SUMMARYThe object of this work is to discuss a further improvement of the material force method for nonlinear hyperelastostatic fracture mechanics. We investigate the accuracy of the material force method within a 'modiÿed boundary layer'-formulation using a Ramberg-Osgood material type for the sake of comparison. The proposed improvement leads to a reliable and very accurate method to compute the vectorial J -integral in fracture mechanics.

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SUMMARYThis paper deals with shape optimization of continuous structures. As in early works on shape optimization, coordinates of boundary nodes of the FE-domain are directly chosen as design variables. Convergence problems and problems with jagged shapes are eliminated by a new regularization technique: an artificial inequality constraint added to the optimization problem limits a fictitious total strain energy that measures the shape change of the design with respect to a reference design. The energy constraint defines a feasible design space whose size can be varied by one parameter, the upper energy limit. By construction, the proposed regularization is applicable to a wide range of problems; although in this paper, the application is restricted to linear elastostatic problems.

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The constitutive modelling of granular, porous and quasi-brittle materials is based on yield (or damage) functions, which may exhibit features (for instance, lack of convexity, or branches where the values go to infinity, or 'false elastic domains') preventing the use of efficient return-mapping integration schemes. This problem is solved by proposing a general construction strategy to define an implicitly defined convex yield function starting from any convex yield surface. Based on this implicit definition of the yield function, a return-mapping integration scheme is implemented and tested for elastic-plastic (or -damaging) rate equations. The scheme is general and, although it introduces a numerical cost when compared to situations where the scheme is not needed, is demonstrated to perform correctly and accurately.Electronic supplementary material The online version of this article