One-point quadrature for second-order elements with viscoelastic material behavior
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Simulating the behavior of materials with microstructure evolution is complex and the simulation time can be significantly longer compared to elastic materials. The reason for this is that the state of the microstructure changes with time and load and therefore evolution equations have to be solved at each quadrature point at each time the residual or tangent matrix is computed. Reducing the simulation time while maintaining the accuracy of the results is a very important and interesting topic nowadays. In this work, the 1-point quadrature method for the behavior of viscoelastic material for 6-node triangular elements (T2 elements) is investigated. Hyperelastic materials have already been simulated in previous studies (Bode 2023 [1]) using the 1-point quadrature method for higher order elements and have shown good results. The evolution equation for viscoelasticity can be derived, for example, using Hamilton’s principle (Junker et al. 2018 [2]). Using the non-conservative model, the virtual strain energy can be approximated by a Taylor series expansion of the stress with respect to the strains. In turn, the strains can be expanded with respect to the spatial terms. The geometric moments required for the one-point integration can be calculated via a surface integral in preprocessing. By using 1-point integration, the viscoelastic evolution equations only have to be evaluated at a single point per element, despite the higher order approach. The investigation of time efficiency in terms of assembly time while maintaining accuracy in the integration is investigated.