von Mises hypothesis revised

The most popular isotropic yield conditions, verified for many ductile metals, were proposed by Tresca in 1864 (maximum shearing stresses theory) and von Mises in 1913. The von Mises yield theory (von Mises in Mathematisch-physikalische Klasse 582–592, 1913), also known as maximum distortion energy criterion, finds considerable experimental support, especially for very ductile materials and plane stress (Banabic et al. in Int. J. Mater. Form. 3:165–189, 2010). For this reason, and for its simplicity, it is common in design. During 100 years, this theory has been developed and improved systematically by Hosford, Christensen, Tsai-Hill, etc. The modified von Mises hypothesis combines the theories of maximum strain energy and maximum distortion energy, and it involves the Poisson ratio. It ensures a smooth transition from the von Mises to the Beltrami criterion. The results obtained by this new yield hypothesis are compared with those obtained both by the classic von Mises criterion and by experiments on different metallic materials. A quite good concordance is observed between these results.