Acta Mech DOI 10.1007/s00707-012-0767-0 V. P. Panoskaltsis · L. C. Polymenakos · D. Soldatos A finite strain model of combined viscoplasticity and rate-independent plasticity without a yield surface Received: 24 April 2012 / Revised: 7 October 2012 © Springer-Verlag Wien 2013 Abstract A new internal variable formulation dealing with mechanisms with different characteristic times in solid materials is proposed within a finite deformation framework. The framework relies crucially on the consistent combination of a general viscoplastic theory and a rate-independent theory (generalized plasticity) which does not involve the yield surface concept as a basic ingredient. The formulation is developed initially in a material setting and then is extended to a covariant one by applying some basic elements and results from the tensor analysis on manifolds. The covariant balance of energy is systematically employed for the derivation of the mechanical state equations. It is shown that unlike the case of finite elasticity, for the proposed formulation the covariant balance of energy does not yield the Doyle–Ericksen formula, unless a further assumption is made. As an application, by considering the material (intrinsic) metric as a primary internal variable accounting for both elastic and viscoplastic (dissipative) phenomena within the body, a constitutive model is proposed. The ability of the model in simulating several patterns of the complex response of metals under quasi-static and dynamic loadings is assessed by representative numerical examples. 1 Introduction The aim of this study is the development of a large deformation internal variable formulation suitable for the description of mechanisms with different characteristic times, namely with characteristic times very short and of the same order compared to a loading process. The first type of mechanisms gives rise to instantaneous inelastic strains and the second type to creep strains, which are developed slowly. Historically, the constitutive modeling of such mechanisms goes back to the early 1960s in the works of Landau et al. [1], Ivlev [2] and Naghdi and Murch [3], where several combinations of a rate-dependent theory with a rate-independent one have been proposed within the context of infinitesimal deformation. In the 1990s Panoskaltsis et al. [54, 55], by combining in series internal variable theories of viscoelasticity and plasticity, developed models for the description of the behavior of concrete materials. Nevertheless, the mechanisms responsible for instantaneous inelastic strains as well as viscoelastic strains are usually accompanied by large deformations and can be found in different materials such as metals (e.g., metal forming processes, high-velocity impact, penetration mechan- ics), shape memory alloys (e.g., finite deformations occurring during phase transformations) and soils (e.g., liquefaction and cyclic mobility in sands). Accordingly, an approach within the context of a large deformation theory seems more fundamental. The proposed approach comprises the following basic characteristics: V. P. Panoskaltsis(B ) · D. Soldatos Department of Civil Engineering, Demokritos University of Thrace, 12 Vassilissis Sofias Street, 67100 Xanthi, Greece E-mail: vpanoska@civil.duth.gr L. C. Polymenakos Autonomic and Grid Computing, Athens Information Technology, 19002 Peania, Greece