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The finite element method has become the most powerful tool for structural analysis. During the last decades, the method has matured to such a state that it can be massively used in practical engineering. However, it is often applied without good understanding of the method's background, leading to incorrect results and inadequate design, possibly causing damage or failure of the structure. A good way to prevent these undesirable effects is to check the quality of the obtained solution. If the results do not meet the prescribed level of accuracy, the discretization of the problem must be adequately adjusted and the problem recalculated. This process of solution enhancement is called the adaptive analysis. One of the advantages of the adaptive finite element analysis is that it can be reliably used by designers without extensive experience and deep understanding of the physical processes acting in the structure and with only limited knowledge of finite element theory.

A very natural goal of the adaptive finite element analysis is to calculate solution of the governing partial differential equation with uniformly distributed error not exceeding a prescribed threshold in the most economical manner. This is achieved by improving the discretization in areas where the finite element solution is not adequate. It is therefore essential to have a quantitative assessment of the quality of the approximate solution and a capability of discretization enrichment.

The aim of this paper is to show the integration of individual components of the h-adaptive analysis into a single framework that can be used for adaptive simulation of behaviour of materials with softening. The remainder of the paper is structured as follows. Firstly, the regularization of the adopted material model using the nonlocal continuum concept is described. Then the philosophy of the residual-based error estimation is recalled. The employed refinement strategy is briefly mentioned afterwards. In the next section, the individual components of the h-adaptive analysis and their integration into a functional unit are outlined. The application of the presented adaptive framework is demonstrated on an example. And finally, some concluding remarks are made.

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Daniel Rypl