Computational Mechanics最新文献

An improved thermomechanical analysis of the evolution of the stress and plastic strain fields near the melt pool has been developed for the Electron Beam Powder Bed Fusion (PBF-EB) process. The analysis focuses on a sub-domain extracted from a larger component, which includes the sequential addition and melt/consolidation of 4 powder layers on a solid substrate. The material’s behavior was described as a function of temperature and material form (powder, semi-consolidated, bulk, and liquid). The yield stress was described as a function of temperature and strain rate to capture key phenomena related to plastic strain accumulation. The thermal component of the model has been validated using melt pool geometry. The importance of the strain rate-dependent yield stress and substrate temperature were identified. Yielding was predicted to occur in the solid directly below the melt pool in association with rapid heating and, to a lesser extent, during cooling in the wake of the melt pool as it solidifies. A linear regression model was proposed, linking the developed compressive plastic strain to substrate temperature for a single set of beam parameters. The model was validated by comparing the substrate temperatures needed to produce the same plastic strains used to predict the distortion in a component with a ledge-type feature fabricated in a commercial PBF-EB machine. It is proposed that the linear regression model may be used to estimate the strain variation in large components as a function of the varying thermal field in the newly consolidated material (the substrate) during component fabrication.

This work explores connections between FFT-based computational micromechanics and a homogenization approach based on the finite Radon transform introduced by Derraz and co-workers. We revisit periodic homogenization from a Radon point of view and derive the multidimensional Radon series representation of a periodic function from scratch. We introduce a general discretization framework based on trigonometric polynomials which permits to represent both the classical Moulinec-Suquet discretization and the finite Radon approach by Derraz et al. We use this framework to introduce a novel Radon framework which combines the advantages of both the Moulinec-Suquet discretization and the Radon approach, i.e., we construct a discretization which is both convergent under grid refinement and is able to represent certain non-axis aligned laminates exactly. We present our findings in the context of small-strain mechanics, extending the work of Derraz et al. that was restricted to conductivity and report on a number of interesting numerical examples.

This paper addresses the numerical modeling of brittle fracture using a phase field approach. We propose solving the coupled phase field / displacement problem by employing the scaled boundary finite element method, which facilitates the use of hierarchical meshes. An adaptive meshing approach based on this method is summarized. Contrary to existing applications of the scaled boundary finite element method in the context of phase field modeling, scaled boundary shape functions are employed in both staggered and monolithic solution schemes. The proposed methodology is verified considering two-dimensional benchmark problems. Very good agreement with finite element results of the force-displacement curves and crack paths is observed regardless of the solution scheme or meshing strategy.

This paper introduces a computational homogenization framework for metamaterial plates consisting of locally resonant acoustic metamaterial (LRAM) unit cells. Based on the linearity assumption, the unit cell model is simplified through the superposition of long-wavelength (quasi-static) and local resonant eigenmode solutions. This method results in closed-form expressions describing the macroscale thin plate (shell) with enriched internal variable fields representing the amplitudes of the local resonant eigenmodes. The homogenized macroscopic shell model is implemented using isogeometric analysis, allowing for a straightforward handling of higher-order continuity requirements. Validation against fully-resolved direct numerical simulations (DNS) is conducted, showcasing the capability of the approach in computing the dispersion spectrum of an infinite LRAM plate, as well as performing frequency and time domain analyses of a finite LRAM plate. Results demonstrate that the homogenized enriched plate model accurately predicts wave attenuation within the frequency band-gaps, vibration modes, and wave propagation outside the band-gaps, achieving significantly reduced computational cost compared to DNS. The developed homogenization framework serves as a valuable computational tool for the analysis and design of LRAM panels of finite sizes and arbitrary shape under non-trivial excitations.

We derive a three-dimensional hydrogel model as a two-phase system of a fibre network and liquid solvent, where the nonlinear elastic network accounts for the strain-stiffening properties typically encountered in biological gels. We use this model to formulate free boundary value problems for a hydrogel layer that allows for swelling or contraction. We derive two-dimensional plain-strain and plain-stress approximations for thick and thin layers respectively, that are subject to external loads and serve as a minimal model for scaffolds for cell attachment and growth. For the collective evolution of the cells as they mechanically interact with the hydrogel layer, we couple it to an agent-based model that also accounts for the traction force exerted by each cell on the hydrogel sheet and other cells during migration. We develop a numerical algorithm for the coupled system and present results on the influence of strain-stiffening, layer geometry, external load and solvent in/outflux on the shape of the layers and on the cell patterns. In particular, we discuss alignment of cells and chain formation under varying conditions.

Spatially-resolved modeling of deformation twinning and its interaction with plastic slip is achieved by coupling the phase-field method and crystal plasticity theory. The intricate constitutive relations arising from this coupling render the resulting computational model prone to inefficiencies and lack of robustness. Accordingly, together with the inherent limitations of the phase-field method, these factors may impede the broad applicability of the model. In this paper, our recent phase-field model of coupled twinning and crystal plasticity is the subject of study. We delve into the incremental formulation and computational treatment of the model and run a thorough investigation into its computational performance. We focus specifically on evaluating the efficiency of the finite-element discretization employing various element types, and we examine the impact of mesh density. Since the micromorphic regularization is an important part of the finite-element implementation, the effect of the micromorphic regularization parameter is also studied.

The Particle Finite Element Method (PFEM) is attractive for the simulation of large deformation problems, e.g. in free-surface fluid flows, fluid–structure interaction and in solid mechanics for geotechnical engineering and production processes. During cutting, forming or melting of metal, quasi-incompressible material behaviour is often considered. To circumvent the associated volumetric locking in finite element simulations, different approaches have been proposed in the literature and a stabilised low-order mixed formulation (P1P1) is state-of-the-art. The present paper compares the established mixed formulation with a higher order pure displacement element (TRI6) under 2d plane strain conditions. The TRI6 element requires specialized handling, involving the deletion and re-addition of edge-mid-nodes during triangulation remeshing. The robustness of both element formulations is analysed along with different state-variable transfer schemes, which are not yet widely discussed in the literature. The influence of the stabilisation factor in the P1P1 element formulation is investigated, and an equation linking this factor to the Poisson ratio for hyperelastic materials is proposed.

The inverse Helmholtz problem is crucial in many fields like non-destructive testing and heat conduction analysis, emphasizing the need for efficient numerical solutions. This paper investigates the parameter identification problems of the Helmholtz equation, based on the stabilized Lagrange interpolation collocation method (SLICM) associated with least-squares solution. This method circumvents the limitations of traditional meshfree methods that cannot perform accurate integrations. It offers advantages of high accuracy, good stability, and high computational efficiency, rendering it suitable for solving inverse problems. Additionally, considering potential errors in measurement data, this study employs the least squares method to directly utilize all available information from the measurement data, minimizing errors and avoiding the iterative calculations based on measurement data in the Galerkin methods. To balance the numerical errors among measurement locations, boundaries, and within the domain, this paper studies the optimal weights for the overdetermined system based on the least squares functional obtained through SLICM, achieving a global error balance. Moreover, to further mitigate the noise in measurement data, this paper introduces the Tikhonov regularization technique and selects suitable regularization parameters to process noisy data through the L-curve. Numerical results in 1D, 2D and even 3D complicated domains indicate that SLICM can attain accurate and convergent results in parameter identification, even when the noise level is as high as 10%.

Predicting the mechanics of large structural networks, such as beam-based architected materials, requires a multiscale computational strategy that preserves information about the discrete structure while being applicable to large assemblies of struts. Especially the fracture properties of such beam lattices necessitate a two-scale modeling strategy, since the fracture toughness depends on discrete beam failure events, while the application of remote loads requires large simulation domains. As classical homogenization techniques fail in the absence of a separation of scales at the crack tip, we present a concurrent multiscale technique: a fully-nonlocal quasicontinuum (QC) multi-lattice formulation for beam networks, based on a conforming mesh. Like the original atomistic QC formulation, we maintain discrete resolution where needed (such as around a crack tip) while efficiently coarse-graining in the remaining simulation domain. A key challenge is a suitable model in the coarse-grained domain, where classical QC uses affine interpolations. This formulation fails in bending-dominated lattices, as it overconstrains the lattice by preventing bending without stretching of beams. Therefore, we here present a beam QC formulation based on mixed-order interpolation in the coarse-grained region—combining the efficiency of linear interpolation where possible with the accuracy advantages of quadratic interpolation where needed. This results in a powerful computational framework, which, as we demonstrate through our validation and benchmark examples, overcomes the deficiencies of previous QC formulations and enables, e.g., the prediction of the fracture toughness and the diverse nature of stress distributions of stretching- and bending-dominated beam lattices in two and three dimensions.

Personalized computational simulations have emerged as a vital tool to understand the biomechanical factors of a disease, predict disease progression, and design personalized intervention. Material modeling is critical for realistic biomedical simulations, and poor model selection can have life-threatening consequences for the patient. However, selecting the best model requires a profound domain knowledge and is limited to a few highly specialized experts in the field. Here we explore the feasibility of eliminating user involvement and automate the process of material modeling in finite element analyses. We leverage recent developments in constitutive neural networks, machine learning, and artificial intelligence to discover the best constitutive model from thousands of possible combinations of a few functional building blocks. We integrate all discoverable models into the finite element workflow by creating a universal material subroutine that contains more than 60,000 models, made up of 16 individual terms. We prototype this workflow using biaxial extension tests from healthy human arteries as input and stress and stretch profiles across the human aortic arch as output. Our results suggest that constitutive neural networks can robustly discover various flavors of arterial models from data, feed these models directly into a finite element simulation, and predict stress and strain profiles that compare favorably to the classical Holzapfel model. Replacing dozens of individual material subroutines by a single universal material subroutine—populated directly via automated model discovery—will make finite element simulations more user-friendly, more robust, and less vulnerable to human error. Democratizing finite element simulation by automating model selection could induce a paradigm shift in physics-based modeling, broaden access to simulation technologies, and empower individuals with varying levels of expertise and diverse backgrounds to actively participate in scientific discovery and push the boundaries of biomedical simulation.