the role of GNL alone on the near-tip fields of a static crack under mode I plane-strain conditions, providing a canonical baseline for integrating material nonlinearities in future investigations. By utilizing a compressible St. Venant-Kirchhoff material model, we analyze crack behavior under large deformations in the absence of material nonlinearity. We propose a robust postprocessing methodology based on the crack-tip opening displacement (CTOD) profile and derive asymptotic analytical solutions. Our results reveal a distinct near-tip region where the CTOD departs from classical linear elastic predictions, transitioning into a nonlinear regime dictated by Poisson's ratio. Using a matched-asymptotics approach, we define a physical nonlinear length scale $λ_\mathrm{nl}$ that bounds this region and scales quadratically with the far-field stress intensity factor $K_I$. We show that GNL acts as an intrinsic strain-stiffening mechanism sufficient to trigger energy partitioning, effectively shielding the crack tip and imparting an apparent toughening. Ultimately, we conclude that the geometrically nonlinear material model serves as a foundational framework for the broader study of nonlinear elastic fracture mechanics.

cond-mat.soft↗

arXiv2026

The fracture resistance of elastic networks increases with the density of defects like a random walk

Disordered spring networks are a well-established model system to study fracture in a wide range of materials, from ceramics to polymer networks and mechanical metamaterials, across length scales from the atomistic to the macroscopic. A central quantity characterizing fracture is the apparent fracture energy $G^c$, which measures the resistance to the propagation of a preexisting dominant crack. While it is well established that disorder can increase $G^c$ through crack arrest by local inhomogeneities, its dependence on the degree of disorder remains poorly understood. Here, we study the effect of varying concentrations of missing bonds on crack propagation of an otherwise perfect two-dimensional triangular network of springs. For a given network with a fixed concentration of missing bonds, the apparent fracture energy $G^c(a)$ increases with crack advance $a$. This behavior can be explained by mapping the effect of the missing bonds onto an equivalent local fracture energy landscape $Γ^{loc}(a)$ and applying established theories linking planar crack arrest with fluctuations in $Γ^{loc}(a)$. For increasing fraction of missing bonds $ν$, the standard deviation of the fluctuations of $Γ^{loc}$ increases with $\sqrtν$, which we explain by considering a random-walk-like superposition of perturbations caused by individual missing bonds. We demonstrate that as a consequence of crack arrest by fluctuations in $Γ^{loc}$, the average $G^c(a)$ follows the same $\sqrtν$ scaling. Furthermore, we observe that the probability density of $Γ^{loc}$ has an exponential tail leading to a logarithmic increase of $G^c(a)$ with crack advance $a$. Our results quantitatively link microstructural disorder to macroscopic fracture energy and paves the way for quantitative predictions of the fracture energy in a wide variety of materials.

cond-mat.soft↗

arXiv2026

Element-deletion-enhanced digital image correlation for automated crack detection and tracking in lattice materials

Architected materials can exhibit remarkable combinations of stiffness, strength, and toughness, yet their application is currently limited by an incomplete understanding of how cracks initiate and propagate through their discrete architecture. Elucidating the mechanisms that underpin these processes is challenging because lattice failure is governed by highly localized deformations of slender beams, which fall outside the resolution and assumptions of optical methods developed for continuum solids, such as digital image correlation (DIC). Thus, characterizing crack propagation within lattice materials requires measurement strategies capable of resolving lattice-scale deformations while accounting for both the intrinsic discreteness of lattice architectures and the progressive formation of material discontinuities during failure. This work introduces a global DIC framework tailored to architected materials, in which the correlation problem is solved directly on the lattice mesh and damaged elements are automatically removed during the analyses. Damage detection, which relies on a data-driven residual criterion, enables the robust tracking of localized deformation and crack-tip motion under different testing conditions. The method provides physically consistent displacement field measurements on the evolving intact lattice topology and resolves the crack path over time. Validations on 3D-printed regular and imperfect triangular lattices under mode-I loading demonstrate that the approach accurately captures both damage initiation and crack propagation. Furthermore, we demonstrate that identifying damaged elements provides an estimate of the critical failure strain, which can be used directly in numerical models or adopted as an alternative element-deletion threshold in DIC analyses.

cond-mat.soft↗

arXiv2026

A versatile FEM framework with native GPU scalability via globally-applied AD

Energy-based finite-element formulations provide a unified framework for describing complex physical systems in computational mechanics. In these energy-based methods, the governing equations can be obtained directly by considering the derivatives of a single global energy functional. While Automatic Differentiation (AD) can be used to automate the generation of these derivatives, current frameworks face a clear trade-off based primarily on the scale upon which the AD method is applied. Globally applied AD offers high expressivity but cannot currently be scaled to large problems. Locally applied AD scales well through traditional assembly methods, but the variety of physics and couplings that the framework can easily represent is more limited than the global approach. Here, we introduce an energy-centric framework tatva (https://github.com/smec-ethz/tatva) that defines the physics of a problem as a single global functional and applies AD globally to generate residual and tangent operators. By leveraging Jacobian-vector products for matrix-free solvers and coloring-based sparse differentiation for materializing sparse tangent stiffness matrices when needed, our flexible design scales linearly with the problem size on GPUs. We demonstrate that our framework can handle large problems (with millions of degrees of freedom) without memory exhaustion. Additionally, it offers a unified, fully differentiable methodology that can address a wide range of problems, including multi-point constraints, mixed-dimensional coupling, and the incorporation of neural networks, while maintaining high performance and scalability on modern GPU architectures.

math.NA↗

arXiv2026

How Geometry Tames Disorder in Lattice Fracture

We investigate the fracture behavior of pre-cracked triangular beam-lattices whose elements have failure stresses drawn from a Weibull distribution. Through a statistical analysis and numerical simulations, we identify and verify the existence of three distinct failure regimes: (i) disorder is effectively suppressed, (ii) disorder manifests locally near the crack tip, modifying the crack morphology, and (iii) disorder manifests globally, leading to initially diffuse failure. Our model naturally reveals the key parameters governing this behavior: the Weibull modulus, quantifying the spread in failure thresholds, and a geometric quantity termed the Slenderness Ratio. We also reproduce the disorder-induced toughening reported in previous experimental and numerical studies, further demonstrating that its manifestation depends non-monotonically on disorder. Crucially, our results indicate that this toughening cannot be simply connected to the amount of damage in the lattice, challenging interpretations that attribute increased fracture energy solely to enhanced crack tortuosity or diffuse failure. Overall, our results establish geometry as a powerful control parameter for regulating how disorder is expressed during fracture in beam-lattices, with broader implications for the disorder-induced toughening in engineered materials.

cond-mat.mtrl-sci↗

arXiv2025

Disordered origins, deterministic outcomes: How the architecture of elastic networks imprints relaxed structure and mechanics

This work targets the influence of disorder on the relaxed structure and macroscopic mechanical properties of elastic networks. We construct network classes of different types of disorder (length, topology and stiffness), which are subsequently equilibrated in a finite kinematics setting. Relaxed network structures are distinct among network classes, which opens the path towards exploiting easily accessible experimental measures as a way of inferring further microstructural details.

cond-mat.soft↗

arXiv2025

Breaking better: How imperfections increase fracture resistance in architected lattices

Fracture behavior in architected materials can be influenced by heterogeneities, yet the mechanisms by which imperfections affect crack propagation remain poorly understood. In this study, we introduce well-controlled, localized defects in the form of isolated missing struts to evaluate their impact on crack growth in brittle lattice specimens. Using mechanical testing combined with digital image correlation (DIC), we track crack propagation and identify failure processes at the scale of individual lattice cells. While the imperfections do not alter the location of crack initiation or the peak load, they consistently lead to an increase in work to failure when the crack path is tortuous or crack bridging occurs. These findings demonstrate how small, targeted modifications to an otherwise regular lattice can significantly influence fracture resistance in brittle architected materials.

cond-mat.soft↗

arXiv2025

Less is more: removing a single bond increases the toughness of elastic networks

We investigate how the removal of a single bond affects the fracture behavior of triangular spring networks, whereby we systematically vary the position of the removed bond. Our simulations show that removing the bond has two contrasting effects on the fracture energy for initiation of crack propagation and on the fracture energy for failure of the entire network. A single missing bond can either lower or raise the initiation fracture energy, depending on its placement relative to the crack tip. In contrast, the failure fracture energy is always equal to or greater than that of a perfect network. For most initial placements of the missing bond, the crack path remains straight, and the increased failure fracture energy results from arrest at the point of maximum local fracture resistance. When the crack deviates from a straight path, we observe an even higher fracture energy, which we attribute primarily to crack bridging. This additional toughening mechanism becomes active only at low failure strains of the springs; at higher failure strains, the crack path tends to remain straight. Altogether, our results demonstrate that even a single bond removal can significantly enhance toughness, offering fundamental insights into the role of defects in polymer networks and informing the design of tough architected materials.

cond-mat.soft↗

arXiv2025

Contact point geometry governs structural build-up at rest in Portland cement-limestone blends

The early stiffening of fresh cement paste plays a key role in shaping and stability during casting and 3D printing. In Portland cement systems, this phenomenon arises from the formation of calcium-silicate-hydrate (C-S-H), which stiffens grain-to-grain contacts. However, the role of powder characteristics such as particle size and morphology remains poorly understood. Here, we vary the fineness and grain shape by blending Portland cement with either coarse or fine limestone, leveraging the affinity of C-S-H to nucleate on limestone surfaces. By coupling calorimetry and rheometry, we relate the amount of formed hydration products to the increase in stiffness, and show that the mechanism of contact stiffening through C-S-H formation remains unchanged with limestone addition. Nevertheless, the rate of stiffening varies across blends. We find that these rates correlate with a characteristic length scale that captures particle size and shape. These results demonstrate that early stiffening depends not only on the amount of hydration products formed, but also on the geometry of the contacts where these products form, offering a framework for understanding more complex systems such as limestone-calcined clay cements.

cond-mat.soft↗

arXiv2025

Elasticity of bidisperse attractive particle systems

Bidisperse particle systems are common in both natural and engineered materials, and it is known to influence packing, flow, and stability. However, their direct effect on elastic properties, particularly in systems with attractive interactions, remains poorly understood. Gaining insight into this relationship is important for designing soft particle-based materials with desired mechanical response. In this work, we study how particle size ratio and composition affect the shear modulus of attractive particle systems. Using coarse-grained molecular simulations, we analyze systems composed of two particle sizes at fixed total packing fraction and find that the shear modulus increases systematically with bidispersity. To explain this behavior, we develop two asymptotic models following limiting cases: one where a percolated network of large particles is stiffened by small particles, and another where a small-particle network is modified by embedded large particles. Both models yield closed-form expressions that capture the qualitative trends observed in simulations, including the dependence of shear modulus on size ratio and relative volume fraction. Our results demonstrate that bidispersity can enhance elastic stiffness through microstructural effects, independently of overall density, offering a simple strategy to design particle-based materials with tunable mechanical properties.

cond-mat.soft↗

arXiv2025

Learning Physics-Consistent Material Behavior from Dynamic Displacements

Accurately modeling the mechanical behavior of materials is crucial for numerous engineering applications. The quality of these models depends directly on the accuracy of the constitutive law that defines the stress-strain relation. However, discovering these constitutive material laws remains a significant challenge, in particular when only material deformation data is available. To address this challenge, unsupervised machine learning methods have been proposed to learn the constitutive law from deformation data. Nonetheless, existing approaches have several limitations: they either fail to ensure that the learned constitutive relations are consistent with physical principles, or they rely on boundary force data for training which are unavailable in many in-situ scenarios. Here, we introduce a machine learning approach to learn physics-consistent constitutive relations solely from material deformation without boundary force information. This is achieved by considering a dynamic formulation rather than static equilibrium data and applying an input convex neural network (ICNN). We validate the effectiveness of the proposed method on a diverse range of hyperelastic material laws. We demonstrate that it is robust to a significant level of noise and that it converges to the ground truth with increasing data resolution. We also show that the model can be effectively trained using a displacement field from a subdomain of the test specimen and that the learned constitutive relation from one material sample is transferable to other samples with different geometries. The developed methodology provides an effective tool for discovering constitutive relations. It is, due to its design based on dynamics, particularly suited for applications to strain-rate-dependent materials and situations where constitutive laws need to be inferred from in-situ measurements without access to global force data.

cond-mat.mtrl-sci↗

arXiv2025

Navigating the Complexities of Multiple Redox State Interactions in Aqueous Systems

Numerous aqueous systems host elements in multiple redox states, with wide ranging implications such as their influence on the formation/dissolution of minerals, water toxicity, and nutrient cycling. To uncover governing mechanisms and complex chemical interactions in aqueous systems, reactive-transport models have increasingly gained importance. However, their predictive capabilities remain limited because existing approaches struggle to accurately account for the full complexities of redox reactions. Here, we develop a reactive-transport framework that leverages recent advancements in thermodynamic modelling, speciation chemistry, and redox kinetics. Distinct from traditional models, we uniquely treat redox kinetics along with transport as transient phenomena, decoupled from Gibbs free energy minimisation. Ensuring ion concentrations are governed by non-equilibrium rate laws, this approach allows predicting the tempo-spatial distribution of speciation and precipitation of species across oxidation states. We illustrate the versatility of our framework through two case studies: manganese speciation in natural waters and the fate of dissolved iron in aqueous/porous media. Our framework significantly enhances the modelling of a diverse range of redox-sensitive environments.

cond-mat.mtrl-sci↗

arXiv2024

Simplifying FFT-based methods for solid mechanics with automatic differentiation

Fast-Fourier Transform (FFT) methods have been widely used in solid mechanics to address complex homogenization problems. However, current FFT-based methods face challenges that limit their applicability to intricate material models or complex mechanical problems. These challenges include the manual implementation of constitutive laws and the use of computationally expensive and complex algorithms to couple microscale mechanisms to macroscale material behavior. Here, we incorporate automatic differentiation (AD) within the FFT framework to mitigate these challenges. We demonstrate that AD-enhanced FFT-based methods can derive stress and tangent stiffness directly from energy density functionals, facilitating the extension of FFT-based methods to more intricate material models. Additionally, automatic differentiation simplifies the calculation of homogenized tangent stiffness for microstructures with complex architectures and constitutive properties. This enhancement renders current FFT-based methods more modular, enabling them to tackle homogenization in complex multiscale systems, especially those involving multiphysics processes. Furthermore, we illustrate the use of the AD-enhanced FFT method for problems that extend beyond homogenization, such as uncertainty quantification and topology optimization where automatic differentiation simplifies the computation of sensitivities. Our work will simplify the numerical implementation of FFT-based methods for complex solid mechanics problems.

cond-mat.mtrl-sci↗

arXiv2024

The role of gouge production in the seismic behavior of rough faults: A numerical study

Fault zones mature through the accumulation of earthquakes and the wearing of contact asperities at multiple scales. This study examines how wear-induced gouge production affects the evolution of fault seismicity, focusing on earthquake nucleation, recurrence, and moment partitioning. Using 2D quasi-dynamic simulations integrating rate-and-state friction with Archard's law of wear, we model the space-time distribution of gouge and its effect on the critical slip distance. The study reveals a shift from single to multi-rupture nucleation, marked by increased foreshock activity. The recurrence interval undergoes two separate phases: an initial phase of steady increase followed by a secondary phase of unpredictable behavior. Finally, we observe a transition in the moment partitioning from faster to slower slip rates and a decrease in the moment released per cycle relative to the case where no gouge formation is simulated. This research sheds light on wear-driven mechanisms affecting fault slip behavior, offering valuable insights into how the evolution of gouge along a fault affects its seismic potential.

physics.geo-ph↗

arXiv2024

A thermo-hygro computational model to determine the factors dictating cold joint formation in 3D printed concrete

Cold joints in extruded concrete structures form once the exposed surface of a deposited filament dries prematurely and gets sequentially covered by a layer of fresh concrete. This creates a material heterogeneity which lowers the structural durability and shortens the designed service life. Many factors concurrently affect cold joint formation, yet a suitable tool for their categorization is missing. Here, we present a computational model that simulates the drying kinetics at the exposed structural surface, accounting for cement hydration and the resulting microstructural development. The model provides a time estimate for cold joint formation as a result. It allows us to assess the drying severity for a given structure's geometry, its interaction with the environment, and ambient conditions. We evaluate the assessed factors and provide generalized recommendations for cold joint mitigation.

cond-mat.soft↗

arXiv2024

Structural build-up at rest in the induction and acceleration periods of OPC

Structural build-up in fresh cement paste at rest is characterized by time evolutions of storage modulus and yield stress, which both increase linearly in time during the induction period of hydration, followed by an exponential evolution after entering the acceleration period. While it is understood that C-S-H formation at contact points between cement particles dictates build-up in the acceleration period, the mechanism in the induction period lacks consensus. Here, we provide experimental evidence that, at least in absence of admixtures, structural build-up at rest originates in both periods from the same mechanism. We couple calorimetry and oscillatory shear measurements of OPC at different w/c ratios, capturing how the storage modulus evolves with changes in cumulative heat. We obtain an exponential relation between stiffness and heat, with the same exponent in both the induction and acceleration periods. This suggests that C-S-H formation dictates build-up at rest in both periods.

cond-mat.soft↗

arXiv2024

Energy dissipation in earthquakes

Earthquakes are rupture-like processes that propagate along tectonic faults and cause seismic waves. The propagation speed and final area of the rupture, which determine an earthquake's potential impact, are directly related to the nature and quantity of the energy dissipation involved in the rupture process. Here we present the challenges associated with defining and measuring the energy dissipation in laboratory and natural earthquakes across many scales. We discuss the importance and implications of distinguishing between energy dissipation that occurs close to and far behind the rupture tip and we identify open scientific questions related to a consistent modeling framework for earthquake physics that extends beyond classical Linear Elastic Fracture Mechanics.

physics.geo-ph↗

arXiv2024

Collective Relational Inference for learning heterogeneous interactions

Interacting systems are ubiquitous in nature and engineering, ranging from particle dynamics in physics to functionally connected brain regions. These interacting systems can be modeled by graphs where edges correspond to the interactions between interactive entities. Revealing interaction laws is of fundamental importance but also particularly challenging due to underlying configurational complexities. The associated challenges become exacerbated for heterogeneous systems that are prevalent in reality, where multiple interaction types coexist simultaneously and relational inference is required. Here, we propose a novel probabilistic method for relational inference, which possesses two distinctive characteristics compared to existing methods. First, it infers the interaction types of different edges collectively by explicitly encoding the correlation among incoming interactions with a joint distribution, and second, it allows handling systems with variable topological structure over time. We evaluate the proposed methodology across several benchmark datasets and demonstrate that it outperforms existing methods in accurately inferring interaction types. We further show that when combined with known constraints, it allows us, for example, to discover physics-consistent interaction laws of particle systems. Overall the proposed model is data-efficient and generalizable to large systems when trained on smaller ones. The developed methodology constitutes a key element for understanding interacting systems and may find application in graph structure learning.

cs.LG↗