Computational Mechanics最新文献

An inverse characterization approach to identify the in-situ elastic properties of composite constituent materials is developed. The approach relies on displacement measurements available from image-based measurement techniques such as digital image correlation and template matching. An optimization problem is formulated, where the parameters of an assumed functional form describing spatially variable material properties are obtained by minimizing the discrepancies between noisy displacement measurements and the corresponding simulated values. The proposed formulation is analyzed from a statistical inference theory standpoint. It is shown that the approach exhibits estimation consistency, i.e. given noisy input data the identified material properties converge to the true material properties as the number of available measurements increases. The performance of the proposed approach is evaluated by a series of virtual characterizations that mimic physical characterization tests in which fiber centroid displacements are obtained through fiber template matching. The virtual characterizations demonstrate that the effect of measurement noise in identifying the in-situ constituent properties can be mitigated by selecting a sufficiently large measurement dataset. The numerical studies also show that, given a rich measurement dataset, the proposed approach is able to describe increasingly complex spatial variation of properties.

Stress reconstruction based on experimentally acquired full-field strain measurements is computationally expensive when using conventional implicit stress integration algorithms. The computational burden associated with repetitive stress reconstruction is particularly relevant when inversely characterizing plastic material behaviour via inverse methods, like the nonlinear Virtual Fields Method (VFM). Spatial and temporal down-sampling of the available full-field strain data is often used to mitigate the computational effort. However, for metals subjected to non-linear strain paths, temporal down-sampling of the strain fields leads to erroneous stress states biasing the identification accuracy of the inverse method. Hence, a significant speedup factor of the stress integration algorithm is required to fully exploit the experimental data acquired by Digital Image Correlation (DIC). To this end, we propose an explicit stress integration algorithm that is independent on the number of images (i.e. strain fields) taken into account in the stress reconstruction. Theoretically, the proposed method eliminates the need for spatial and temporal down-sampling of the experimental full-field data used in the nonlinear VFM. Finally, the proposed algorithm is also beneficial in the emerging field of real-time DIC applications.

This paper introduces a continuous finite element model to simulate fluid flow-bedform interaction problems. The approach utilizes a non-oscillatory finite element algorithm to compute the fluid dynamics by solving the complete Navier–Stokes equations. Additionally, it addresses the evolution of the fluid–bedform interface as a consequence of spatially non-balanced sediment fluxes through the solution of a conservation equation for the erodible layer thickness. A sign preservation algorithm is particularly relevant for landform tracking because a positive definite thickness of the erodible sediment layer is essential to model the interaction between evolving cohesionless sediment layers and rigid beds. The fluid/terrain interface is explicitly captured through a surface tracking methodology. First, new nodes fitting the interface are incorporated into the finite element mesh; then, elements beneath this interface are deactivated, while intersected elements are restructured to get a mesh composed exclusively of tetrahedral elements. Numerical experiments demonstrate capabilities of the method by exploring relevant problems related with civil engineering, such as the evolution of trenches and the scour of a submerged pile.

A new crack-tip finite element able to improve the accuracy of Finite Element Method (FEM) solutions for cracks growing along the Winkler-type spring interfaces between linear elastic adherents is proposed. The spring model for interface fracture, sometimes called Linear-Elastic (perfectly) Brittle Interface Model (LEBIM), can be used, e.g., to analyse fracture of adhesive joints with a thin adhesive layer. Recently an analytical expression for the asymptotic elastic solution with logarithmic stress-singularity at the interface crack tip considering spring-like interface behaviour under fracture Mode III was deduced by some of the authors. Based on this asymptotic solution, a special 5-node triangular crack-tip finite element is developed. The generated special singular shape functions reproduce the radial behaviour of the first main term and shadow terms of the asymptotic solution. This special element implemented in a FEM code written in Matlab has successfully passed various patch tests with spring boundary conditions. The new element allows to model cracks in spring interfaces without the need of using excessively refined FEM meshes, which is one of the current disadvantages in the use of LEBIM when stiff spring interfaces are considered. Numerical tests carried out by h-refinement of uniform meshes show that the new singular element consistently provides significantly more accurate results than the standard finite elements, especially for stiff interfaces, which could be relevant for practical applications minimizing computational costs. The new element can also be used to solve other problems with logarithmic stress-singularities.

We describe an algorithm for generating fiber-filled volume elements for use in computational homogenization schemes which accounts for a coupling of the fiber-length and the fiber-orientation. For prescribed fiber-length distribution and fiber-orientation tensor of second order, a maximum-entropy estimate is used to produce a fiber-length-orientation distribution which mimics real injection molded specimens, where longer fibers show a stronger alignment than shorter fibers. We derive the length-orientation closure from scratch, discuss its integration into the sequential addition and migration algorithm for generating fiber-filled microstructures for industrial volume fractions and investigate the resulting effective elastic properties. We demonstrate that accounting for the length-orientation coupling permits to match the measured Young’s moduli in principal fiber direction and transverse to it more accurately than for closure approximations ignoring the length-orientation coupling.

A curved non-isoparametric Reissner–Mindlin shell element is developed for analyzing thin-walled structures. The standard kinematic description of the element requires the calculation of the director vector. To address this demand accurately, similar to isogeometric analysis (IGA), the geometry is defined by utilization of the non-uniform rational B-splines (NURBS) imported directly from computer-aided design (CAD) files. Then, shape functions of the Legendre spectral element method (SEM) are used to interpolate the displacements. Consequently, the shell director vector and Jacobian of the transformation are calculated properly according to the presented formulation. On the other hand, in Legendre SEM combined with Gauss–Lobatto–Legendre quadrature, the integration points and the element nodes coincide. Thus, the easily computable local coordinate systems at the integration points can be used directly as nodal basis systems. A separate calculation of nodal basis systems at control points, which is the source of either complexity or error in IGA shells, is not required. Given the condition number of the stiffness matrix in the developed method, super high-order elements can also be used. Very high order p-refined elements are used in addition to h-refinement of the mesh to show the capability of higher order elements to analyze problems without mesh refinement. The validity and convergence rate of the method are investigated and verified through various cases of h- and p-refinement in challenging obstacle course problems.

Abstract

This paper introduces a metamodelling technique that employs gradient-enhanced Gaussian process regression (GPR) to emulate diverse internal energy densities based on the deformation gradient tensor (varvec{F}) and electric displacement field (varvec{D}_0) . The approach integrates principal invariants as inputs for the surrogate internal energy density, enforcing physical constraints like material frame indifference and symmetry. This technique enables accurate interpolation of energy and its derivatives, including the first Piola-Kirchhoff stress tensor and material electric field. The method ensures stress and electric field-free conditions at the origin, which is challenging with regression-based methods like neural networks. The paper highlights that using invariants of the dual potential of internal energy density, i.e., the free energy density dependent on the material electric field (varvec{E}_0) , is inappropriate. The saddle point nature of the latter contrasts with the convexity of the internal energy density, creating challenges for GPR or Gradient Enhanced GPR models using invariants of (varvec{F}) and (varvec{E}_0) (free energy-based GPR), compared to those involving (varvec{F}) and (varvec{D}_0) (internal energy-based GPR). Numerical examples within a 3D Finite Element framework assess surrogate model accuracy across challenging scenarios, comparing displacement and stress fields with ground-truth analytical models. Cases include extreme twisting and electrically induced wrinkles, demonstrating practical applicability and robustness of the proposed approach.

The aim of this work is the derivation and examination of a material model, accounting for large elastic deformations, coupled with species diffusion and thermal effects. This chemo-thermo-mechanical material model shows three key aspects regarding its numerical formulation. Firstly, a multiplicative split of the deformation gradient into a mechanical, a swelling and a thermal part. Secondly, temperature-scaled gradients for a numerical design comprising symmetric tangents and, thirdly, dissipation potentials for the modelling of dissipative effects. Additionally, the derived general material model is specialised to thermoresponsive hydrogels to study its predictive capabilities for a relevant example material class. An appropriate finite element formulation is established and its implementation discussed. Numerical examples are investigated, including phase transition and stability phenomena, to verify the ability of the derived chemo-thermo-mechanical material model to predict relevant physical effects properly. We compare our results to established models in the literature and discuss emerging deviations.

The Smoothed Particle Finite Element Method (SPFEM) has gained popularity as an effective numerical method for modelling geotechnical problems involving large deformations. To promote the research and application of SPFEM in geotechnical engineering, we present ESPFEM2D, an open-source two-dimensional SPFEM solver developed using MATLAB. ESPFEM2D discretizes the problem domain into computable particle clouds and generates the finite element mesh using Delaunay triangulation and the ( alpha )-shape technique to resolve mesh distortion issues. Additionally, it incorporates a nodal integration technique based on strain smoothing, effectively eliminating defects associated with the state variable mapping after remeshing. Furthermore, the solver adopts a simple yet robust approach to prevent the rank-deficiency problem due to under-integration by using only nodes as integration points. The Drucker-Prager model is adopted to describe the soil’s constitutive behavior as a demonstration. Implemented in MATLAB, this open-source solver ensures easy accessibility and readability for researchers interested in utilizing SPFEM. ESPFEM2D can be easily extended and effectively coupled with other existing codes, enabling its application to simulate a wide range of large geomechanical deformation problems. Through rigorous validation using four numerical examples, namely the oscillation of an elastic cantilever beam, non-cohesive soil collapse, cohesive soil collapse, and slope stability analysis, the accuracy, effectiveness and stability of this open-source solver have been thoroughly confirmed.

The Carrier-Domain Method was introduced for high-resolution computation of time-periodic long-wake flows. The cost-effectiveness of the method makes such computations practical in 3D. A short segment of the wake domain, the carrier domain, moves in the free-stream direction, from the beginning of the long wake domain to the end. The data at the moving inflow plane comes from the time-periodic data computed at an earlier position of the carrier domain. With the high mesh resolution that can easily be afforded over the short domain segment, the wake flow patterns can be carried, with superior accuracy, far downstream. Computing the long-wake flow with a high-resolution moving mesh that covers a short segment of the wake domain at any instant during the computation would certainly be far more cost-effective than computing it with a high-resolution fixed mesh that covers the entire length. We present high-resolution 3D computation of time-periodic long-wake flow for a cylinder and a wind turbine, both computed with isogeometric discretization and the Space–Time Variational Multiscale method. In the isogeometric discretization, the basis functions are quadratic NURBS in space and linear in time. The cylinder flow is at Reynolds number 100. At this Reynolds number, the flow has an easily discernible vortex shedding period. The wake flow is computed up to 350 diameters downstream of the cylinder, far enough to see the secondary vortex street. In the wind turbine long-wake flow computation, the velocity data at the inflow boundary of the wake domain comes from an earlier wind turbine computation, with the turbine rotor having a diameter of ({126},hbox {m}), extracted by projection from a plane located ({10},hbox {m}) downstream of the turbine. The wake flow is computed up to ({482},hbox {m}) downstream of the wind turbine. In both the cylinder and wind turbine wake flow computations, the flow patterns obtained with the full domain and carrier domain show a near-perfect match, clearly demonstrating the effectiveness and practicality of the Carrier-Domain Method in high-resolution 3D computation of time-periodic long-wake flows.