model continuum mechanics

Existing material model calibration methods suffer from four key limitations: reliance on simplified specimens and global measurements, non-targeted data acquisition, deterministic optimization that neglects uncertainty quantification, and inefficient sequential workflows. This paper proposes an Interleaved Characterization and Calibration (ICC) framework—the first to implement a closed-loop workflow—integrating full-field digital image correlation (DIC), Bayesian optimal experimental design, principal component analysis (PCA)-based dimensionality reduction, finite element-based surrogate modeling, and Markov Chain Monte Carlo (MCMC)-driven uncertainty inference. The ICC framework enables demand-driven loading-path planning and real-time feedback, markedly improving information utilization efficiency. Applied to biaxial deformation calibration of an aluminum cruciform specimen, it achieves high parameter accuracy, rigorous uncertainty quantification, and over 70% reduction in computational cost. Results demonstrate that high-fidelity constitutive models can be efficiently and reliably deployed for engineering decision-making.

Conventional constitutive modeling heavily relies on expert knowledge and suffers from low automation. Method: This paper proposes a large language model (LLM)-driven, end-to-end framework for constitutive modeling. It is the first approach enabling an LLM to autonomously design physics-constrained neural networks (CANNs) tailored for solid mechanics—automatically embedding physical laws, generating network architectures, and producing executable code based solely on input material type and experimental data. The framework tightly integrates domain knowledge with data-driven learning, eliminating manual architecture design and hard-coded physical constraints. Contribution/Results: Evaluated on multiple benchmark problems, the automatically generated models achieve accuracy comparable to or exceeding that of handcrafted models, while demonstrating superior extrapolation capability and generalization across diverse loading conditions.

This work addresses the widespread lack of built-in support for physical dimensions in existing finite element frameworks, which often leads to unit inconsistencies and numerical instabilities. For the first time, automated dimensional analysis is integrated into the Unified Form Language (UFL) by introducing a symbolic Quantity class that tracks physical units within variational forms. Leveraging the Abelian group structure of dimensions, units are encoded as rational-number vectors, and consistency checks along with nondimensionalization are automatically performed via a visitor pattern over expression trees. This approach reformulates nondimensionalization as a physics-aware diagonal preconditioner, substantially improving the condition number of saddle-point systems arising from the Navier–Stokes equations, identifying floating-point cancellation errors in Neo-Hookean hyperelastic models, and effectively handling parameter scaling in multiphysics Poisson–Nernst–Planck systems.

This work addresses the challenge of balancing numerical discretization error and model complexity in the inverse identification of temperature-dependent nonlinear thermal conductivity from transient temperature data. A Bayesian calibration framework is proposed that jointly optimizes the parametrization of the thermal conductivity function and the numerical discretization strategy. By integrating gradient-based optimization, adaptive mesh refinement, and an uncertainty-driven stopping criterion grounded in Morozov’s discrepancy principle, the method effectively mitigates overfitting while maintaining high accuracy. Validation on both synthetic and experimental data demonstrates that the approach achieves precise inference of thermal conductivity at low computational cost, aligning numerical and modeling errors with the level of measurement noise and thereby significantly enhancing the robustness and efficiency of nonlinear constitutive relation identification.

Traditional constitutive models rely on pre-specified functional forms, suffering from poor generalizability and limited interpretability. To address this, we propose a graph-structured equation discovery framework: symbolic expressions are modeled as parameter-dependent directed graphs, where nodes represent variables and operators, and edges encode computational relationships and parameter dependencies. Integrating graph neural networks with symbolic regression, our method enables end-to-end joint optimization of constitutive equation structure and parameters. Crucially, it operates without expert-defined priors, supporting discovery of arbitrary physical relations directly from data. Evaluated on strain-rate effects in alloy steel and deformation modeling of lithium metal, the framework automatically discovers novel constitutive models that are structurally more compact and achieve significantly higher prediction accuracy than classical empirical models. These results demonstrate its effectiveness and interpretability for modeling complex material responses.

This study addresses the challenge of accurately capturing the highly nonlinear response of hyperelastic materials under large-deformation impact, which traditional constitutive models struggle to represent. The authors integrate physics-augmented neural networks (PANNs) into industrial-scale explicit finite element solvers—Simcenter Radioss and OpenRadioss—by automatically generating Fortran user material subroutines for data-driven constitutive modeling. Key contributions include the first deployment of PANNs within industrial explicit solvers, the introduction of a computationally more efficient SQuarePlus activation function as a replacement for SoftPlus, and an open-source, automated toolchain enabling end-to-end subroutine generation. Experimental results demonstrate that the proposed approach achieves high accuracy while significantly reducing neural network evaluation overhead, offering an efficient and practical machine learning–based constitutive modeling paradigm for impact simulations.

This work addresses the limitations imposed by polyconvexity constraints, which often hinder accurate representation of complex material responses. The study systematically analyzes how polyconvexity restricts modeling fidelity and proposes a physics-enhanced neural network architecture based on structural tensor invariants and signed singular values. The model is evaluated on microstructure homogenization data, demonstrating superior performance. Theoretically, the paper elucidates the root causes of modeling deficiencies induced by polyconvexity and provides analytical ellipticity guarantees for two classes of non-polyconvex Mooney–Rivlin–type energy functions. Experimentally, finite element simulations confirm that the proposed non-polyconvex model significantly improves prediction accuracy while maintaining numerical stability, with quantitative error reductions consistently observed across multiple material datasets.

This work addresses the challenge of efficiently inferring constitutive response functions from experimental data, a task traditionally hindered by time-consuming parameter optimization in classical material models. The authors propose two novel frameworks—Physics-Augmented Neural Operator (PANO) and Constitutive Artificial Neural Operator (CANO)—which, for the first time, apply neural operators to solve the inverse problem of constitutive modeling in infinite-dimensional input–output spaces. By encoding inputs via Laplacian eigenfunctions, the approach achieves discretization independence and robustness to noise, while embedding physical constraints in the output layer ensures thermodynamic consistency of the predicted strain energy density function. Requiring only a single forward pass, the model enables near real-time inference of hyperelastic constitutive laws and demonstrates exceptional generalization across unseen geometries, noisy or incomplete data, varying meshes, and different scales.

This work investigates whether pretrained image editing models can serve as a universal interface for solving diverse physical equations. The approach encodes both inputs and solutions of physical problems as images, incorporates lightweight adapters to embed scalar parameters, and trains the model under a unified architecture using numerical or analytical solutions across multiple equation types—including elliptic, heat, and Navier-Stokes equations. For the first time, it systematically demonstrates that general-purpose generative models can effectively represent both static and dynamic physical mappings, even capturing shocks and unstable phenomena, thereby expanding their applicability in scientific computing. Experiments across more than ten problem classes yield promising results, yet also reveal limitations of image-based representations in handling wide numerical ranges, enforcing constraints, and simulating long-term chaotic dynamics, such as those in the Kuramoto–Sivashinsky equation.

This study addresses the challenge of accurately calibrating strongly coupled thermomechanical materials under finite strains using only surface experimental data. To this end, the authors propose a full-field calibration framework that leverages boundary displacements, reaction forces, and surface temperature measurements. The forward problem is formulated as a nearly incompressible thermo-hyperelastic system based on a Helmholtz free energy constitutive model, and the inverse problem is solved via PDE-constrained optimization. Innovatively relying solely on surface observables—without requiring volumetric measurements—the method integrates weighted multi-source observational terms and exploits automatic differentiation for efficient computation of adjoint gradients. Validation on both synthetic and real experimental data demonstrates the framework’s ability to accurately identify key coupling parameters, such as thermal expansion and directional contraction coefficients.