We present a rezoning method for three‐dimensional arbitrary Lagrangian–Eulerian (ALE) and ALE with adaptive mesh refinement (ALE‐AMR) simulations. The method combines linesweep smoothing with an aspect‐ratio‐preserving target‐matrix optimization paradigm (TMOP) formulation. It is designed to preserve anisotropic mesh structures produced by the Lagrangian phase while maintaining mesh validity and reducing shear, sliver formation, and cell bunching in block‐structured, optionally nonconformal meshes. The approach combines a patch‐local TMOP objective and a convexity‐based disentanglement metric within an existing linesweep framework. The TMOP target matrix is built from local edge geometry and includes a prescribed aspect‐ratio cap, which provides an explicit control parameter for mesh relaxation. The metric is evaluated on an extended nodal patch, so that the objective couples the motion of a node to the quality of neighboring elements affected by that motion. Combined with sequential updates, this ensures that accepted steps are tested against the updated quality of the local coupled patch, rather than only against the elements directly incident on the node. When invalid configurations are detected, the TMOP objective is replaced by a convexity objective that drives signed volumes back to positive values. Parallelism is recovered through a distance‐1 coloring of the nodal graph, allowing independent node updates to be performed concurrently. Mesh‐only and hydrodynamic tests assess shear reduction, aspect‐ratio control, and mesh validity. Among the configurations examined, only the TMOP combined method consistently satisfies these requirements together while retaining anisotropic mesh structures, with no observed invalid post‐rezoning states. The prescribed target cap provides explicit control over excessive elongation without imposing an isotropic target. Strong and weak scaling measurements quantify the cost of the parallel optimization.
In this work, a stabilized second‐order virtual element method is proposed for two‐dimensional elasticity problems. Relying solely on low‐order degrees of freedom, a Euclidean orthogonal projection in the degree of freedom space is constructed using a least‐squares approach. Leveraging this projection, a streamlined serendipity virtual element scheme is established that eliminates redundant moment degrees of freedom within the standard virtual element, achieving a significant reduction in implementation complexity while preserving high accuracy. To validate the performance of the new element, classical numerical examples are presented, with a special emphasis on bending problems of various beam types solved on an extremely coarse mesh—a demanding capability that is scarcely reported in the existing literature on the virtual element method. The proposed element demonstrates superior accuracy in displacement and stress fields, achieving optimal convergence rates in both the norm and energy semi‐norm. Numerical results indicate that the new element model exhibits remarkable robustness against mesh distortion and inherent geometric adaptability, outperforming existing standard finite element and virtual element models while delivering highly competitive computational accuracy relative to hybrid virtual element models, thereby establishing itself as a reliable and efficient computational tool for continuum solid mechanics.
ABSTRACT The design of compliant mechanisms with integrated actuation requires consistent treatment of structural topology, actuator dimensions, and actuator placement. This work presents a coupled optimization framework based on modal formulations that combines the optimization of structural topology and linear actuators into a unified design approach. The method minimizes actuator volume while ensuring prescribed deformations by explicitly capturing the interaction between modal stiffness and actuator‐induced work. A scalable actuator model reflects the proportional dependence of actuator properties on geometric dimensions as exhibited by piezoelectric stack actuators, enabling flexible sizing and placement. The coupling is formulated through a modal stiffness to coordinate the adjustment of structural compliance and actuator effort. Analytical investigations reveal a characteristic dependence of actuator volume on this stiffness, including the existence of a unique volume minimum. Motivated by these findings, the coupled framework combines a modal‐synthesis approach for topology design with an analytical procedure for volume‐optimal actuator sizing, governed by an outer golden‐section search that varies the modal stiffness to minimize the resulting actuator volume. Demonstrated across several case studies – including classical single‐input‐single‐output mechanisms, problems with mechanical amplification requirements, robustness against external loads, and shape‐adaptive structures – the proposed framework systematically reduces actuator volume while maintaining the prescribed deformation behavior.
ABSTRACT Data‐driven material modeling techniques have gained significant attention due to their ability to capture the complex constitutive behavior beyond the limitations of classical material models. Physics‐augmented neural networks (PANNs), which incorporate physical restrictions into their architecture, combine the flexibility of machine learning with properties required for reliable engineering simulations. As a result, they have become increasingly relevant in computational material modeling. This work presents an approach to integrate pretrained isotropic, nearly incompressible, invariant‐based hyperelastic PANNs into the explicit finite element solvers Simcenter Radioss and OpenRadioss (Siemens). To this end, a Python framework transfers the trained parameters and the required constitutive expressions of the supported feed‐forward architecture to a standalone Fortran user material routine. The analytically expressed first derivatives of the strain‐energy density are included in the generated code. The finite element simulation therefore does not require an external machine‐learning library or a specialized solver. In addition to the integration strategy, particular emphasis is placed on the computational efficiency of the resulting user material subroutine. The influence of the network architecture on the overall simulation performance is investigated, and approaches for reducing evaluation costs while preserving the quality of the fitted material response are discussed. In this context, replacing the commonly used SoftPlus activation function by the SQuarePlus function reduces the additional constitutive evaluation costs for the investigated networks. To facilitate practical use, a publicly available GitHub repository ( https://github.com/OVGU‐CoMe/PANN_Radioss ) provides the code generator and the implemented material routines. Within the supported model class, the generator accounts for different numbers and widths of fully connected hidden layers. Additional invariant inputs can be incorporated through localized changes to the input and derivative definitions, whereas different constitutive formulations or solver interfaces require more comprehensive adaptations. As a complex example, an impact simulation demonstrates that the generated PANN user materials can be applied to explicit analyses involving large strains and (self‐)contact. The results illustrate the feasibility and computational performance of the investigated hyperelastic PANNs in Simcenter Radioss and OpenRadioss . They also show how a commercial and an open‐source finite element solver can be used to study this specified class of machine‐learning‐based constitutive models.
ABSTRACT With increasing mining depths, elevated geo‐stress and gas pressure substantially raise the risk of coal and gas outbursts (CGO), posing serious threats to mining safety. Conventional approaches including triaxial mechanical experiments, large‐scale physical simulations, and existing numerical models have been limited in delineating the distinct roles of geo‐stress and gas pressure during the CGO process. In this study, we developed a novel method coupling particle flow with computational fluid dynamics to unravel the underlying CGO mechanisms. Our simulations reveal that geo‐stress predominately accelerates damage via tensile and shear cracking, whereas gas pressure exerts a comparatively modest effect on crack propagation. Under coupled geo‐stress and gas pressure, the CGO failure zone evolves from a spindle‐like to a quarter‐ellipsoidal morphology. The internal stress of coal body change appears in four forms: continuous decrease, increase‐then‐decrease, continuous increase, and periodic decrease–increase. Furthermore, the increase in gas pressure and geo‐stress not only leads to higher velocity and greater quantity of outburst coal particles but also accelerates the formation of cracks, promotes earlier coal damage, and premature stress release. These findings provide mechanistic insights into the initiation and evolution of CGO, offering a quantitative basis for the design of targeted prevention strategies in deep mining.
