A generalized finite element method for grain-boundary sliding in polycrystals (2024)

FAQs

What is Generalised finite element method? ›

Generalized finite element method

Then a partition of unity is used to “bond” these spaces together to form the approximating subspace. The effectiveness of GFEM has been shown when applied to problems with domains having complicated boundaries, problems with micro-scales, and problems with boundary layers.

In contrast, polycrystalline materials are composed of multiple smaller crystalline grains with varying orientations. The region where these grains meet is called a grain boundary, which can act as a barrier to dislocation motion and lead to improved mechanical strength.

It is generally accepted that grain boundary sliding occurs by the motion of dislocations rather than simultaneous shear of the entire boundary. Different models for GBS have been proposed on the basis of the movement of lattice or grain boundary dislocations (GBDs).

The finite element method (FEM) has effectively predicted and verified vibration problems. In the quest to analyze the dynamic response of a flat plate subjected to various moving loads, the FEM approach was employed. Plate elements were utilized to carry out the analysis.

Engineers use FEM when they need to develop an adoptable design that's practical but not necessarily perfect for a particular application. FEA: The mathematical equations behind FEM are applied to create a simulation, or what's known as a finite element analysis (FEA).

FEM can be used, for example, to determine the structural mechanics of different parts of a car under different loading conditions, the heat flow through engine part, or the distribution of electromagnetic radiation from an antenna.

Explanation: Positron annihilation technique is used to measure resistivity after quenching, Thermal imaging this technique is used to measure the concentration of vacancy to determine the activation energy for its formation and Photo micrographic technique is used to determine the grain size of polycrystalline ...

Grain boundaries are two-dimensional defects in the crystal structure, and tend to decrease the electrical and thermal conductivity of the material. Most grain boundaries are preferred sites for the onset of corrosion and for the precipitation of new phases from the solid.

The grain growth process (dislocation nucleation from the GBs) can be roughly divided into three stages: (i) rapid decline stage, the liquid phase gradually disappears, the grain grows rapidly, and the free energy decreases rapidly with the progress of solidification; (ii) slow decline stage, the internal stress ...

A Grain Boundary is a general planar defect that separates regions of different crystalline orientation (i.e. grains) within a polycrystalline solid.

How do grain boundaries affect strength of a material? ›

Grain boundaries are essentially a wall of dislocations and also hinder dislocation movement. If grain growth is limited, there will be a higher number of smaller grains, which can be considered "finer" in terms of the grain structure. More grain boundaries mean less dislocation movement and higher strength.

Transform plate boundaries are where plates slide laterally past one another, producing shallow earthquakes but little or no volcanic activity.

The finite element method is a systematic way to convert the functions in an infinite dimensional function space to first functions in a finite dimensional function space and then finally ordinary vectors (in a vector space) that are tractable with numerical methods.

Process: Divide the object into finite elements via meshing and apply the relevant physics representations and/or equations to each element. Then assemble the equations and solve them. Post-process: Compute results to analyze and interpret implications for the whole domain.

Ansys Mechanical is a finite element analysis (FEA) software used to perform structural analysis using advanced solver options, including linear dynamics, nonlinearities, thermal analysis, materials, composites, hydrodynamic, explicit, and more.

FEM: FEM naturally conserves mass, momentum, and energy due to its variational formulation. FDM: FDM can directly handle conservation laws by discretizing the derivatives in the governing equations. FVM: FVM is inherently conservative as it integrates the governing equations over control volumes, ensuring conservation.

Generalized finite difference method (GFDM) The basic idea of the GFDM is to utilize Taylor series expansions and moving least-squares method to express the derivatives at a given node as linear summation of its neighboring nodal values.

The finite element formulation is a straightforward application of the above displacement-based minimum principle, in exactly the same way as for classical elastic continuum problems, by discretizing both the matrix material domain and reinforcement beam into (for instance) triangular elements, as shown in Figure 1.4 ...

The finite volume method is essentially a three-dimensional application of the well-known finite difference method. Like the FEM, the FVM seeks to reduce the exact governing differential equations to approximate algebraic equations.