Computational Mechanics最新文献

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.

Fatigue simulation requires accurate modeling of unloading and reloading. However, classical ductile damage models treat deformations after complete failure as irrecoverable—which leads to unphysical behavior during unloading. This unphysical behavior stems from the continued accumulation of plastic strains after failure, resulting in an incorrect stress state at crack closure. As a remedy, we introduce a discontinuous strain in the additive elasto-plastic strain decomposition, which absorbs the excess strain after failure. This allows representing pre- and post-cracking regimes in a fully continuous setting, wherein the transition from the elasto-plastic response to cracking can be triggered at any arbitrary stage in a completely smooth manner. Moreover, the presented methodology does not exhibit the spurious energy release observed in hybrid approaches. In addition, our approach guarantees mesh-independent results by relying on a characteristic length scale—based on the discretization’s resolution. We name this new methodology the discontinuous strain method. The proposed approach requires only minor modifications of conventional plastic-damage routines. To convey the method in a didactic manner, the algorithmic modifications are first discussed for one- and subsequently for two-/three-dimensional implementations. Using a simple ductile constitutive model, the discontinuous strain method is validated against established two-dimensional benchmarks. The method is, however, independent of the employed constitutive model. Elastic, plastic, and damage models may thus be chosen arbitrarily. Furthermore, computational efforts associated with the method are minimal, rendering it advantageous for accurately representing low-cycle fatigue but potentially also for other scenarios requiring a discontinuity representation within a plastic-damage framework. An open-source implementation is provided to make the proposed method accessible.

This paper presents an effective high-fidelity multi-physics model for metal additive manufacturing (AM). Using a mixed interface-capturing/interface-tracking approach, the model integrates level set and variational multiscale formulation for thermal multi-phase flows and explicitly handles the gas-metal interface evolution without mesh motion and re-meshing schemes. We integrate the mixed formulation with an energy-conservative ray tracing-based laser model and a mass-fixing algorithm that accounts for phase transitions. First, we present the mathematical details of the proposed model. Then, we apply the model to simulate the NIST A-AMB2022-01 Benchmark test, emphasizing the prediction of thermal history, laser absorption rate, melt pool dimensions, and pore formation. The results show the model’s strong capability to accurately capture the complex physics of metal AM processes and its potential in simulation-based process optimization.

In this paper, we present a discrete formulation of nonlinear shear- and torsion-free rods introduced by Gebhardt and Romero (Acta Mechanica 232(10):3825–3847, 2021) that uses isogeometric discretization and robust time integration. Omitting the director as an independent variable field, we reduce the number of degrees of freedom and obtain discrete solutions in multiple copies of the Euclidean space (left( mathbb {R}^3right) ), which is larger than the corresponding multiple copies of the manifold (left( mathbb {R}^3 varvec{times } S^2right) ) obtained with standard Hermite finite elements. For implicit time integration, we choose the same integration scheme as Gebhardt and Romero in (2021) that is a hybrid form of the midpoint and the trapezoidal rules. In addition, we apply a recently introduced approach for outlier removal by Hiemstra et al. (Comput Methods Appl Mech Eng 387:114115, 2021) that reduces high-frequency content in the response without affecting the accuracy, ensuring robustness of our nonlinear discrete formulation. We illustrate the efficiency of our nonlinear discrete formulation for static and transient rods under different loading conditions, demonstrating good accuracy in space, time and the frequency domain. Our numerical example coincides with a relevant application case, the simulation of mooring lines.

The material point method (MPM) is a hybrid Eulerian Lagrangian simulation technique for solid mechanics with significant deformation. Structured background grids are commonly employed in the standard MPM, but they may give rise to several accuracy problems in handling complex geometries. When using (2D) unstructured triangular or (3D) tetrahedral background elements, however, significant challenges arise (e.g., cell-crossing error). Substantial numerical errors develop due to the inherent ({mathcal {C}}^0) continuity property of the interpolation function, which causes discontinuous gradients across element boundaries. Prior efforts in constructing ({mathcal {C}}^1) continuous interpolation functions have either not been adapted for unstructured grids or have only been applied to 2D triangular meshes. In this study, an unstructured moving least squares MPM (UMLS-MPM) is introduced to accommodate 2D and 3D simplex tessellation. The central idea is to incorporate a diminishing function into the sample weights of the MLS kernel, ensuring an analytically continuous velocity gradient estimation. Numerical analyses confirm the method’s capability in mitigating cell crossing inaccuracies and realizing expected convergence.

The space–time (ST) computational method “ST-SI-TC-IGA” and recently-introduced complex-geometry isogeometric analysis (IGA) mesh generation methods have enabled high-fidelity computational analysis of tire aerodynamics with near-actual tire geometry, road contact, tire deformation, and aerodynamic influence of the car body. The tire geometries used in the computations so far included the longitudinal and transverse grooves. Here, we bring the tire geometry much closer to an actual tire geometry by using a complex, asymmetric tread pattern. The complexity of the tread pattern required an updated version of the NURBS Surface-to-Volume Guided Mesh Generation (NSVGMG) method, which was introduced recently and is robust even in mesh generation for complex shapes with distorted boundaries. The core component of the ST-SI-TC-IGA is the ST Variational Multiscale (ST-VMS) method, and the other key components are the ST Slip Interface (ST-SI) and ST Topology Change (ST-TC) methods and the ST Isogeometric Analysis (ST-IGA). They all play a key role. The ST-TC, uniquely offered by the ST framework, enables moving-mesh computation even with the topology change created by the contact between the tire and the road. It deals with the contact while maintaining high-resolution flow representation near the tire.The computational analysis we present is the first of its kind and shows the effectiveness of the ST-SI-TC-IGA and NSVGMG in tire aerodynamic analysis with complex tread pattern, road contact, and tire deformation.