Symmetry groups and the pseudo-Riemann spacetimes for mixed-hardening elastoplasticity

The constitutive postulations for mixed-hardening elastoplasticity are selected. Several homeomorphisms of irreversibility parameters are derived, among which Xa0 and Xc0 play respectively the roles of temporal components of the Minkowski and conformal spacetimes. An augmented vector Xa:=(YQat,YQa0)t is constructed, whose governing equations in the plastic phase are found to be a linear system with a suitable rescaling proper time. The underlying structure of mixed-hardening elastoplasticity is a Minkowski spacetime ...on which the proper orthochronous Lorentz group SOo(n,1) left acts. Then, constructed is a Poincaré group ISOo(n,1) on space X:=Xa+Xb, of which Xb reflects the kinematic hardening rule in the model. We also find that the space (Qat,q0a) is a Robertson–Walker spacetime, which is conformal to Xa through a factor Y, and conformal to Xc:=((rho) Qat,(rho)Qa0)t through a factor (rho)as given by (rho)(q0a)=Y(q0a)/[1-2(rho)0Qa0(0)+2(rho)0Y(q0a)Qa0(q0a)]. In the conformal spacetime the internal symmetry is a conformal group.