**process hill_stability_sd

Description

This post-processor computes the second order work

\[d^2 W=d \ten{\sigma}: d \ten{\varepsilon}\]

A state is stable under Hill’s criterion if every stress/strain increment (\(d \ten{\sigma}, d \ten{\varepsilon}\) ) yields positive second-order work.

Syntax

**process hill_stability_sd \(~\,\) *sig stress \(~\,\) *eto total_strain

*sig stress

Cauchy stress tensor.

*eto total_strain

total strain tensor.

Output

• SOW_SD: second order work;

• dsig: increment \(d \ten{\sigma}\);

• deps: increment \(d \ten{\varepsilon}\).

Example

**process hill_stability_sd
 *sig sig
 *eto eto