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arXiv2026

Data-Driven Discovery of Composition-Dependent Constitutive Models for Hyperelasticity and Viscoelasticity of Digital Materials

Digital materials fabricated by multi-material 3D printing are designed as controlled mixtures of stiff and compliant constituents, yielding effective responses that span more than an order of magnitude in apparent stiffness and exhibit strongly nonlinear, composition-dependent, and rate-dependent dissipative behavior. Classical finite-strain viscoelastic models represent such behavior with closed-form strain energy functions for equilibrium and non-equilibrium stresses as well as evolution of internal variables, which may limit flexibility when a single constitutive model is expected to generalize across materials and loading rates. Here, we present a data-driven multi-material constitutive modeling framework that generalizes a formulation by Bergström and Boyce. The proposed framework retains the structure of the classical model, namely multiplicative kinematics, invariant-based strain-energy functions, and a scalar dissipative evolution law directed along the normalized nonequilibrium deviatoric stress. For the equilibrium branch, the data-driven discovery framework either directly predicts closed-form model parameters as functions of composition or automatically constructs a polyconvex strain-energy function using neural ordinary differential equations (NODEs). The nonequilibrium branch kinetics are learned similarly, either by directly identifying closed-form parameters across compositions or by using appropriately constrained artificial neural networks. Using multi-rate uniaxial compression data across multiple material compositions, we show that the proposed formulation captures rate-dependent stiffness and hysteresis across compositions while preserving thermodynamic consistency.

cs.AI↗

arXiv2026

Data Driven Equation Discovery for Phase-Ordering Dynamics : From Allen Cahn to the Ising Model

Data-driven discovery of governing equations from spatiotemporal data offers a promising route to obtaining coarse-grained descriptions of complex dynamical systems. Here, we investigate the performance of PDE-SINDy for discovering phase-ordering dynamics using the Allen--Cahn equation as a benchmark and the Ising model with Glauber spin-flip dynamics as a microscopic system. We systematically analyze the effects of data availability, size of the candidate library, and noise on the efficiency of the equation discovery. We find that stability-selection PDE-SINDy can robustly identify the relevant terms in the governing dynamics even under limited or noisy data, while the recovered coefficient values are substantially more sensitive to these factors. We further show that enlarging the candidate library can strongly affect both term identification and coefficient recovery. Incorporating library bagging with stability selection reduces this sensitivity and improves the efficiency of equation discovery. For the Glauber spin flip Ising model dynamics, the resulting coarse-grained equation reproduces the characteristic phase-separation and coarsening dynamics of the underlying microscopic system. Overall, our results demonstrate the potential of PDE-SINDy for phase-ordering systems while highlighting the importance of carefully assessing the factors that influence the efficiency of equation discovery.

cond-mat.soft↗

arXiv2026

Computing stable configurations of confined smectic liquid crystals with a deep variational framework

Smectic liquid crystals are layered liquid-crystalline phases characterized by orientational order and periodic density modulation. Although their structures can be modeled using continuum theories, computing stable configurations remains challenging in complex geometries, particularly when the high-frequency density modulations associated with smectic layering should be resolved. We propose a deep variational framework (DVF) for computing these configurations within the modified Landau--de Gennes model, in which the coupled orientational and positional order parameters are represented on a regular reference domain while physical confinement is incorporated through coordinate mappings. A warmup penalty mitigates the spectral bias of neural networks toward smooth, nonlayered fields, enabling robust recovery of oscillatory smectic states. Comparisons with a neural-network baseline and finite-difference relaxation demonstrate the essential role of this penalty and the numerical stability of the resulting layered states. The DVF reproduces experimentally established smectic-A defect structures and layer morphologies across diverse confinement geometries and further predicts a chevron-like smectic-C state in a tangent-anchored sphere. Together, these results demonstrate the applicability of the DVF to computing stable smectic configurations across experimentally relevant confinement geometries and anchoring conditions.

cond-mat.soft↗

arXiv2026

Recovering molecules from coarse-grained beads: free-energy-conditioned generative backmapping across chemical space

Transferable coarse-grained (CG) force fields compress chemical space: by aggregating atoms into a reduced set of interaction beads, models such as MARTINI reduce the number of distinguishable compounds by roughly three orders of magnitude, making high-throughput screening of thermodynamic properties tractable across soft matter, with drug--membrane permeability as a well-developed example. The compression is lossy and, so far, one-way: a screen returns a combination of beads, with no established route back to the compounds it stands for. Recovering those compounds--compositional backmapping--is a one-to-many inverse map, distinct from the better-studied conformational problem of rebuilding atomic coordinates from a known mapping. Here we formulate compositional backmapping as conditional graph generation by introducing juniper, a discrete denoising diffusion model over molecular graphs conditioned on the octanol--water partition free energy $ΔG_{\mathrm{W} \mapsto \mathrm{O}}$, the principal driver of MARTINI bead type assignment and hence a proxy for bead identity. Trained on molecules of up to 9 heavy atoms mapped onto one or two beads, juniper generates molecules that are 93\% valid and 92\% unique for two-bead targets, and whose $ΔG_{\mathrm{W} \mapsto \mathrm{O}}$ distributions track the target $ΔG^{\mathrm{CG}}_{\mathrm{W} \mapsto \mathrm{O}}$ linearly ($r^{2} \geq 0.96$), departing only in the hydrophobic and hydrophilic tails. Although the model receives no chemical information beyond a single scalar, the functional groups shift systematically with the imposed free energy, from branched hydrocarbons at the apolar end to amides, imides, and isocyanates at the polar end. A bead combination flagged by a CG screen can therefore be turned into candidate molecules for atomistic study or synthesis.

physics.chem-ph↗

arXiv2026

Physics-Informed Neural Networks for Depth-Averaged Granular Avalanche Dynamics on Curved Topography

Physics-informed neural networks (PINNs) provide a mesh-free framework for solving governing equations, but their application to granular avalanche dynamics over curved terrain remains largely unexplored. This study extends a depth-averaged PINN formulation based on the Savage-Hutter equations to an exponentially curved chute with spatially varying inclination and a strain-rate-dependent Mohr-Coulomb earth-pressure closure. The model is validated against measured front- and rear-edge trajectories from a laboratory granular-avalanche experiment, with selected observations withheld from training. A staged temporal curriculum proved essential for accurate prediction, reducing the held-out trajectory error by approximately two orders of magnitude compared with training over the full time domain from the outset. Sparse-data experiments further showed that observation placement was more influential than observation number within the configurations tested. Four observations bracketing the transition from acceleration to deceleration achieved nearly the same accuracy as the eight-observation reference configuration, whereas observations clustered at early or late times performed poorly. The results demonstrate the importance of both training strategy and informative data placement when applying PINNs to granular flows over curved topography.

cond-mat.soft↗

arXiv2026

Importance and methods to control, vary, and characterize mud strength for studying locomotion

Animals and robots encounter mud at the water-land interface. Like sand, mud can stay solid or flow like a fluid. Unlike sand, the yield strength of mud at which solid-fluid transitions occur depends on not only the amount of solid relative to fluid (water in mud, air in dry sand), but also how much coarse grains and fine clay are within the solid. Despite understanding of locomotion on/within dry sand dominated by coarse grains with repulsive normal forces and friction, little is known for mud dominated by fine clay with strong cohesion. Here, we developed methods to prepare uniform mud of controlled, variable yield strength and characterize and track its drift from water evaporation. Compared to other flowable substrates, mud strength measured by upward force during penetration is weaker and can vary more, and mud sticks more during extraction to pull downward, making it more challenging for locomotion.

physics.bio-ph↗

arXiv2026

Mudskippers use tail thrusting to help crutching to move on mud of various wetness

At the water-land interface, amphibious fishes encounter wet flowable substrates made of granular solid-water mixtures, which can stay solid or flow like a fluid. As these substrates become wetter or drier, their yield strength (at which solid-fluid transition occurs) and cohesion (how sticky they are) both change, challenging locomotion. Despite substantial understanding of tetrapod locomotion on flowable substrates (mostly dry sand), we know little about how amphibious fishes cope with wet flowable substrates of various wetness. Here, we studied mudskippers on clay mud of controlled, variable wetness over the range where solid-fluid transition occurs. As mud became wetter, its strength decreased by 100-fold, leading the animal to sink deeper, with larger areas of body and fins contacting mud. By contrast, mud stuck most easily at intermediate wetness. The increased sinkage and contact and stickiness change caused more mud to stick to and pull against the animal on wetter mud. We also tested dry mud, which stuck to animal fins as its mucus dried. Despite these challenges, the mudskipper predominately used a conserved crutching gait on all except the wettest mud tested, with a modest performance reduction. When normal crutching became less effective, the animal assisted it with tail thrusting, by bending and straightening it to push downward and backward to generate additional thrust and lift, or even thrusting the tail to jump. These observations suggest that mudskipper's crutching motor program is well adapted to its native muddy substrates but inflexible, with most novelty in tail use.

physics.bio-ph↗

arXiv2026

A unified geometric design framework for kirigami structures

In recent years, kirigami metamaterials have been widely studied and applied in science and engineering. While various two- and three-dimensional kirigami design methods have been developed, most of them are only applicable to a limited class of kirigami structures. In this work, we develop a unified framework for kirigami design that encompasses a wide range of 2D-to-2D, 2D-to-3D, and 3D-to-3D shape-morphing effects, as well as additional geometric and physical properties such as compact reconfigurability and rigid deployability. In particular, by reformulating the design task as a length-based constrained optimization problem and solving it simultaneously for multiple target states of the kirigami structure, our unified design framework enables greater design flexibility and stronger theoretical support. Experimental results with a wide range of shape-morphing effects are presented to demonstrate the effectiveness of our framework. We further present a rigorous theoretical analysis of several key aspects of kirigami design, covering inertia transposition, aspect-ratio law, and angle defects, thereby elucidating important design rules and limitations. Altogether, our work paves a new way for the design of shape-morphing mechanical metamaterials.

cond-mat.soft↗

arXiv2026

Unraveling the PFAS helix: A statistical approach

The extreme persistence of per- and polyfluoroalkyl substances (PFAS) in the environment is rooted in their three-dimensional molecular conformation. The helical twist adopted by perfluoroalkyl chains due to hyperconjugation involving their recalcitrant C-F bonds governs their resistance to degradation, yet a quantitative, continuous metric for helicity has remained absent. Here we introduce a data-driven framework that quantifies backbone helicity using three statistical descriptors: void-state (binary occupancy) spatial autocorrelations, local backbone principal component analysis, and persistent homology. We further validate each statistical descriptor against geometric dihedral benchmarks and DFT-calculated Vibrational Circular Dichroism (VCD) spectra. The framework is initially established on a homologous series of perfluorocarboxylic acids (FC2 through FC16) and their hydrogenated analogues, then extended across perfluorosulfonic acids, fluorotelomer alcohols, polyfluoroalkyl hexanoic acid analogues, and longer-chain PFOA and PFOS analogues. Agreement between statistical, geometric, and spectroscopic definitions of helicity is established for PFCAs and extended to structurally distinct subfamilies, including PFOA analogues of varying fluorine content and perfluorosulfonic acids, demonstrating that the descriptors are robust to changes in headgroup chemistry and fluorine substitution pattern. The framework provides a chemistry-agnostic toolset for incorporating backbone conformation into predictive models of PFAS environmental fate and degradation reactivity.

physics.chem-ph↗

arXiv2026

Electrospun Fields: 3D Nano-Fiber Material Computation as Design Method

We present a robotic electrospinning platform and design method for depositing nanofiber membranes onto non-planar, three-dimensional conductive geometries. Conventional electrospinning relies on fixed emitters and planar grounded collectors, which restricts deposition to flat substrates: on concave geometries, field shielding prevents fibers from reaching recessed regions, and material bridges across elevated features instead. We address this with a custom end-effector integrated with a six-axis UR20 arm. The tool carries a localized stepper-driven syringe pump that maintains consistent polymer flow independent of orientation, and routes high-voltage DC (up to 25 kV) directly to a robot-mounted needle, turning the arm into a mobile emitter with full kinematic control over position, orientation, working distance, and traversal velocity. Toolpaths that continuously reorient the emitter along surface normals give access to concave topologies unreachable by fixed-axis systems. We characterize the resulting deposition behavior in two parts. A catalog of four bio-compatible polymer systems (PEO, PVA, keratin-PEO, silk-PEO) establishes the operating envelope, reporting deposition speed, jet stability, fiber size, alignment, and durability for each. A taxonomy of 3D-printed conductive scaffolds spanning geometric primitives, hybrid compositions, and square, triangular, and hexagonal lattices links collector geometry to fiber alignment, density, and cross-void bridging. We also demonstrate programmable grounding, in which selectively energized pins in an array steer deposition without changing physical geometry. Assembly instructions and toolpath-generation code are released as an open-source repository.

cond-mat.soft↗