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A non-local continuum model for strain-softening simply taking plastic strain or damage vari-able as a non-local variable is derived by using the additive decomposition principle of finite deformation gra-dient.At the same time,variational equations,their finite element formulations and numerical convolutedintegration algorithm of the model in current configuration usually called co-moving coordinate system aregiven.Stability and convergence of the model are proven by means of the weak convergence theorem of gen-eral function and the convoluted integration theory.Mathematical and physical properties of the characteris-tic size for material or structure are accounted for within the context of a statistical weighted or kernel func-tion,and way is investigated.Numerical simulation shows that this model is suitable for to analyzing defor-mation localization problems.
A non-local continuum model for strain-softening simply taking plastic strain or damage vari-able as a non-local variable is derived by using the additive decomposition principle of finite deformation gradient. At the same time, variational equations, their finite element formulations and numerical convolutedintegration algorithm of the model in current configuration usually called co-moving coordinate system are given. Stability and convergence of the model are proven by means of the weak convergence theorem of gen-eral function and the convoluted integration theory. Mathematical and physical properties of the characteris-tic size for material or structure are accounted for within the context of a statistical weighted or kernel func- tion, and way is investigated. Numerical simulation shows that this model is suitable for to analyzing defor-mation localization problems.