arXiv subjects

L. River Spencer

Publications and source records attributed to L. River Spencer.

6 recordsLinked to original sources

arXiv2026

Mixed-Dimensional Electromechanical Coupling of Embedded Beam Networks in Soft Dielectric Composites

Soft electroactive composites can exhibit strongly architecture-dependent mechanical and electrical responses, but explicitly resolving dense fiber networks in three dimensions is computationally expensive. We develop a mixed-dimensional finite-element formulation in which electroactive fibers are represented by geometrically exact beams embedded in a deformable dielectric matrix. Unlike existing electroactive beam formulations in which the electric potential is defined directly on the beam, the embedded fibers here are driven by the three-dimensional electric field of the surrounding matrix. The matrix field is sampled along the beam centerlines and enters the beam dielectric enthalpy directly, providing two-way electromechanical coupling without introducing independent electric-potential degrees of freedom on the beams. Beam and matrix mechanics are coupled through projected mortar constraints, and the electromechanical problem is solved monolithically. We use the formulation as the microscale model in a periodic homogenization framework to compute effective stress and electric displacement. Verification studies quantify discretization and field-sampling sensitivity, followed by structured and irregular network examples that demonstrate architecture-dependent mechanical and electrical responses without body-fitted three-dimensional fiber meshes.

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arXiv2026

Bayesian Posterior Sampling for Synthetic Shape Generation of Heart Valves

Statistical shape models (SSMs) for heart valves commonly rely on principal component analysis (PCA). They are used to support downstream tasks, including \textit{in silico} modeling, morphological analysis, and interventional planning. However, PCA-based SSMs lack a mechanism for conditional shape generation, i.e., they can create non-physical shapes and perform poorly in low-data regimes (<20 shapes). To overcome these problems, we propose instead a Bayesian posterior sampling framework to generate valve shapes from a posterior estimate. The prior relies on a Gaussian mixture model with data-driven mixture modes. The likelihood estimate is obtained through a classifier trained to distinguish valid from invalid regions in the compact proper orthogonal decomposition (POD) coefficient space. We verify the framework on a model problem and validate it on parametrically constructed aortic valve datasets. Thereby, we demonstrate that our method captures multiple modes, respects decision boundaries in shape space, and outperforms PCA-based SSMs in low-data regimes. We also characterize the framework's performance as a function of dataset size, identifying where diminishing returns arise for the proposed generative shape model. Finally, we apply the framework to a cohort of ten three-dimensional transesophageal echocardiography images of adult human tricuspid valves. We first segment images to extract shapes, then generate a set of physiologically plausible new shapes. We demonstrate downstream applications for both valves, including \textit{in silico} modeling of valve mechanics and synthetic image-mask creation to augment limited datasets. The proposed approach bootstraps building image-mask datasets more efficiently than PCA-based SSMs. Although demonstrated only for the aortic and tricuspid valves, the methodology is broadly applicable to all valves.

cs.CE↗

arXiv2026

Full-Field Calibration of Coupled Thermomechanical Material Models at Finite Strain

Calibrating thermomechanical material models from experiments is challenging because deformation, temperature, and force responses are strongly coupled, while measurements are usually restricted to specimen surfaces. We present a full-field calibration framework for coupled finite-strain thermomechanical material models using boundary displacement, reaction-force data, and temperature. The forward model is formulated as a near-incompressible thermo-hyperelastic problem with thermomechanical coupling derived from a Helmholtz free energy, and the inverse problem is posed as a PDE-constrained optimization problem with weighted observation terms for the available data streams. Reduced gradients are computed with adjoint sensitivities that are obtained by automatic differentiation, enabling gradient-based calibration of nonlinear transient thermomechanical systems. The formulation is first verified on synthetic examples involving uniform thermal preconditioning and localized transient rod contact, where the ground-truth parameters are recovered from full-field measurements and force observations. The same workflow is then applied to experimental thermomechanical data by first calibrating a hyperelastic mechanical baseline from cyclic equibiaxial loading and subsequently identifying thermal expansion and directional shrinkage parameters from surface-temperature and boundary-force histories. The results demonstrate that coupled thermomechanical parameters can be inferred from experimentally accessible surface data without requiring volumetric observations.

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arXiv2026

Fully Differentiable Ultrasound Simulation Utilizing Ray-Tracing

Ultrasound imaging tasks such as calibration, inverse parameter estimation, and acquisition design require models that are physically grounded, efficient, and differentiable with respect to meaningful material and system parameters. While full-wave solvers offer high fidelity, they are often too expensive for iterative optimization, and existing ray-based methods have mostly been limited to forward simulation. In this work, we present a fully differentiable end-to-end ultrasound simulation framework based on full-path Monte Carlo ray tracing. Building on UltraRay, the method propagates gradients from image-space losses back through acoustic transport, beamforming, and post-processing, enabling gradient-based optimization over scene and acquisition parameters. The framework combines differentiable ray transport in Mitsuba 3/Dr.Jit with a custom differentiable bridge through the ultrasound image-formation pipeline. Forward examples reproduce expected geometric image features and capture more complex anatomical structures. In inverse problems, the method recovers known parameters in a simulated-reference setting and identifies effective parameters that improve agreement between simulated and experimental B-mode images in a simulation-to-real setting. Finite-difference comparisons further support the consistency of the computed gradients. Overall, this work provides a practical foundation for differentiable, physics-based ultrasound simulation and optimization.

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arXiv2026

Multiscale topology optimization of compressible and nearly incompressible anisotropic hyperelastic structures using physics-augmented neural networks

Multiscale topology optimization (TO) of hyperelastic materials remains computationally prohibitive due to the repeated solution of microscale boundary value problems. In this work, we present a concurrent multiscale topology optimization framework that overcomes this limitation by leveraging physics-augmented neural networks (PANNs) as surrogate constitutive models. The proposed approach enables the simultaneous optimization of macroscale material distribution and microscale descriptors, within a unified nonlinear finite strain setting. The surrogate models are constructed using input-specific neural networks (ISNNs) that enforce key physical principles directly within the architecture, including convexity and material symmetry through invariant-based representations and structural tensors. This ensures thermodynamic consistency and numerical stability while accurately representing homogenized anisotropic hyperelastic responses. The trained PANNs replace the microscale boundary value problem and provide efficient evaluations of stresses and consistent tangent moduli using analytical first and second derivatives of the neural network, enabling tractable large-scale multiscale optimization. The framework is demonstrated on representative microstructures exhibiting transversely isotropic, cubic anisotropic, and nearly incompressible isotropic behavior. The results show that the proposed method captures complex multiscale interactions and enables physically meaningful spatial tailoring of material properties, while significantly reducing computational cost compared to classical FE$^2$ approaches. These findings establish PANNs as a powerful tool for high-fidelity multiscale topology optimization of nonlinear anisotropic materials.

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arXiv2026

A Monolithic Computational Homogenization Framework for Nearly Incompressible Magnetoelastic Composites

Magneto-active elastomers exhibit large, nonlinear deformations under combined mechanical loading and magnetic fields, and their effective behavior is strongly governed by microstructural heterogeneity. Predictive modeling of these materials is challenging because their response involves strong magneto-mechanical coupling, large deformations, and the nearly incompressible behavior of elastomeric matrices. Existing multiscale approaches often rely on staggered strategies or formulations that do not robustly treat near-incompressibility in strongly coupled settings. This work presents a fully coupled computational homogenization framework for nearly incompressible magnetoelastic composites in which the mechanical deformation and magnetostatic fields are solved monolithically on a representative volume element (RVE). The microscale problem uses a mixed finite-element discretization with Lagrangian displacement degrees of freedom and a N'ed'elec-based magnetic vector potential, enabling a curl-conforming representation of magnetic induction together with periodic boundary constraints for both mechanical and magnetic fields. Near-incompressibility is treated using J-bar stabilization, in which the volumetric response is controlled by the cell-averaged dilatation while the isochoric response is evaluated using a scaled deformation gradient. The constitutive behavior is derived from an additive free-energy decomposition with hyperelastic, vacuum magnetic, and saturation-type magnetization contributions. The resulting formulation enables robust three-dimensional RVE simulations of heterogeneous magneto-elastic composites with complex particle distributions under large deformations and strong coupling. Numerical examples show how particle interactions, microstructural arrangement, and inclusion compressibility influence deformation patterns and the effective magneto-mechanical response.

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