heat-mpm phase coupling

This work addresses the compatibility and stability challenges that arise when coupling the approximate full mass matrix method (FMPM(k)) with lumped-mass-dependent Material Point Method (MPM) features—such as velocity boundary conditions and multi-material contact. To resolve these issues, the authors propose a reformulated FMPM(k) implementation that streamlines the FMPM loop to execute only once per time step and adapts the algorithm to seamlessly integrate with standard MPM functionalities. This study presents the first successful integration of FMPM(k) with lumped-mass-dependent MPM capabilities, while systematically analyzing the influence of the polynomial order \(k\) on time-step stability and computational efficiency. The proposed approach significantly enhances the applicability and performance of high-order FMPM(k) in complex multiphysics simulations.

Existing neural rendering approaches generally overlook the influence of temperature on visual appearance, making it difficult to faithfully simulate thermally coupled phenomena such as melting and solidification. This work introduces thermal phase-change dynamics into 3D Gaussian splatting for the first time by endowing Gaussian points with temperature attributes. It couples a numerical heat conduction–convection solver with Material Point Method (MPM) dynamics and proposes a topology-adaptive rendering strategy to mitigate visual artifacts caused by large deformations. The resulting framework achieves high-fidelity, physically consistent rendering of thermophysical dynamic scenes, demonstrating significantly improved realism and controllability over existing methods in complex phase-transition processes like melting and solidification.

Explicit Material Point Method (MPM) suffers from numerical instability under large time steps, hindering its integration with partitioned large-step solvers and multi-physics frameworks. Method: This paper proposes a plug-and-play substepping algorithm that encapsulates explicit MPM as a pseudo-implicit scheme without modifying the underlying explicit integrator code. By introducing internal substeps coupled with constraint enforcement and projection operations, the method ensures numerical stability and physical consistency at macroscopic large time steps. Contribution/Results: The approach is inherently compatible with multi-solver coupling, complex constraint handling, and multi-physics integration, significantly enhancing computational robustness and efficiency. Experiments demonstrate that, while preserving accuracy, the method enables time-step enlargement by several-fold—providing a practical pathway for embedding MPM into large-scale, multi-physics simulation frameworks.

Material fracture under coupled multiphysics fields—such as thermo-mechanical, fluid–structure, hydrogen diffusion, and corrosion—remains a significant challenge in computational mechanics. Method: This paper proposes a general phase-field fracture modeling paradigm that enables multiphysics coupling via analogy to the heat conduction equation. The framework supports 2D/3D finite element implementation within Abaqus through user-defined subroutines (UMAT/UMATHT), offering integration-point-level customization and seamless compatibility with commercial software. Contribution/Results: It establishes the first unified, modular, and open-source phase-field framework for multiphysics fracture analysis, covering thermo-mechanical fracture, hydraulic fracturing, hydrogen-assisted cracking, and stress corrosion cracking. Numerical results demonstrate excellent agreement with experimental data and analytical solutions, validating its accuracy, robustness, and engineering applicability. The open-source implementation promotes standardization of phase-field methods for fracture simulation under complex service conditions.

Explicit material point method (MPM) struggles with quasi-static or long-term geomechanical simulations involving large deformations and history-dependent behavior, while implicit MPM remains limited by the analytical derivation of Jacobian matrices—especially consistent tangent operators for complex constitutive models. Method: This paper proposes an automatic-differentiation-based implicit MPM framework built on NVIDIA Warp, integrating reverse-mode automatic differentiation (eliminating manual tangent derivation), GPU-accelerated sparse Jacobian assembly, and implicit time integration. The framework supports efficient forward and inverse modeling for elastoplasticity and coupled poromechanics. Contribution/Results: Experiments demonstrate substantial improvements in computational efficiency and scalability without compromising numerical robustness. To our knowledge, this is the first open-source, differentiable, and fully GPU-accelerated implicit MPM implementation for computational geomechanics.

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.

This study addresses the challenge of inferring and extrapolating complex physical dynamics—such as those of deformable solids and fluids—from video observations. To this end, the authors construct a 2D physics simulation dataset based on the Material Point Method (MPM) and present the first systematic comparison between code generation models and video diffusion models on physical dynamics inference tasks. Experimental results demonstrate that code generation models produce temporally stable and physically consistent extrapolations, whereas video diffusion models, while adept at capturing geometric details, often generate extrapolations lacking physical plausibility. The work reveals complementary strengths of the two approaches: code generation excels in parameter inference and physical consistency, while diffusion models are more effective at geometric recognition. This study establishes a new benchmark and offers key insights for physics-aware video understanding.

This study addresses the complex microstructural evolution and residual stress challenges in glass additive manufacturing induced by extreme thermal histories. The authors propose a unified variational framework based on the extended Hamilton’s principle, which for the first time couples thermo-mechanical and phase transformation processes to simultaneously capture both the first-order melting and second-order glass transition under large deformations. A kinetic freezing mechanism is incorporated to model glass formation. The framework integrates a temperature-dependent viscosity constitutive law, the single-slice neighborhood element method (NEM), and a three-dimensional finite element implementation in ANSYS. The approach successfully reproduces time–temperature–transformation (TTT) behavior across varying cooling rates and accurately predicts residual stresses and macroscopic warpage during laser-based deposition, establishing a high-fidelity multiphysics simulation foundation for glass additive manufacturing.

This work addresses the challenge in laser metal processing where conventional diffuse-interface methods fail to accurately resolve the steep thermal gradients across the gas–liquid interface, leading to inaccurate predictions of vapor recoil pressure and surface tension. To overcome this limitation, the authors propose a hybrid interface modeling strategy that combines a sharp-interface CutFEM approach for high-fidelity heat conduction with a level-set-based diffuse-interface single-fluid finite element method for multiphase flow simulation. Coupling between the two solvers is achieved through a narrow-band temperature field extension. The resulting framework preserves robustness in capturing complex interfacial dynamics while significantly enhancing interfacial temperature accuracy, achieving second-order spatial convergence in the thermal model. Compared to purely diffuse-interface approaches, the method permits mesh sizes two orders of magnitude larger at equivalent accuracy, yielding an overall improvement of one order of magnitude in solution accuracy for representative test cases.

This work addresses the challenge of numerical diffusion and premature mesh-driven topological changes in multiphase flow simulations. It proposes a fully Lagrangian framework based on the Particle Finite Element Method (PFEM), which integrates dynamic mesh adaptivity with a node-based empty circumcircle criterion to guarantee that interface edges always conform to the Delaunay triangulation. This approach preserves sharp interface geometry without imposing explicit constraints on the triangulation, effectively decoupling interfacial physics from mesh resolution and enabling independent control of topological evolution at sub-grid scales. Validated against standard multiphase benchmarks, the method achieves excellent agreement with reference solutions using significantly fewer nodes and successfully simulates a 16-phase Rayleigh–Taylor instability, demonstrating its scalability and geometric versatility.