International audienceAn important feature that drives the auxetic behaviour of the star-shaped auxetic structures is the hinge-functional connection at the vertex connections. This feature poses a great challenge for manufacturing and may lead to significant stress concentrations. To overcome these problems, we introduced smoothed petal-shaped auxetic structures, where the hinges are replaced by smoothed connections. To accommodate the curved features of the petal-shaped auxetics, a parametrisation modelling scheme using multiple NURBS patches is proposed. Next, an integrated shape design frame work using isogeometric analysis is adopted to improve the structural performance. To ensure a minimum thickness for each member, a geometry sizing constraint is imposed via piece-wise bounding polynomials. This geometry sizing constraint, in the context of isogeometric shape optimization, is particularly interesting due to the non-interpolatory nature of NURBS basis. The effective Poisson ratio is used directly as the objective function, and an adjoint sensitivity analysis is carried out. The optimized designs – smoothed petal auxetic structures – are shown to achieve low negative Poisson’s ratios, while the difficulties of manufacturing the hinges are avoided. For the case with six petals, an in-plane isotropy is achieved
a b s t r a c tMany rate-independent models for metals utilize the gradient of effective plastic strain to capture sizedependent behavior. This enhancement, sometimes termed as ''explicit'' gradient formulation, requires higher-order tractions to be imposed on the evolving elasto-plastic boundary and the resulting numerical framework is complicated. An ''implicit'' scalar gradient model was thus developed in Peerlings [Peerlings, R.H.J., 2007. On the role of moving elastic-plastic boundaries in strain gradient plasticity. Model. Simul. Mater. Sci. Eng. 15, 109-120] that has only C 0 continuity requirements and its implementation is straightforward. However, both explicit and implicit scalar gradient models can be problematic when the effective plastic strains do not have smooth profiles. To address this limitation, an implicit tensorial gradient model is proposed in this paper based on the generalized micromorphic framework. It is also demonstrated that the scalar and tensorial implicit gradient models give similar results when the effective plastic strains fluctuate smoothly.
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