Since the previous post already obtained the stress intensity factor and energy release rate, we can use them to simulate the crack growth progress. In fracture mechanics, a typical example for energy release rate calculation is the double cantilever beam (DCB). Also, the DCB test is one of the widely used test metdho to measure the Mode I fracture toughness of different materials (ASTM D5528). This post will use a double cantilever beam to simulate the crack growth based on VCCT, this is also a classical example in Ansys document.

# Ansys central crack energy release rate

I previously analyzed the stress intensity factor for an edge crack of a plate. Now, I want to extend the previous example to calculate the crack energy release rate. The energy release rate calculation is quite straightforward since Ansys CINT supports the VCCT method to obtain the energy release rate. In this example, I move the crack to the plate center and set different material properties for the left and right side of the plate.

# Ansys reticulated shell buckling analysis

In structural analysis, the reticulated shell is one of the structure forms used for long span spatial structure design. There are several types for reticulaed shell structures. I am interested in creating such structure in Ansys. Hence, this post mainly focuses on the creation and buckling analysis for single-layer reticulated shell structure.

# Ansys crack SIF under dynamic loading

Since my study has something to do with the fatigue under dynamic loading, I have to simulate the crack behavior and its SIF with dynamic effect. Thus, this post analyzes an example including the evolution of crack stress intensity factor under dynamic loading. In the prevous post, we do not have to set the density since the model is under static analysis. However, for dynamic loading, density is critical and should be set correctly

# Ansys fracture under thermal effect

Since Ansys can support various fracture analysis types, this post analyze a typical 2D fracture behavior under the thermal effect. Unlike the general static analysis, the thermal effect analysis requires us to save the results file first. Therefore, we should split the analysis into two steps.

# Ansys 3D crack stress intensity factor

Previously, I analyzed the crack stress intensity factor for a 2D plate. An edge crack is created at the bottom of the plate and the SIF is obtained at the crack tip. When I try to create a 3D model, I found there are some difference for defining parameters associated with the crack tip. So, I create another example to determine the SIF in a 3D model.

# Ansys edge crack stress intensity factor

To determine the stress intensity factors with Ansys, we analyze the following 2D example with an edge crack. The width and height of the plate are W = 1.0 m and H = 1.0 m respectively. The left edge is fixed while the stress of 5 MPa is applied to the right edge. At the bottom edge, there exists an edge crack with the length a = 0.2 m. The thickness of the plate is 5 mm. The model is shown in the following figure,

# Abaqus accelerating explicit analysis

Working with Abaqus explicit calculations recently, I encountered a common issue: the model and materials were fine, and calculations were possible, but the computation speed was extremely slow. With the stable time increment step at the magnitude of $10^{-7}$, even simulating just one second could require thousands of hours of computation, which is impractical. After studying various sources, I’ve summarized methods to accelerate Abaqus explicit calculations.

# VS Code Fortran configuration

Despite Fortran being an ancient language, its still comes with its own set of advantages. Recently, while debugging Abaqus subroutines, I have to repeatedly running code for testing. Although the integration with Abaqus is necessary for running the entire code, the individual modules can still be tested separately. The best method for testing modules is to run them as small, standalone programs. However, VS Code does not seem to support running Fortran code directly. A useful plugin for this purpose is Code Runner, but unfortunately, it doesn’t support Fortran by default and requires some adjustments. First, let’s start with a test code.

# Calculus of variations I

Here is my notes about the calculus of variations that deals with optimizing functionals, which are mappings from a set of functions to the real numbers. It involves finding a function that minimizes or maximizes a given functional, often subject to certain constraints. This field has applications in various areas, including physics, engineering, and economics, by providing a systematic way to deal with optimization problems where the quantity to be optimized is dependent on a function.