Advantages of New Yield Function

The new yield function provides fundamental theoretical improvements over HiSS for modeling material behavior under the classical plasticity problems of constant temperature loading, as also for the case of thermomechanical loading, wherein HiSS has been shown to have numerous issues. For simplicity, these issues are discussed here graphically. Mathematical derivations are in Dube (2004). The practical significance of any particular issue depends upon the specific material being modeled.

Isothermal Issues

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From the graphical demonstration,

• HiSS yield surfaces for small plastic strains do not include the stress-free state

  • the first yield surface passing through zero stress has nonzero plastic strain

  • physically a material may have zero plastic strain at zero stress

  • determination of a1 and h1 assumes zero initial plastic strain at zero stress

• HiSS does not provide continuous yielding starting at zero stress for tensile loads

  • typically materials yield earlier under tensile loads than compressive

• compressive elastoplastic matrix in the limit of zero stress is not the elastic matrix

  • elastic parameters for materials are obtained from initial stress‑strain slope

In comparison, the new yield function

• starts at the origin of the stress axes

• provides continuous yielding in all loading directions

• includes the stress-free state of zero plastic strain within the yield surface

• has an elastoplastic matrix that tends to the elastic matrix in the limit of zero stress

• does not have any inconsistency in parameter determination procedures

Thermomechanical Issues

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From the graphical demonstration,

• HiSS may generate spurious plastic strains under unconstrained thermal loading

• this also affects plastic strains under nonzero stresses and thermal loading

• alternately, the yield surface may harden spuriously under temperature change

• this leads to lack of continuous yielding if the temperature is changed

• yield behavior depends spuriously on thermal history

• simulation results depend on the length of thermal history included

The new yield function does not suffer from the issue, as the initial plastic strain trajectory has a temperature-independent value of zero.

Alternate Partial Solutions

Since HiSS has been used extensively for material modeling in prior research, several simplified solutions were also developed to ameliorate some of specific the issues with HiSS. However, for comprehensive resolution of all issues, the new yield function is required.