Liu Jinxing's blog

I have an idea: In abaqus, I want to simulate crack propagation by XFEM, and meanwhile I also want to define the stress update algorithm by writing a UMAT.
Anybody wants to share related experiences?

In all textbooks, when iteration methods are introduced, the iterative formula is always H(x)x+f=0, where f is the external force applied on the system. All methods are stated when f is fixed.

Recently, I find that definitions of secant stiffness and tangent stiffness in many books seem pretty confused.Therefore, here I am giving the definitions I think correct, then give my questions on them.

Consider the equation

H(x)x+f=0

(1) Definition of tangent stiffness. As for the above equation, what is the tangent stiffness for some particular value x0?

Let's give the definition according basic knowledge of advanced mathematics. Let's consider the curve H(x)x~x. For this curve, y=H(x)x, so the tangent at x0 is

A question has arised when I read a book about fracture mechanics recently.

This question is about the calculation of potential energy in "fixed-grips" (prescribed displacement) and "dead-load" (prescribed displacement).