9 Search Results

In many applications, physical domains are geometrically complex making it challenging to perform coarse-scale approximation. A defeaturing process is often used to simplify the domain in preparation for approximation and analysis at the coarse scale. In this paper, a methodology is presented for constructing a coarse-scale reproducing basis on geometrically complex domains given an initial fine-scale mesh of the fully featured domain. The initial fine-scale mesh can be of poor quality and extremely refined. The construction of the basis functions begins with a coarse-scale covering of the domain and generation of weighting functions with local support. Manifold geodesics are usedmore » to define distances within the local support for general applicability to non-convex domains. Conventional moving least squares is used to construct the coarse-scale reproducing basis. Applications in quasi-interpolation and linear elasticity are presented.« less

The paper deals with a new effective numerical technique on unfitted Cartesian meshes for simulations of heterogeneous elastic materials. Here, we develop the optimal local truncation error method (OLTEM) with 27- point stencils (similar to those for linear finite elements) for the 3-D time-independent elasticity equations with irregular interfaces. Only displacement unknowns at each internal Cartesian grid point are used. The interface conditions are added to the expression for the local truncation error and do not change the width of the stencils. The unknown stencil coefficients are calculated by the minimization of the local truncation error of the stencil equationsmore » and yield the optimal second order of accuracy for OLTEM with the 27-point stencils on unfitted Cartesian meshes. A new post-processing procedure for accurate stress calculations has been developed. Similar to basic computations it uses OLTEM with the 27-point stencils and the elasticity equations. The post-processing procedure can be easily extended to unstructured meshes and can be independently used with existing numerical techniques (e.g., with finite elements). Numerical experiments show that at an accuracy of 0.1% for stresses, OLTEM with the new post-processing procedure significantly (by 10⁵-10⁹ times) reduces the number of degrees of freedom compared to linear finite elements. OLTEM with the 27-point stencils yields even more accurate results than high-order finite elements with wider stencils.« less

An improved electrical contact resistance (ECR) model for elastic rough electrode contact is proposed, incorporating the effects of asperity interactions and temperature rise by frictional and joule heating. The analytical simulation results show that the ECR decreases steeply at the beginning of the contact between Al and Cu. However, it becomes stabilized after reaching a specific contact force. It is also found that the longer elapsed sliding contact time, the higher ECR due to the increase in electrical resistivity of electrode materials by the frictional temperature rise at the interface. The effects of surface roughness parameters on ECR are studiedmore » through the 3² full-factorial design-of-experiment analysis. Based on the two representative roughness parameters, i.e., root-mean-square (rms) roughness and asperity radius, their individual and coupled effects on the saturated ECR are examined. The saturated ECR increases with the rms roughness for a rough machined surface condition, but it is hardly affected by the asperity radius. On the other hand, the saturated ECR increases with both the rms roughness and the asperity radius under a smooth thin film surface condition.« less

This study employs nonlinear ultrasonic techniques to track microstructural changes in additively manufactured metals. The second harmonic generation technique based on the transmission of Rayleigh surface waves is used to measure the acoustic nonlinearity parameter, β. Stainless steel specimens are made through three procedures: traditional wrought manufacturing, laser-powder bed fusion, and laser engineered net shaping. The β parameter is measured through successive steps of an annealing heat treatment intended to decrease dislocation density. Dislocation density is known to be sensitive to manufacturing variables. In agreement with fundamental material models for the dislocation-acoustic nonlinearity relationship in the second harmonic generation, βmore » drops in each specimen throughout the heat treatment before recrystallization. Geometrically necessary dislocations (GNDs) are measured from electron back-scatter diffraction as a quantitative indicator of dislocations; average GND density and β are found to have a statistical correlation coefficient of 0.852 showing the sensitivity of β to dislocations in additively manufactured metals. Moreover, β shows an excellent correlation with hardness, which is a measure of the macroscopic effect of dislocations.« less

General polyhedral discretizations offer several advantages over classical approaches consisting of standard tetrahedra and hexahedra. These include increased flexibility and robustness in the meshing of geometrically complex domains and higher-quality solutions for both finite element and finite volume schemes. Currently, the use of general polyhedra is hampered by the lack of general-purpose polyhedral meshing algorithms and software. One approach for generating polyhedral meshes is the use of tetrahedral subdivisions and dual-cell aggregation. In this approach, each tetrahedron of an existing tetrahedral mesh is subdivided using one of several subdivision schemes. Polyhedral-dual cells may then be formed and formulated as finitemore » elements with shape functions obtained through the use of generalized barycentric coordinates. We explore the use of dual-cell discretizations for applications in nonlinear solid mechanics using a displacement-based finite element formulation. We present verification examples that yield optimal rates of convergence. Accuracy of the methodology is demonstrated via several nonlinear examples that include large deformation and plasticity.« less

Meshfree methods for solid mechanics have been in development since the early 1990's. Initial motivations included alleviation of the burden of mesh creation and the desire to overcome the limitations of traditional mesh-based discretizations for extreme deformation applications. Here, the accuracy and robustness of both mesh-free and meshbased Lagrangian discretizations are compared using manufactured extreme-deformation fields. For the meshfree discretizations, both moving least squares and maximum entropy are considered. Quantitative error and convergence results are presented for the best approximation in the H¹ norm.

Here, the repetitive rapid solidification that occurs in metal additive manufacturing (AM) processes creates microstructures distinctly different from wrought materials. Local variability in AM microstructures (either by design or unintentional) raises questions as to how AM structures should be modeled at the part-scale to minimize modeling error. The key goal of this work is to demonstrate a posteriori error estimation applied to an AM part. It is assumed that the actual microstructure is unknown and an approximate, spatially uniform material model is used. Error bounds are calculated for many reference models based on AM microstructures with elongated grain morphology andmore » localized or global fiber textures during a post-processing step. The current findings promote confidence that a posteriori model form error estimation could be used effectively in mechanical performance simulations of AM parts to quickly obtain quantitative error metrics between an approximate model result and many microstructure-based reference models. The a posteriori error estimation introduces significant time savings compared to computing the full reference model solutions. Tight bounds on model form error are obtained when texture variations in the reference models occur on large length scales. For materials with property variation at small length scales, multi-scale error estimation techniques are needed to properly account for the many interfaces present between areas with different properties.« less

In engineering practice, models are typically kept as simple as possible for ease of setup and use, computational efficiency, maintenance, and overall reduced complexity to achieve robustness. In solid mechanics, a simple and efficient constitutive model may be favored over one that is more predictive, but is difficult to parameterize, is computationally expensive, or is simply not available within a simulation tool. In order to quantify the modeling error due to the choice of a relatively simple and less predictive constitutive model, we adopt the use of a posteriori model-form error-estimation techniques. Based on local error indicators in the energymore » norm, an algorithm is developed for reducing the modeling error by spatially adapting the material parameters in the simpler constitutive model. The resulting material parameters are not material properties per se, but depend on the given boundary-value problem. As a first step to the more general nonlinear case, we focus here on linear elasticity in which the “complex” constitutive model is general anisotropic elasticity and the chosen simpler model is isotropic elasticity. As a result, the algorithm for adaptive error reduction is demonstrated using two examples: (1) A transversely-isotropic plate with hole subjected to tension, and (2) a transversely-isotropic tube with two side holes subjected to torsion.« less

Two fundamental approximations in macroscale solid-mechanics modeling are (1) the assumption of scale separation in homogenization theory and (2) the use of a macroscopic plasticity material model that represents, in a mean sense, the multitude of inelastic processes occurring at the microscale. With the goal of quantifying the errors induced by these approximations on engineering quantities of interest, we perform a set of direct numerical simulations (DNS) in which polycrystalline microstructures are embedded throughout a macroscale structure. The largest simulations model over 50,000 grains. The microstructure is idealized using a randomly close-packed Voronoi tessellation in which each polyhedral Voronoi cellmore » represents a grain. An face centered cubic crystal-plasticity model is used to model the mechanical response of each grain. The overall grain structure is equiaxed, and each grain is randomly oriented with no overall texture. The detailed results from the DNS simulations are compared to results obtained from conventional macroscale simulations that use homogeneous isotropic plasticity models. The macroscale plasticity models are calibrated using a representative volume element of the idealized microstructure. Furthermore, we envision that DNS modeling will be used to gain new insights into the mechanics of material deformation and failure.« less