The g-based Jordan Algebra and Lie Algebra with Application to the Model of Visco-Elastoplasticity
By a matrix representation the g-based Jordan algebra  is proved to form a g-based Lie algebra under the commutator product. Then we derive a new dynamical system based on the composition of the g-based Jordan and Lie algebras, which possesses internal symmetry group DSOo(n,1), and its projection PDSOo(n,1). Utilizing this concept we obtain a linear representation of a constitutive model of visco-elastoplasticity with large deformation. The irreducible representation in the vector space admits of the projective dilation proper orthochronous Lorentz group PDSOo(5,1) in the visco-elastoplastic phase and the dilation special Euclidean group DSE(5) in the viscoelastic phase. The input path and the relaxation time decide that when the symmetry switches between the two groups. Based on such symmetry a numerical scheme which satisfies the consistency condition for every time step is devised, which preserves the internal symmetry PDSOo(5,1) of the model in the visco-elastoplastic phase so as to locate the stress point automatically on the yield surface at each time step without iterations at all.
"The g-based Jordan Algebra and Lie Algebra with Application to the Model of Visco-Elastoplasticity,"
Journal of Marine Science and Technology: Vol. 9:
1, Article 1.
Available at: https://jmstt.ntou.edu.tw/journal/vol9/iss1/1