Large deformation plasticity From basic relations to finite deformation

The theory of plasticity as a special field of continuum mechanics deals with the irreversible,i.e.permanent,deformation of solids.Under the action of given loads or deformations,the state of the stresses and strains or the strain rates in these bodies is described.In this way,it complements the theory of elasticity for the reversible behavior of solids.In practice,it has been observed that many materials behave elastically up to a certain load(yield point),beyond that load,however,increasingly plastic or liquid-like.The combination of these two material properties is known as elastoplasticity.The classical elastoplastic material behavior is assumed to be time-independent or rate-independent.In contrast,we call a time-or rate-dependent behavior visco-elastoplastic and visco-plastic—if the elastic part of the deformation is neglected.In plasticity theory,because of the given loads the states of the state variables stress,strain and temperature as well as their changes are described.For this purpose,the observed phenomena are introduced and put into mathematical relationships.The constitutive relations describing the specific material behavior are finally embedded in the fundamental relations of continuum theory and physics.Historically,the theory of plasticity was introduced in order to better estimate the strength of constructions.An analysis based purely on elastic codes is not in a position to do this,and can occasionally even lead to incorrect interpretations.On the other hand,the entire field of forming techniques requires a theory for the description of plastic behavior.Starting from the classical description of plastic behavior with small deformations,the present review is intended to provide an insight into the state of the art when taking into account finite deformations.

An Elasto-plastic Damage Constitutive Theory Based on Pair Functional Potentials and Slip Mechanism

The deformation work rate can be expressed by the time rate of pair functional potentials which describe the energy of materi- als in terms of atomic bonds and atom embedding interactions. According to Cauchy-Born rule, the relations between the micro- scopic deformations of atomic bonds and electron gas and macroscopic deformation are established. Further, atomic bonds are grouped according to their directions, and atomic bonds in the same direction are simplified as a spring-bundle component. Atom embedding interactions in unit reference volume are simplified as a cubage component. Consequently, a material model com- posed of spring-bundle components and a cubage component is established. Since the essence of damage is the decrease and loss of atomic bonding forces, the damage effect can be reflected by the response functions of these two kinds of components. For- mulating the mechanical responses of two kinds of components, the corresponding elasto-damage constitutive equations are de- rived. Considering that slip is the main plastic deformation mechanism of polycrystalline metals, the slip systems of crystal are extended to polycrystalline, and the slip components are proposed to describe the plastic deformation. Based on the decomposition of deformation gradient and combining the plastic response with the elasto-damage one, the elasto-plastic damage constitutive equations are derived. As a result, a material model iormulated with spring-bundle components, a cubage component and slip components is established. Different from phenomenological constitutive theories, the mechanical property of materials depends on the property of components rather than that directly obtained on the representative volume element. The effect of finite deformation is taken into account in this model. Parameter calibration procedure and the basic characteristics of this model are discussed.

A work-hardening and softening constitutive model for sand:modified plastic strain energy approach

The paper describes an energy-based constitutive model for sand, which is modified based on the modified plastic strain energy approach, represented by a unique relationship between the modified plastic strain energy and a stress parameter, independent of stress history. The modified plastic strain energy approach was developed based on results from a series of drained plastic strain compression tests along various stress paths on saturated dense Toyoura sand with accurate stress and strain measurements. The proposed model is coupled with an isotropically work-hardening and softening, non-associtated, elasto-plastic material description. The constitutive model concerns the inherent and stress system-induced cross-anisotropic elastic deformation properties of sand. It is capable of simulating the deformation characteristics of stress history and stress path, the effects of pressure level, anisotropic strength and void ratio, and the strain localization.