In this work, we generalize the mass-conserving mixed stress (MCS) finite element method for Stokes equations (Gopalakrishnan et al., 2019), involving normal velocity and tangential-normal stress continuous fields, to incompressible finite elasticity. By means of the three-field Hu–Washizu principle, introducing the displacement gradient and 1st Piola–Kirchhoff stress tensor as additional fields, we

Traditional constitutive models rely on hand-crafted parametric forms with limited expressivity and generalizability, while neural network-based models can capture complex material behavior but often lack interpretability. To balance these trade-offs, we present monotonic Input-Convex Kolmogorov-Arnold Networks (ICKANs) for learning polyconvex hyperelastic constitutive laws. ICKANs leverage the Kolmogorov-Arnold

This paper focuses on the numerical solution of elliptic partial differential equations (PDEs) with Dirichlet and mixed boundary conditions, specifically addressing the challenges arising from irregular domains. Both finite element method (FEM) and finite difference method (FDM), face difficulties in dealing with arbitrary domains. The paper introduces a novel nodal symmetric ghost method based on

This paper introduces a novel computational design framework for topology and fiber path optimization of variable stiffness laminated composites. Based on the finite element discretization of the design domain, the topology and material stiffness are represented using elemental densities and lamination parameters (LPs), respectively. The density distribution is optimized via the discrete-variable topology

Many materials, such as clays, fresh concrete, and biological fluids, exhibit elasto-viscoplastic (EVP) behaviour, transitioning between solid and fluid states under varying stress conditions. Among EVP models, Saramito’s constitutive law stands out for its thermodynamic consistency, smooth solid-to-fluid transition, and ability to accurately represent diverse materials with only four easily determinable

We introduce an FFT-based Galerkin homogenization scheme, which, in combination with the level-set method, allows us to study the evolution of ferroelectric domain nuclei in the experimentally relevant stress-driven setting. Our proposed framework includes an accelerated FFT-solver for solving the electromechanically coupled balance laws and a unified regularized driving force formulation for the level-set

Adaptive Kriging model has gained growing attention for its effectiveness in reducing the computational costs in time-dependent reliability analysis (TRA). However, the existing methods struggle to identify critical sample regions, leverage parallel computational resources, and assess the value for sample trajectories, thus restricting improvement in accuracy and efficiency. To address the challenges

We present a likelihood-free probabilistic inversion method based on normalizing flows for high-dimensional inverse problems. The proposed method is composed of two complementary networks: a summary network for data compression and an inference network for parameter estimation. The summary network encodes raw observations into a fixed-size vector of summary features, while the inference network generates

This work outlines a Lattice Boltzmann Method (LBM) for geometrically and constitutively non-linear solid mechanics to simulate large deformations under dynamic loading conditions. The method utilises the moment chain approach, where the non-linear constitutive law is incorporated via a forcing term. Stress and deformation measures are expressed in the reference configuration. Finite difference schemes

Shakedown analyses require a precise evaluation of pointwise elastic stresses and, at the same time, an accurate representation of the elastoplastic solution for capturing the ratcheting mechanisms effectively. However, existing discretization methods often face a trade-off: techniques that optimize plasticity performance may compromise elastic accuracy, and vice versa. The Hybrid Virtual Element Method

This paper proposes an effective and robust decoupled approach for addressing reliability-based design optimization (RBDO) problems. The method iteratively performs a parallel constrained Bayesian optimization (PCBO) with deterministic parameters based on the most probable point (MPP) underpinning limit-state functions (LSFs) sequentially updated through an enhanced active learning-based reliability

In density-based topology optimization of flow problems, flow in the solid domain is generally inhibited using a penalization approach. Setting an appropriate maximum magnitude for the penalization traditionally requires manual tuning to find an acceptable compromise between flow solution accuracy and design convergence. In this work, three penalization approaches are examined, the Darcy (D), the Darcy

In this paper, a time-dependent reliability-based double-scale topology optimization (TO) framework considering manufacturability is proposed. The proposed TO model focuses on the structural transient dynamic performance subjected to general dynamic loads. A time-dependent interval non-probabilistic reliability theory based on the idea of first-passage is introduced into the double-scale TO model to

We present a quantum computing formulation to address a challenging problem in the development of probabilistic learning on manifolds (PLoM). It involves solving the spectral problem of the high-dimensional Fokker–Planck (FKP) operator, which remains beyond the reach of classical computing. Our ultimate goal is to develop an efficient approach for practical computations on quantum computers. For now

The Multiscale Finite Element Method (MsFEM) decomposes the problem of solving partial differential equations with multiscale characteristics into two subproblems at two discrete resolution levels, i.e., the macroscopic one on a coarse mesh and the microscopic one on a fine mesh. The microscopic subproblems are used for constructing the Equivalent Stiffness Matrices (ESMs) of the coarse elements, and

A graph neural network (GNN) approach is introduced in this work which enables mesh-based three-dimensional super-resolution of fluid flows. In this framework, the GNN is designed to operate not on the full mesh-based field at once, but on localized meshes of elements (or cells) directly. To facilitate mesh-based GNN representations in a manner similar to spectral (or finite) element discretizations

The fracture of flexoelectric materials involves strain gradients, which pose challenges for theoretical and numerical analysis. The phase-field model (PFM) is highly effective for simulating crack propagation. However, PFM within the finite element method (FEM) framework faces certain challenges in simulating the fracture behavior of flexoelectric materials since the conventional FEM can only provide

Locally resonant metamaterial structures have gained significant attention across multiple engineering disciplines due to their ability to exhibit vibration stop bands not found in regular materials. These structures are composed of an assembly of unit cells, which are often discretized into large finite element models due to their sub-wavelength nature and intricate design. Moreover, due to the contribution

Interfacial debonding, a critical failure mechanism in heterogeneous materials, is often characterized by mixed-mode fracture. This study develops a numerical framework to simulate bulk and interfacial fractures in composite materials. A phase-field cohesive zone model, incorporating a directional energy decomposition scheme and a modified toughness method, is employed to capture complex fracture behaviors

Accurately modeling the mechanical behavior of materials is crucial for numerous engineering applications. The quality of these models depends directly on the accuracy of the constitutive law that defines the stress–strain relation. However, discovering these constitutive material laws remains a significant challenge, in particular when only material deformation data is available. To address this challenge

Surrogate models are critical for accelerating computationally expensive simulations in science and engineering, particularly for solving parametric partial differential equations (PDEs). Developing practical surrogate models poses significant challenges, particularly in handling geometrically complex and variable domains, which are often discretized as point clouds. In this work, we systematically

We present Wideband Back-Projection Diffusion, an end-to-end probabilistic framework for approximating the posterior distribution induced by the inverse scattering map from wideband scattering data. This framework produces highly accurate reconstructions, leveraging conditional diffusion models to draw samples, and also honors the symmetries of the underlying physics of wave-propagation. The procedure

In this study, we present a new framework of physics-informed non-intrusive reduced-order modeling (ROM) of dynamical systems modeled by parametric, partial differential equations (PDEs). Given new time and parameter values of a PDE, the framework utilizes trained physics-informed ML models to quickly estimate high-fidelity solutions while simultaneously observing the constraints and dynamics of the

The Fast Forward Quantum Optimization Algorithm (FFQOA) is a novel quantum-inspired heuristic search algorithm, drawing inspiration from the movement and displacement activities of wavefunctions associated with quantum particles. This algorithm has demonstrated remarkable effectiveness in predicting time series, clustering biomedical images, and optimizing the performance of convolutional neural networks

The designability of Continuous fiber-reinforced polymers (CFRPs) and the advance in additive manufacturing create more opportunities for tailorable topology and fiber-paths, thereby enhancing structural performance. However, challenges for structural optimization imposed by the complex failure modes of composite require further resolution. This study develops a novel strength-based optimization method

Conventional phase field modeling of fracture uses the degraded strain energy density (SED) at the crack tip as a material damage index to drive crack growth. To avoid non-physical evolution in crack phase-field, various SED splitting schemes have been adopted, resulting in the development of “anisotropic”-SED-based formulations to better capture the realistic crack nucleation and propagation under

This paper proposes a topology optimization framework for three-dimensional continuum structures subjected to design-dependent loads, including gravity, centrifugal, and hydrostatic pressure loads. First, this study utilizes the parameterized level set method (PLSM) with unstructured meshes to effectively handle complex structural shapes and boundary conditions. Second, this work employs parallel computing

The Finite Element Method (FEM) is a widely used technique for simulating crash scenarios with high accuracy and reliability. To reduce the significant computational costs associated with FEM, the Finite Element Method Integrated Networks (FEMIN) framework integrates neural networks (NNs) with FEM solvers. We discuss two different approaches to integrate the predictions of NNs into explicit FEM simulation:

We present and analyze two stabilized finite element methods for solving numerically the Poisson–Nernst–Planck equations. The stabilization we consider is carried out by using a shock detector and a discrete graph Laplacian operator for the ion equations, whereas the discrete equation for the electric potential need not be stabilized. Discrete solutions stemmed from the first algorithm preserve both

Goal-oriented a posteriori error estimation is crucial for solving partial differential equations (PDEs) efficiently and reliably. The Virtual Element Method (VEM) shows promise in this context due to its ability to handle general polygonal elements, eliminating the need for special treatment of hanging nodes. However, a suitable framework for goal-oriented error estimation in VEM has not been developed

Seismic response prediction presents a significant challenge in earthquake engineering, particularly in balancing computational efficiency with physical accuracy. Traditional numerical methods are computationally expensive for performing large-scale nonlinear analyses, while data-driven machine learning approaches, though computational efficiency, often lack physical constraints and sufficient training

The discrete unified gas kinetic scheme (DUGKS) has emerged as a promising Boltzmann solver capable of effectively capturing flow physics across all Knudsen numbers. However, simulating rarefied flows at high Knudsen numbers remains computationally demanding. This paper introduces a parametric Gaussian quadrature (PGQ) rule designed to improve the computational efficiency of DUGKS. The PGQ rule employs

How to accurately quantify the uncertainty of stochastic dynamical responses affected by uncertain loads and structural parameters is an important issue in structural safety and reliability analysis. In this paper, the conditional uncertainty propagation problem for the dynamical response of stochastic structures considering the measurement data with random error is studied in depth. A method for extracting

The design of high-resolution topology-optimised (TO) structures is important for many industrial and medical applications because of their better mechanical performance under different load conditions. Traditional density-based TO methods, like the Solid Isotropic Material with Penalisation (SIMP) method, can produce detailed designs but are very computationally expensive, especially for fine meshes

This study is dedicated to the multi-material topology optimization formulation (MMTO) for finite strain nonlocal elastoplasticity. The subloading surface model is newly incorporated into the primal problem to achieve the gradual change of the deformation process from pure elastic to material-specific plastic hardening. The stress–strain relationship of the model is a smooth continuous function, which

We present a quantitative comparison between two different Implicit–Explicit Runge–Kutta (IMEX-RK) approaches for the Euler equations of gas dynamics, specifically tailored for the low Mach limit. In this regime, a classical IMEX-RK approach involves an implicit coupling between the momentum and energy balance so as to avoid the acoustic CFL restriction, while the density can be treated in a fully

In recent years, the phase field method has been widely used in the simulation of fatigue crack propagation. However, fine mesh and cyclic simulation cycle by cycle significantly increase the computational cost of phase field simulation, which poses challenges in simulating the entire process of fatigue crack propagation. This paper proposes a cycle jump method considering the effect of plasticity

Physics-informed neural network (PINN) prevails as a differentiable computational network to unify forward and inverse analysis of partial differential equations (PDEs). However, PINN suffers limited ability in complex transient physics with nonsmooth heterogeneity, and the training cost can be unaffordable. To this end, we propose a novel framework named physics-encoded convolutional attention network

Metal additive manufacturing via laser-based powder bed fusion (PBF-LB/M) faces performance-critical challenges due to complex melt pool and vapor dynamics, often oversimplified by computational models that neglect crucial aspects, such as vapor jet formation. To address this limitation, we propose a consistent computational multi-physics mesoscale model to study melt pool dynamics, laser-induced evaporation

Hamiltonian operator inference has been developed in Sharma et al. (2022) to learn structure-preserving reduced-order models (ROMs) for Hamiltonian systems. The method constructs a low-dimensional model using only data and knowledge of the functional form of the Hamiltonian. The resulting ROMs preserve the intrinsic structure of the system, ensuring that the mechanical and physical properties of the

The Dimension-Reduced Probability Density Evolution Equation (DR-PDEE) provides a promising tool for evaluating the evolution of probability density in high-dimensional stochastic dynamical systems. However, solving DR-PDEE relies heavily on accurately identifying unknown spatio-temporal-dependent intrinsic drift coefficients, which drive the evolution of probability density. Recognizing the potential

A novel plastic-damage model is presented for the study of materials exhibiting combined plastic strain accumulation and stiffness degradation. This constitutive law is based on a phenomenological pseudo-composite theory, the Rule of Mixture (RoM), in which each constitutive behaviour, damage and plasticity, act as a virtual material component of the whole physical entity. In this way, each nonlinearity

Continuous monitoring and real-time control of high-dimensional distributed systems are often crucial in applications to ensure a desired physical behavior, without degrading stability and system performances. Traditional feedback control design that relies on full-order models, such as high-dimensional state-space representations or partial differential equations, fails to meet these requirements

Hydromechanical models of Darcy–Brinkman–Stokes type consider mass- and momentum conservation of an incompressible fluid on a domain with varying permeability. They include the two important limits of free flow governed by the classical Navier–Stokes equations and porous Darcy flow. The conceptual simplicity makes the model attractive from a modeling perspective, but any numerical solution procedure

In this paper, an implicit cell-based material point method (MPM) with particle boundaries is proposed to effectively solve large deformation static problems. The volume integrals of the incremental weak form based on an updated Lagrangian approach are evaluated at integration points defined by equally sub-dividing grid cells, which eliminates the cell-crossing error and reduces the integration error

Flexoelectricity is an electromechanical coupling phenomenon in which electric polarization is generated in response to strain gradients. This effect is size-dependent and becomes increasingly significant at micro- and nanoscale dimensions. While heterogeneous flexoelectric materials demonstrate enhanced electromechanical properties, their effective application in nanotechnology requires robust homogenization

Accurately analyzing the probabilistic responses of high-dimensional nonlinear dynamical structures subjected to non-white and non-stationary stochastic excitations is a critical and challenging task. To address this issue, an efficient stochastic response analysis method is proposed by constructing an auxiliary diffusion process related to the non-white and non-stationary excitation process and incorporating

Porous structures have gained widespread applications in aerospace, biomedical, and other fields due to their lightweight, high specific strength, and energy absorption properties. However, existing gradient design methods for Voronoi porous structures predominantly rely on iterative optimization and explicit modeling, which suffer from high computational costs, insufficient precision in local density

The goal of this work is to develop a machine-learning enabled digital-twin to rapidly ascertain optimal programming to achieve desired tactical multi-drone swarmlike behavior. There are two main components of this work. The first main component is a framework comprised of a multibody dynamics model for multiple interacting agents, augmented with a machine-learning paradigm that is based on the capability

This work proposes a novel Isogeometric Analysis (IGA) extension of the assumed natural strain (ANS) method to alleviate locking phenomena in solid beams, which are modeled as 3D elements accounting for displacement degrees of freedom solely and designed such that accurate analyses can be generally obtained using only one element to discretize the structure’s cross-section. ANS methods substitute covariant

3D swept volume, enabled by advancements in additive manufacturing, present new opportunities for lightweight and functional optimization. However, efficient design methodologies for conformal filling gradient lattice structures (CFGLSs) remain scarce. This paper proposes a modified level set function (MLSF) that matches lattice structures to the geometry of 3D swept volume. Furthermore, a multiscale

The Material Point Method (MPM) has been shown to be an effective approach for analysing large deformation processes across a range of physical problems. However, the method suffers from a number of spurious artefacts, such as a widely documented cell crossing instability, which can be mitigated by adopting basis functions with higher order continuity. The larger stencil of these basis functions exacerbate

We develop a strain gradient elastodynamics model for heterogeneous materials based on the two-scale asymptotic homogenization theory. Utilizing only the first-order cell functions, the present model is more concise and more computationally efficient than previous works with high-order truncations. Furthermore, we rigorously prove that the coefficient tensors, including the homogenized elasticity tensor

The application of geometrically nonlinear topology optimization (GNTO) poses a substantial challenge due to the extensive memory requirements and prohibitive computational demands involved. To tackle this challenge, a discrete physics-informed neural network (dPINN) is suggested as a promising approach to alleviate computational demands and enhance the applicability to large-scale problems. In comparison

Time-variant uncertainties are omnipresent in engineering systems. These significantly impact the structural performance. The main challenge in this context is how to handle them in dynamic domain response topology optimization. To tackle this challenge, a new transient dynamic robust topology optimization (TDRTO) method is proposed to optimize the topology of continuous structures. This method comprehensively

Variable stiffness laminates offer the advantage of tailoring structural performance by adjusting in-plane stiffness through curved fiber paths. Additionally, material distribution at the structural level can further fine-tune performance by varying the topology. If both the structural topology and curved fiber paths are optimized together, super-efficient composite laminates can be achieved. In this

In this paper, a decoupled, linearized, unconditionally stable, and fully discrete numerical scheme is presented for simulating two-phase ferrofluid flows. This scheme is constructed by introducing two scalar auxiliary variables. It is based on the backward Euler scheme with variable time step and mixed finite element discretization. Nonlinear terms are treated explicitly to simplify the computational

Randomized neural networks (RaNNs), characterized by fixed hidden layers after random initialization, offer a computationally efficient alternative to fully parameterized neural networks trained using stochastic gradient descent-type algorithms. In this paper, we integrate RaNNs with overlapping Schwarz domain decomposition in two primary ways: firstly, to formulate the least-squares problem with localized