Bezier5YS and SHYqp: A general framework for generating data and for modeling symmetric and asymmetric orthotropic yield surfaces

The design of conventional yielding criteria, within the phenomenological theory of metal plasticity, is based on a pointwise interpolation of experimental data, an approach originating in the early days of plasticity when it was believed that material parameters should be explicitly linked to experimental data. Since the latter is most often a numerical set of a small size, the inherent consequence was that yield functions were, by design, conceived with a small number of parameters as well. For decades, under the constraints of limited computational resources, this approach has had remarkable successes, particularly in the numerical simulation of metal forming operations. However, with the ever increasing level of automation of the assembly lines of most manufacturers, the demand for tight tolerances has pushed the current modeling establishment to its limits. Furthermore, in the current context of climate change, the need for the reduction of energy consumption in the transportation industries has motivated a significant amount of new research into the plasticity of lighter materials such as magnesium alloys. For these, the conventional approach to yield surface modeling has failed to produce adequate models of their yielding and flow properties. This work explores, in the broader framework of data-driven plasticity, a model based on harmonics expansion with data generated by Bezier interpolation. The resulting parameter identification scheme is a quadratic problem with linear constraints (to enforce convexity). It is shown, by applications to magnesium, titanium, aluminum and steel alloys, that the plasticity of virtually any metal can be modeled within this framework with an arbitrary degree of precision. Python code at: https://github.com/stefanSCS/SHYqp • SHYqp: A general framework based on harmonic monomials for high-precision modeling of the yielding and flow properties of metals. • Bezier5YS: A data generating scheme based on Bezier interpolation. • Applications to all major lattice structures (HCP, FCC, BCC) with emphasis on magnesium alloys. • The identification of material parameters is a quadratic problem with linear constraints. • The formulation is general and amenable to automation: Python code is provided.