A generalized elastoplastic plate theory and its algorithmic implementation

Abstract In continuum mechanics within specific classes of problems, one‐ or two‐dimensional theories are often simpler to apply than the more complete three‐dimensional one. This is, for example, the case of thin bodies, such as plates or shells, which may be studied using appropriate two‐dimensionai theories. Within this approach, the reduction of the dimension is traded for a loss of information relative to the motion in the transverse direction. For example, in the case of non‐linear material behaviour, classical plasticity plate theories are usually not able to model the effects related to the spreading of plasticity through the cross‐section. In the present paper we discuss a generalized plasticity plate model, which can be used to reproduce some of the three‐dimensional effects in a two‐dimensional setting. We present the continuous and the discrete time model, including both isotropic and kinematic hardening mechanisms; moreover, the form of the tangent matrix consistent with the discrete model is addressed. Finally, some examples (cantilever beam, clamped circular plate and clamped square plate under monotonic and cyclic loading) are studied numerically using a three‐dimensional classical plasticity theory, a classical plasticity plate theory and the proposed plate theory. The generalized plasticity plate model matches the three‐dimensional response with greater accuracy, than the classical plasticity plate model.