Gradient-dependent plasticity: Formulation and algorithmic aspects. (English) Zbl 0768.73019

De Borst, René; Mühlhaus, Hans-Bernd

Int. J. Numer. Methods Eng. 35, No. 3, 521-539 (1992).

A plasticity theory is proposed in which the yield strength not only depends on an equivalent plastic strain measure (hardening parameter), but also on the Laplacian thereof. The consistency condition now results in a differential equation instead of an algebraic equation as in conventional plasticity. To properly solve the set of nonlinear differential equations, the plastic multiplier is discretized in addition to the usual discretization of the displacements. For appropriate boundary conditions this formulation can also be derived from a variational principle.

MSC:

74C99	Plastic materials, materials of stress-rate and internal-variable type
74S30	Other numerical methods in solid mechanics (MSC2010)

Keywords:

yield strength; Laplacian; consistency condition; plastic multiplier; variational principle; strain-softening solids

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