Abstract
The aim of this paper is to improve the shape of specimens for biaxial experiments with respect to optimal stress states, characterized by the stress triaxiality. Gradient-based optimization strategies are used to achieve this goal. Thus, it is crucial to know how the stress state changes if the geometric shape of the specimen is varied. The design sensitivity analysis (DSA) of the stress triaxiality is performed using a variational approach based on an enhanced kinematic concept that offers a rigorous separation of structural and physical quantities. In the present case of elastoplastic material behavior, the deformation history has to be taken into account for the structural analysis as well as for the determination of response sensitivities. The presented method is flexible in terms of the choice of design variables. In a first step, the approach is used to identify material parameters. Thus, material parameters are chosen as design variables. Subsequently, the design parameters are chosen as geometric quantities so as to optimize the specimen shape with the aim to obtain a preferably homogeneous stress triaxiality distribution in the relevant cross section of the specimen.
Highlights
In biaxial tests the stress state can be characterized by the stress triaxiality η defined by η = σm = √ I1(σ ), (1)
The stress triaxiality classifies the stress state to be tensile if η > 0, compressive if η < 0, or pure shear if η = 0
New specimens for biaxial tests have been developed in Gerke et al (2017), which widen the range of stress triaxiality compared to traditional specimens
Summary
The gradient information is determined by means of a variational approach proposed in Barthold (2002); Barthold (2008); Barthold et al (2016); Barthold and Stein (1996) It is based on an enhanced kinematic concept that offers a rigorous separation of structural and physical quantities and provides exact gradient information efficiently with moderate effort. It allows simultaneous computation of stress states and sensitivities within a finite element framework.
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