Computational Mechanics最新文献

Abstract

This paper presents an approach to evaluate the failure of arbitrarily inclined interfaces using FE models with structured spatial discretization, providing accurate prediction of crack propagation along paths known a priori that are not constrained to the element boundaries. The combination of algorithms for the generation of structured discretization of representative polycrystalline microstructures with novel cohesive element formulations allow modelling the failure of complex topologies along rasterised boundaries, with noticeably higher computational efficiency and comparable accuracy. Two formulations of raster cohesive elements are presented, adopting either elastic-brittle or Tvergaard–Hutchinson traction separation laws. The formulations proposed are first validated comparing the failure of the interface within bi-crystal structures discretised using hexahedral elements either within a structured mesh (i.e. with rasterised boundaries) or an unstructured mesh (i.e. with planar boundary). Subsequently, the effectiveness of the formulations is demonstrated comparing the inter-granular crack propagation within complex polycrystalline microstructures. The behaviour of the novel cohesive element formulation in structured meshes consisting of regular hexahedral elements is in excellent agreement with the deformation and failure of classic cohesive element formulations placed along the planar boundaries of unstructured meshes consisting of tetrahedral elements. The higher computational cost of the raster cohesive elements is more than compensated by the increase in computational efficiency of structured meshes when compared to unstructured meshes, leading to a reduction of the simulation time of up to over 200 times for the simulations presented in the paper, thus allowing the simulation of large domains.

Time discontinuous Galerkin space-time finite element method (ST/FEM) can be used for developing arbitrary high-order accurate and unconditionally stable time integration schemes for elastodynamics problems. The existing ST/FEMs can be classified as the single-field and two-field ST/FEM: in the former method, either displacement or velocity, is independent and discontinuous in time. In contrast, in the latter method, both displacement and velocity fields are independent and discontinuous in time. Both methods have third-order accuracy for linear interpolation in time, higher than typical time integration schemes used in semi-discretized. However, these methods currently lack a unified computational framework, so each method requires a separate implementation. Therefore, the main goal of the present study is to develop a generalized computational framework that can facilitate the derivation and implementation of the existing linear-in-time ST/FEMs in a unified manner. This framework is developed by realizing that existing methods differ through the treatments of displacement-velocity relationships, which can be unified through displacement functions. In addition, by employing this framework, a new ST/FEM, which is designated as LC v-ST/FEM, is derived from the linear combination of displacement functions of single-field and two-field ST/FEMs. LC v-ST/FEM contains a user-defined parameter (alpha in [0,1]), which can be used for controlling the high-frequency dissipation characteristics. From finite difference analysis and numerical solutions of benchmark problems, it is demonstrated that the proposed method is the third order accurate in time, unconditionally stable, and contains negligible numerical dispersion error for all (0 le alpha le 1). Moreover, for (alpha ne 0), the method can attenuate the spurious high-frequency components from the velocity and displacement fields.

An alternative approach is proposed and applied to solve boundary value problems within the strain gradient elasticity theory. A mixed variation formulation of the finite element method (FEM) based on the concept of the Galerkin method is used. To construct finite-dimensional subspaces separate approximations of displacements, deformations, stresses, and their gradients are implemented by choosing the different sets of piecewise polynomial basis functions, interrelated by the stability condition of the mixed FEM approximation. This significantly simplifies the pre-requirement for approximating functions to belong to class C¹ and allows one to use the simplest triangular finite elements with a linear approximation of displacements under uniform or near-uniform triangulation conditions. Global unknowns in a discrete problem are nodal displacements, while the strains and stresses and their gradients are treated as local unknowns. The conditions of existence, uniqueness, and continuous dependence of the solution on the problem’s initial data are formulated for discrete equations of mixed FEM. These are solved by a modified iteration procedure, where the global stiffness matrix for classical elasticity problems is treated as a preconditioning matrix with fictitious elastic moduli. This avoids the need to form a global stiffness matrix for the problem of strain gradient elasticity since it is enough to calculate only the residual vector in the current approximation. A set of modeling plane crack problems is solved. The obtained solutions agree with the results available in the relevant literature. Good convergence is achieved by refining the mesh for all scale parameters. All three problems under study exhibit specific qualitative features characterizing strain gradient solutions namely crack stiffness increase with length scale parameter and cusp-like closure effect.

The present endeavour numerically exploits the use of a phase-field model to simulate and investigate fracture patterns, deformation mechanisms, damage, and mechanical responses in a human vertebra after the incision of pedicle screws under compressive regimes. Moreover, the proposed phase field framework can elucidate scenarios where different damage patterns, such as crack nucleation sites and crack trajectories, play a role after the spine fusion procedure, considering several simulated physiological movements of the vertebral body. Spatially heterogeneous elastic properties and phase field parameters have been computationally derived from bone density estimation. A convergence analysis has been conducted for the vertebra-screws model, considering several mesh refinements, which has demonstrated good agreement with the existing literature on this topic. Consequently, by assuming different angles for the insertion of the pedicle screws and taking into account a few vertebral motion loading regimes, a plethora of numerical results characterizing the damage occurring within the vertebral model has been derived. Overall, the phase field results confirm and enrich the current literature, shed light on the medical community, which will be useful in enhancing clinical interventions and reducing post-surgery bone failure and screw loosening. The proposed computational approach also investigates the effects in terms of fracture and mechanical behaviour of the vertebral-screws body within different metastatic lesions opening towards major life threatening scenarios.

The present study aims to develop an original solid-like shell element for large deformation analysis of hyperelastic shell structures in the context of isogeometric analysis (IGA). The presented model includes a new variable to describe the thickness change of the shell and allows for the application of unmodified three-dimensional constitutive laws defined in curvilinear coordinate systems and the analysis of variable thickness shells. In this way, the thickness locking affecting standard solid-shell-like models is cured by enhancing the thickness strain by exploiting a hierarchical approach, allowing linear transversal strains. Furthermore, a patch-wise reduced integration scheme is adopted for computational efficiency reasons and to annihilate shear and membrane locking. In addition, the Mixed-Integration Point (MIP) format is extended to hyperelastic materials to improve the convergence behaviour, hence the efficiency, in Newton iterations. Using benchmark problems, it is shown that the proposed model is reliable and resolves locking issues that were present in the previously published isogeometric solid-shell formulations.

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.