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

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The constitutive postulations for mixed-hardening elastoplasticity are selected. Several homeomorphisms of irreversibility parameters are derived, among which X a 0 and X c 0 play respectively the roles of temporal components of the Minkowski and conformal spacetimes. An augmented vector X a:=( Y Q a t, YQ a 0) 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 M n+1 on which the proper orthochronous Lorentz group SO o( n,1) left acts. Then, constructed is a Poincaré group ISO o( n,1) on space X:= X a+ X b, of which X b reflects the kinematic hardening rule in the model. We also find that the space ( Q a t, q 0 a ) is a Robertson–Walker spacetime, which is conformal to X a through a factor Y, and conformal to X c:=( ρ Q a t, ρQ a 0) t through a factor ρ as given by ρ( q 0 a )= Y( q 0 a )/[1−2 ρ 0 Q a 0(0)+2 ρ 0 Y( q 0 a ) Q a 0( q 0 a )]. In the conformal spacetime the internal symmetry is a conformal group.