Computational Mechanics最新文献

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.

This paper presents a methodology where a macroscopic linear material response incorporates microscopic variations, such as transient interactions and micro-inertia effects. This is achieved by implementing the temporal coupling between macro and microstructures, along with the spatial coupling, within a dynamic computational homogenisation framework. In the context of dynamic multiscale modelling, the temporal coupling method offers significant advantages by effectively reducing deviations emerging from micro-inertia effects and transient phenomena. The effectiveness of the developed procedure is validated by a comparison of the macroscopic results with the solutions of direct numerical simulation for a one-dimensional periodic laminate bar with different contrast levels. The homogenised results obtained using the developed procedure indicate that a better prediction of the macroscopic requires a larger Representative Volume Element (RVE) which improves the estimation of multiscale strain energy and a larger time window which improves the estimation of multiscale kinetic energy. The simultaneous increase in the RVE size and the time averaging window yields the best results in predicting the macroscopic response.

This paper presents a new mixed finite element model for material and geometric non-linear analysis of composite beams in partial interaction taking into account the non-penetration condition between layers. The Hu–Washizu functional with three independent fields is chosen for the developed mixed formulation. The force fields in the connection are chosen as the redundant forces and approximated using interpolation functions. The remaining force fields are obtained from solving equilibrium equations so that the element equlibrium is verified. Nevertheless, the compatibility as well as the constitutive law is satisfied only in a weak sense. The geometric non-linearity is taken into account by adopting the co-rotational approach. In this paper, the contact condition is imposed at the element level. Augmented Lagrangian method with Uzawa iteration algorithm is used to solve the contact problem. It has been shown that the proposed mixed formulation gives a more accurate result with less elements comparing to classical displacement based model. Besides, the buckling behaviour of delaminated two-layered composite columns has been studied by using the developed mixed formulation model. It has been observed that the buckling strength of the composite column can be overestimated if the uplift is not considered in the model.

This study proposes an implicit algorithm applying the primal–dual interior point method (PDIP method) to stabilize the stress update when using a class of the Gurson–Tvergaard–Needleman model (GTN model). The GTN model is widely used to realize the change in void volume fraction that governs ductile fracture in metals, but numerical instabilities arise due to shrinkage of the yield surface and the accelerated void growth. In fact, such shrinkage can lead to misjudgment of yield conditions when using conventional return mapping algorithms, since trial elastic stresses are computed assuming zero incremental plastic strain. In addition, the change in void volume fraction is often approximated in bilinear form to represent the acceleration of void growth, but should be smooth to apply nonlinear solution methods such as the Newton’s method. To avoid such inconvenience in the implicit stress update for the GTN model and ensure numerical stability, we propose an algorithm that replaces the constitutive equations with inequality constraints with an equivalent constrained optimization problem by applying the PDIP method. After verifying the numerical accuracy and convergence of the proposed implicit algorithm using iso-error maps, we demonstrate its capability through several numerical examples that cannot be solved by the conventional return mapping algorithm or the PDIP method applied only to the inequality constraint corresponding to the yield condition.

We present and analyze computationally Geometric MultiGrid (GMG) preconditioning techniques for Generalized Minimal RESidual (GMRES) iterations to space-time finite element methods (STFEMs) for a coupled hyperbolic–parabolic system modeling, for instance, flow in deformable porous media. By using a discontinuous temporal test basis, a time marching scheme is obtained. Higher order approximations that offer the potential to inherit most of the rich structure of solutions to the continuous problem on computationally feasible grids increase the block partitioning dimension of the algebraic systems, comprised of generalized saddle point blocks. Our V-cycle GMG preconditioner uses a local Vanka-type smoother. Its action is defined in an exact mathematical way. Due to nonlocal coupling mechanisms of 348 unknowns, the smoother is applied on patches of elements. This ensures damping of higher order error frequencies. By numerical experiments of increasing complexity, the efficiency of the solver for STFEMs of different polynomial order is illustrated and confirmed. Its parallel scalability is analyzed. Beyond this study of classical performance engineering, the solver’s energy efficiency is investigated as an additional and emerging dimension in the design and tuning of algorithms on the hardware.

Worldwide communication bandwidth growth has largely been driven by (1) multimedia demands, (2) multicommunication-point demands and (3) multicommunication-rate demands, and has increased dramatically over the last two decades due to e-commerce, internet communication and the explosion of cell-phone use, in particular for in-flight services, all of which necessitate broadband use and low latency. In order to accommodate this huge surge in demand, next generation “mega-constellations” of satellites are being proposed combining a mix of heterogeneous unit types in LEO, MEO and GEO orbital shells, in order to provide continuous lower-latency and high-bandwidth service which exploits a wide-range of frequencies for fast internet connections (broadband, which is not possible with single satellite-type orbital shell systems). Accordingly, in this work, we develop a computationally-efficient digital-twin framework for a constellation of satellites around an arbitrary planet (“Planet-X”). The rapid speed of these simulations enables the ability to explore satellite infrastructure parameter combinations, represented by a multicomponent satellite constellation design vector (varvec{Lambda }{mathop {=}limits ^textrm{def}}) (number of satellites, satellite orbital radii, satellite orbital speeds, satellite types), that can deliver desired communication signal or camera coverage on “Planet-X", while simultaneously incorporating satellite infrastructural resource constraints. In order to cast the objective mathematically, we set up the system design as an inverse problem to minimize a cost function via a Genetic Machine Learning Algorithm (G-MLA), which is well-suited for nonconvex optimization. Numerical examples are provided to illustrate the framework.