A robust approach to the optimization of structures made of unilateral material

A method to cope with the topology optimization of two-dimensional structures in case of unilateral material is presented. It is based on a volume-constrained minimum compliance formulation that combines orthotropic modeling of the medium along with a suitable set of strength constraints. Previous investigations mainly adopted an isotropic modeling of the continuum because they were especially conceived to the optimization of truss-like structures. Struts and ties are governed by an uniaxial stress regime and an extremely non-symmetric behavior in tension and compression can be controlled e.g. by penalizing some energy contribution of the isotropic continuum (Cai 2011) or enforcing isotropic strength criteria such as the Drucker-Prager one (Bruggi & Duysinx 2013). However, an isotropic modeling of the material does not allow for handling the optimal design of structures involving members of large thickness. In this case some regions of the domain can experience biaxial stresses, which call for an ad hoc orthotropic modeling of the constitutive behavior of the unilateral material, see in particular Del Piero (1989) and Bruggi (2014). The proposed approach distributes an assigned amount of an orthotropic phase such that the symmetry axes of the orthotropicmaterial are aligned with the principal stress directions, whereas a suitable set of constraints avoid the arising of any tensile/compressive stress throughout the domain. This allows decoupling the constitutive behavior of the material along the principal stress directions thus handling effectively both uniaxial and biaxial stress states. Numerical simulations assess the robustness of the proposed optimization framework in comparison with methods based on a full non-linear modeling of the constitutive behavior of unilateral materials, as implemented e.g. Chang, Zheng, & Gea (2007). The achieved optimal layouts are critically analyzed focusing on the effect of the unilateral assumption on the arising topology. An extension to the assessment of the safety of structures made of no-tension material is also highlighted, searching for a compressive-only load path through the proposed numerical method.