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Geometrical localization analysis of gradient-dependent parabolic Drucker-Prager elastoplasticity. (Análysis geométrico de localización del modelo elastoplástico parabólico de Drucker-Prager dependiente de gradientes.) (Spanish. English summary) Zbl 1210.74157

Summary: In this work the geometrical method for the analysis of the localization properties of the thermodynamically consistent gradient-dependent parabolic Drucker-Prager elastoplastic model is presented. From the analytical solution of the discontinuous bifurcation condition of small strain gradient-dependent elastoplasticity the elliptical envelope for localization is formulated in the coordinates of Mohr. The tangency condition of the locilization ellipse with the major principal circle of Mohr defines the type of failure (diffuse or localized) and the critical directions for discontinuous bifurcation. The results of the geometrical localization analysis illustrate the capability of the gradient-dependent elastoplastic Drucker-Prager material to suppresses the discontinuous bifurcations of the related local or classical elastoplastic model formulation that take place when the adopted hardening/softening modulus \(\overline H\) equals the critical (maximum) one for localization \(\overline H\_{c}\). On the other hand, the results in this work also demonstrate that the thermodynamically consistent gradient-dependent Drucker-Prager model may lead to discontinuous bifurcation not only when the characteristic length \(l\) turns zero but also when \(\overline H\leq \overline H\_{c}\).

MSC:

74R20 Anelastic fracture and damage
74C15 Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)
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