Hardening rule

The more rigorous stress/strain nonlinear material model, oflen referred to as the plastic zone method, is theoretically capable of handling any general cross section Both isotropic and kinematic hardening rules are usually available. This method is... 

The incremental strain-stress relation is obtained following the standard procedure in which the consistency condition, the flow rule and the hardening rule are used. This relation reads... 

De Angelis F. (2012)—A comparative analysis of hnear and nonhnear kinematic hardening rules in computational elastoplastidty, Technische Mechanik, Vol. 32 (2-5), pp. 164-173. 

In continuum mechanics, constitutive modeling of materials follows certain steps, including deformation response, stress response, as well as other particular steps based on materials studied, such as structural relaxation for polymers and a plastic flow mle, and a hardening rule for materials with plastic deformation. In the following, we will present the deformation response, structural relaxation, stress response, and flow rule for the thermosetting SMP programmed by cold-compression programming. 

To construct an elastoplastic model, we need to define a hardening rule ... 

Based on the mathematical theory of plasticity, the plastic deformation behavior of the material can be described by the three components of the rate-independent plasticity model, namely yield criterion, flow rule, and hardening rule. The yield criterion determines the stress level at which yielding is initiated. This is represented by the equivalent stress Ueq, which is a function of the individual stress vector components a. Plastic strain is developed in the metal parts when the equivalent stress is equal to a material yield parameter ay finally, the flow rule determines the direction of plastic straining ... 

Let us apply the associated flow rule (g = /) and assume that / is an w-th order homogeneous function, so that the work-hardening rule (2.320) can be written as... 

For simplicity, we introduce the following isotropic hardening rule with the strain hardening parameter ... 

The hardening rule is introduced under an isotropic hardening model with a strain hardening parameter, which is the same as the original Cam clay model ... 

Application of a yield criterion, flow rule, and hardening rule... 

Yield stress and work hardening rules are two experimentally related phenomena that... 

In the stress relaxation process, JNC assumes a strain hardening rule for the calculation of the creep strain rate.The loading conditions, the geometry of the plates and the dimensions of the initial notches are given in Table 1. The membrane stress Gm and the bending stress Gb can be calculated elastically. The material properties are given in Table 2. The cyclic stress-strain curve at 650°C is expressed as follows [5]. 

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