Energy-Based Yield Criteria for Orthotropic Materials, Exhibiting Strength-Differential Effect. Specification for Sheets under Plane Stress State

Abstract

A general proposition of an energy-based limit condition for anisotropic materials exhibiting strength-differential effect (SDE) based on spectral decomposition of elasticity tensors and the use of scaling pressure-dependent functions is specified for the case of orthotropic materials. A detailed algorithm (based on classical solutions of cubic equations) for the determination of elastic eigenstates and eigenvalues of the orthotropic stiffness tensor is presented. A yield condition is formulated for both two-dimensional and three-dimensional cases. Explicit formulas based on simple strength tests are derived for parameters of criterion in the plane case. The application of both criteria for the description of yielding and plastic deformation of metal sheets is discussed in detail. The plane case criterion is verified with experimental results from the literature.

Analytical modelling and shape optimization of composite girder with adhesive bondline

“…In the considered optimization process, a general plane stress state is considered. For this reason, the energy-based limit state condition for orthotropic material exhibiting asymmetry of elastic range is used (Szeptyński, 2017)…”

“…The parameter κ is a function of the stiffness distributor. In (Szeptyński, 2017), one may find formulas for the parameter κ as well as coefficients A I , A II , A III , B I , B II , expressed in terms of elastic constants and strength values. All these parameters can be found e.g.…”

Archives of Metallurgy and Materials

“…The formulation of energy-based hypothesis of material effort for anisotropic solids revealing SDE was attempted by [24,25,35] and [34]. The study is based on the concept of energyorthogonal decompositions of stress state introduced by [31,32] and [23].…”

“…General formulation of a new limit criterion as well as its specification for certain elastic symmetries was given in [25] and general methodology of acquiring necessary data for the criterion specification was presented. The general formulation was specified for orthotropic materials and formulated both for two-dimensional and threedimensional cases by [34]. Explicit formulae based on simple strength tests were derived for parameters of criterion in the plane case.…”