Computational Mechanics最新文献

Large-scale structural simulations based on micro-mechanical models of paper products require extensive numerical resources and time. In such models, the fibrous material is often represented by connected beams. Whereas previous micro-mechanical simulations have been restricted to smaller sample problems, large-scale micro-mechanical models are considered here. These large-scale simulations are possible on a non-specialized desktop computer with 128GB of RAM using an iterative method developed for network models and based on domain decomposition. Moreover, this method is parallelizable and is also well-suited for computational clusters. In this work, the proposed memory-efficient iterative method is numerically validated for linear systems resulting from large networks of Timoshenko beams. Tensile stiffness and out-of-plane bending stiffness are simulated and validated for various commercial-grade three-ply paperboards consisting of layers composed of two different types of paper fibers. The results of these simulations show that a linear network model produces results consistent with theory and published experimental data

Practical multibody systems usually consist of flexible bodies of complex shapes, but existing dynamic modeling methods work efficiently only for the systems with bodies of simple and regular shapes. This study proposes a novel computational method for simulating dynamics of flexible multibody systems with flexible bodies of complex shapes via an integration of the finite cell method (FCM) and the absolute nodal coordinate formulation. The classic mesh of FCM is not aligned to the body boundaries, leading to a large number of integration points in cut cells. This study utilizes the Boolean FCM with compressed sub-cell method to reduce the number of integration points and improve computation efficiency. Seven static and dynamic numerical examples are used to validate the proposed method.

We present a machine-learning strategy for finite element analysis of solid mechanics wherein we replace complex portions of a computational domain with a data-driven surrogate. In the proposed strategy, we decompose a computational domain into an “outer” coarse-scale domain that we resolve using a finite element method (FEM) and an “inner” fine-scale domain. We then develop a machine-learned (ML) model for the impact of the inner domain on the outer domain. In essence, for solid mechanics, our machine-learned surrogate performs static condensation of the inner domain degrees of freedom. This is achieved by learning the map from displacements on the inner-outer domain interface boundary to forces contributed by the inner domain to the outer domain on the same interface boundary. We consider two such mappings, one that directly maps from displacements to forces without constraints, and one that maps from displacements to forces by virtue of learning a symmetric positive semi-definite (SPSD) stiffness matrix. We demonstrate, in a simplified setting, that learning an SPSD stiffness matrix results in a coarse-scale problem that is well-posed with a unique solution. We present numerical experiments on several exemplars, ranging from finite deformations of a cube to finite deformations with contact of a fastener-bushing geometry. We demonstrate that enforcing an SPSD stiffness matrix drastically improves the robustness and accuracy of FEM–ML coupled simulations, and that the resulting methods can accurately characterize out-of-sample loading configurations with significant speedups over the standard FEM simulations.

We present an approach for the data-driven modeling of nonlinear viscoelastic materials at small strains which is based on physics-augmented neural networks (NNs) and requires only stress and strain paths for training. The model is built on the concept of generalized standard materials and is therefore thermodynamically consistent by construction. It consists of a free energy and a dissipation potential, which can be either expressed by the components of their tensor arguments or by a suitable set of invariants. The two potentials are described by fully/partially input convex neural networks. For training of the NN model by paths of stress and strain, an efficient and flexible training method based on a long short-term memory cell is developed to automatically generate the internal variable(s) during the training process. The proposed method is benchmarked and thoroughly compared with existing approaches. Different databases with either ideal or noisy stress data are generated for training by using a conventional nonlinear viscoelastic reference model. The coordinate-based and the invariant-based formulation are compared and the advantages of the latter are demonstrated. Afterwards, the invariant-based model is calibrated by applying the three training methods using ideal or noisy stress data. All methods yield good results, but differ in computation time and usability for large data sets. The presented training method based on a recurrent cell turns out to be particularly robust and widely applicable. We show that the presented model together with the recurrent cell for training yield complete and accurate 3D constitutive models even for sparse bi- or uniaxial training data.

The numerical solution of continuum damage mechanics (CDM) problems suffers from convergence-related challenges during the material softening stage, and consequently existing iterative solvers are subject to a trade-off between computational expense and solution accuracy. In this work, we present a novel unified arc-length (UAL) method, and we derive the formulation of the analytical tangent matrix and governing system of equations for both local and non-local gradient damage problems. Unlike existing versions of arc-length solvers that monolithically scale the external force vector, the proposed method treats the latter as an independent variable and determines the position of the system on the equilibrium path based on all the nodal variations of the external force vector. This approach renders the proposed solver substantially more efficient and robust than existing solvers used in CDM problems. We demonstrate the considerable advantages of the proposed algorithm through several benchmark 1D problems with sharp snap-backs and 2D examples under various boundary conditions and loading scenarios. The proposed UAL approach exhibits a superior ability of overcoming critical increments along the equilibrium path. Moreover, in the presented examples, the proposed UAL method is 1–2 orders of magnitude faster than force-controlled arc-length and monolithic Newton–Raphson solvers.

Titan aluminium alloys belong to the group of (alpha )–(beta )-alloys, which are used for many applications in industry due to their advantageous mechanical properties, e.g. for laser powder bed fusion (PBF-LB) processes. However, the composition of the crystal structure and the respective magnitude of the solid fraction highly influences the material properties of titan aluminium alloys. Specifically, the thermal history, i.e. the cooling rate, determines the phase composition and microstructure for example during heat treatment and PBF-LB processes. For that reason, the present work introduces a phase transformation framework based, amongst others, on energy densities and thermodynamically consistent evolution equations, which is able to capture the different material compositions resulting from cooling and heating rates. The evolution of the underlying phases is governed by a specifically designed dissipation function, the coefficients of which are determined by a parameter identification process based on available continuous cooling temperature (CCT) diagrams. In order to calibrate the model and its preparation for further applications such as the simulation of additive manufacturing processes, these CCT diagrams are computationally reconstructed. In contrast to empirical formulations, the developed thermodynamically consistent and physically sound model can straightforwardly be extended to further phase fractions and different materials. With this formulation, it is possible to predict not only the microstructure evolution during processes with high temperature gradients, as occurring in e.g. PBF-LB processes, but also the evolving strains during and at the end of the process.

A general formalism is proposed, based on the definition of a space-time potential, for developing space-time formulations adapted to nonlinear and time dependent behaviors. The focus is given to the case of standard generalized materials that are expressed from the knowledge of two potentials, a strain energy and a dissipation potential in a convex framework with the help of internal variables. Viscoplasticity with isotropic hardening and nonlinear finite viscoelasticity are investigated. Starting from the definition of an appropriate space-time potential, time discontinuous Galerkin forms are developed for use in the case of time singularities (in particular with regard to time integration of internal variables). Furthermore, NURBS approximation are used, such as to propose Space-Time Isogeometric Analysis models. Numerical examples allow to compare the obtained isogeometric space-time models with standard finite-element models (that are based on standard time integration procedures: radial return for viscoplasticity and backward euler for viscosity) and allow to illustrate the new possibilities offered with the proposed space-time formulations.

This study focuses on predicting and quantifying fragmentation phenomena under high impulsive dynamic loading, such as blast, impact, and penetration events, which induce plastic deformation, fracture, and fragmentation in materials. The research addresses the challenge of accurately quantifying fragmentation through individual fragment mass and velocities. To achieve this, the Lattice Discrete Particle Model (LDPM) is utilized to predict failure modes and crack patterns and analyze fragments in reinforced concrete protective structures subjected to dynamic loads. An innovative unsupervised learning clustering technique is developed to identify and characterize fragment mass and velocity. The study demonstrates that the proposed method efficiently and accurately quantifies fragmentation, offering significant speed and efficiency gains while maintaining high fidelity. By combining a high-fidelity physics-based model for fragment formation with advanced geometric algorithms and distance-based approximations, the method accurately characterizes fragment size, position, and velocity. This approach circumvents computational costs associated with simulations across various time scales of fragment generation, trajectory, and secondary impacts. Experimental validation confirms the effectiveness of the proposed method in simulating real-world fragmentation phenomena, making it a valuable tool for applications in materials science, engineering, and beyond. The integrated workflow of LDPM simulations with machine learning clustering also offers an efficient means for structural engineers and designers to develop protective structures for dynamic impulsive loads.

Shakedown analysis with Melan’s theorem is an important approach to predicting the ultimate load-bearing capacity of heterogeneous materials under varying loads. However, this approach entails dealing with a large-scale nonlinear mathematical programming problem with numerous element-wise yielding constraints and unknown time-independent beneficial residual stress variables, resulting in a substantial computational burden. The well-known basis reduction method expresses the unknown time-independent beneficial residual stress as a linear combination of a set of self-equilibrium stress (SES) bases, and the corresponding coefficients are the unknowns. This method is effective only if the set of SES basis vectors is small and easily available. Based on the representative volume element (RVE) and FEM-cluster based analysis (FCA) method, this paper proposes a FEM cluster-based basis reduction method to fast predict the shakedown domain of heterogeneous materials. The novel data-driven clustering method is introduced to divide the RVE into several clusters. The SES basis is constructed by applying the cluster eigenstrain to RVE under periodic boundary conditions. Numerical experiments show that the unknown time-independent beneficial residual stress can be well represented with this small set of SES basis vectors. In this way, the unknown variables are reduced dramatically. In addition, to further reduce the number of nonlinear constraints, a constraint reduction strategy based on the reduced-order model of FCA is implemented to remove the element-wise yielding constraints for the elements far from yielding. Several numerical examples demonstrate its efficiency and accuracy.

Most currently available methods for modeling multiphysics, including thermoelasticity, using machine learning approaches, are focused on solving complete multiphysics problems using data-driven or physics-informed multi-layer perceptron (MLP) networks. Such models rely on incremental step-wise training of the MLPs, and lead to elevated computational expense; they also lack the rigor of existing numerical methods like the finite element method. We propose an integrated finite element neural network (I-FENN) framework to expedite the solution of coupled transient thermoelasticity. A novel physics-informed temporal convolutional network (PI-TCN) is developed and embedded within the finite element framework to leverage the fast inference of neural networks (NNs). The PI-TCN model captures some of the fields in the multiphysics problem; then, the network output is used to compute the other fields of interest using the finite element method. We establish a framework that computationally decouples the energy equation from the linear momentum equation. We first develop a PI-TCN model to predict the spatiotemporal evolution of the temperature field across the simulation time based on the energy equation and strain data. The PI-TCN model is integrated into the finite element framework, where the PI-TCN output (temperature) is used to introduce the temperature effect to the linear momentum equation. The finite element problem is solved using the implicit Euler time discretization scheme, resulting in a computational cost comparable to that of a weakly-coupled thermoelasticity problem but with the ability to solve fully-coupled problems. Finally, we demonstrate I-FENN’s computational efficiency and generalization capability in thermoelasticity through several numerical examples.