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Nonlinear problem

Giorgio Carta's picture

Temperature induced crack propagation in structured media

This paper describes the propagation of an edge crack in a semi-infinite triangular lattice, consisting of identical point masses connected by thermoelastic links. A change of temperature, represented by a time-periodic series of high-gradient temperature pulses, is applied at the boundary of the lattice. In order to make the initial crack advance in the lattice a failure criterion is imposed, whereby the links break as soon as they attain a prescribed elongation.

Solving nonlinear equilibrium problem

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I am trying to solve (for equilibrium points) a geometrically nonlinear problem of the form

f(u) = F

where u is the displacement and F is the load. At first I tried the plain

Newton method, with, perhaps obviously, limited success. I then tried to use

linesearch and trustregion strategies to improve the situation. Eventually, however,

I realized that I needed to use some form of continuation method. Though the most

commonly used methods in mechanics seems to be based on gradually increasing the

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