Analytical CPP in energy-mapped stress space: Application to a modified Drucker–Prager yield surface

In conventional stress space, the closest point projection (CPP) of computational plasticity in general does not provide the closest point in a Euclidean sense but rather in an energy metric. As an alternative, this contribution discusses an energy-mapped stress space such that CPP is indeed the closest point in a strict Euclidean sense. This perspective clarifies which yield surfaces can be handled analytically: analytical solutions are possible if the CPP can be expressed as a polynomial of order 4 or less. This is demonstrated by means of a modified Drucker–Prager yield surface in which the hydrostatic tensile apex is removed through the use of hyperbolic meridians.