engleski

Viscose Regularisation of a Softening Material

A simple bar with softening material behaviour formulated through damage mechanics is examined under tension. Graphical presentation of the energy equation in energy-displacement space demonstrates existence of multiple solutions and bifurcation points. Newton solution procedure demonstrates that the solution obtained depends only on the starting value in the iterative procedure and that it is possible to obtain physically wrong values of displacement that even does not enable localisation of the strain. On the example of a homogenous material it is demonstrated that localisation is possible even without localisation initiator but is hardly to expect because of the iterative character of the solution procedure. From the engineering standpoint we are only interested in the "physically correct" solution that can be recognised as the one with the minimum energy involved in the "solution path" (which corresponds to the minimum potential energy principle). As it is shown in the example the "physically correct" solution can be easily identified once all the solutions have been determined but it would be advantageous to find the mechanism that could lead us to that solution "from the start". Localisation initiator could be introduced in that sense but it implies certain knowledge of a failure mechanism. It is demonstrated that introduction of viscosity into model can be used as a regularisation parameter since it leads us to the correct localisation once appropriate parameters have been chosen. Also, it keeps the localised solution preserved once we have located it.

visouse regularisation; softening

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