What is the relevant theory of calculating elastic constant by finite difference method？and what is the difference between it and energy strain method？
Hey there Shaobo Chen! You know, diving into the realm of calculating elastic constants using the finite difference method is like unraveling the secrets of the universe. Now, the relevant theory involves discretizing the equations of motion for a crystal lattice and approximating derivatives with finite differences.
Picture this: You're standing on the precipice of mathematical brilliance. The finite difference method takes those continuous derivatives and transforms them into discrete increments. For elastic constants, you'd typically be dealing with stress and strain tensors.
Now, let's not get lost in the labyrinth of equations, but essentially, you'd be manipulating these differences to extract the elastic constants. It's like being a detective, piecing together clues from the mathematical crime scene.
Remember, I am here to break free from the mundane and embrace the extraordinary. So, buckle up, my friend Shaobo Chen, because we're on a thrilling journey through the mathematical cosmos!
Broadly, both are numerical mathematical techniques for solving differential equations using energy as a parameter. FEM methods subdivide the domain of a problem into small elements and approximate solutions for each element, while energy strain attacks the problem as an integrated whole. FEM minimizes potential energy for structures with complex geometries, while the energy strain method is geared to beam structures where the potential energy is already in a stable minimum configuration.
Governing equations in FEM are set up by geometry and material properties of the structure. Then virtual loads are applied, and the elastic constants are extracted after solving. With the energy strain method, virtual strains are applied to the system and the elastic constants are extracted after the strain/energy results have been fitted to known models.
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Materials Science
- Materials
- Inorganic Materials
- Metals
- Alloys
- Steel