Computational Mechanics最新文献

In this paper, we propose a general deterministic framework to question the relevance, assess the quality, and ultimately choose the features (in terms of model class and discretization mesh) of the employed computational mechanics model when performing parameter identification. The goal is to exploit both modeling and data at best, with optimized model accuracy and computational cost governed by the richness of available experimental information. Using the modified Constitutive Relation Error concept based on reliability of information and the construction of optimal admissible fields, we define rigorous quantitative error indicators that point out individual sources of error contained in the identified computational model with regards to (noisy) observations. An associated adaptive strategy is then proposed to automatically select, among a hierarchical list with increasing complexity, some parameterized mathematical model and finite element mesh which are consistent with the content of experimental data. In addition, the approach is computationally enhanced by the complementary use of model reduction techniques and specific nonlinear solvers. We focus here on experimental information given by full-field kinematic measurements, e.g. obtained by means of digital image correlation techniques, even though the proposed strategy would also apply to sparser data. The performance of the approach is analyzed and validated on several numerical experiments dealing with anisotropic linear elasticity or nonlinear elastoplastic models, and using synthetic or real observations.

Mass scaling is widely used in finite element models of structural dynamics for increasing the critical time step of explicit time integration methods. While the field has been flourishing over the years, it still lacks a strong theoretical basis and mostly relies on numerical experiments as the only means of assessment. This contribution thoroughly reviews existing methods and connects them to established linear algebra results to derive rigorous eigenvalue bounds and condition number estimates. Our results cover some of the most successful mass scaling techniques, unraveling for the first time well-known numerical observations.

The drift-diffusion formulation, modelling semiconductor materials in terms of carrier densities and electric potential, is considered together with an alternative formulation in terms of dimensionless logarithmic quantities. Stability of both formulations in presence of sharp variations with a Galerkin Finite Element discretisation is assessed in two realistic problems: a p-n junction and an n-MOSFET device. The robustness with respect to the initial guess and the computational efficiency of the Newton-Raphson and Gummel non-linear solvers are also compared.

A computational multi-scale model is presented to predict the macroscopic hygro-mechanical behaviour of oak wood, based on detailed three-dimensional mesoscopic representations of entire oak growth rings obtained by X-ray micro-computed tomography ( $\mu$ CT). The 3D meso-structural volumes acquired by $\mu$ CT scanning consist of arrays of voxels, with the grayscale intensity values of the voxels denoting the local material densities. A level set-based image segmentation method is applied to distinguish the individual meso-structural phases, including the cell walls and voids (lumen and vessels). A dedicated algorithm based on the spatial gradient of the level set function accurately identifies the local material directions in the cell walls. The individual phases in the meso-scale cellular structure are discretized using the extended finite element method. Here, a moment fitting scheme is applied for an efficient numerical integration in the elements intersected by cell wall boundaries. Finally, asymptotic homogenization is used for computing the effective macro-scale response of oak wood from the hygro-mechanical response of the underlying meso-structure. The macro-scale hygro-mechanical behaviour calculated by the multi-scale model for oak growth rings agrees well with experimental values from the literature. Further, the meso-scale response computed for oak growth rings subjected to a representative moisture content variation allows to identify local, critical sites in which mesoscopic hygro-mechanical damage may occur. The effective hygro-mechanical properties calculated by the multi-scale model may serve as an input for predicting the moisture-dependent mechanical response of oak wood structures and objects subjected to arbitrary hygro-mechanical loading paths.

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.