Modelling of shear localization in solids by means of energy relaxation

Asia Pacific Journal on Computational Engineering

Table 1 Minimization problem: inf _s W(s)

	Expression
Scalar minimization problem	infs W(s)
Potential	W(s)=a s²+b s+c\|s\| (c>0, a>0)
Solution	$inf s W (s) = − 1 4 a (b − c) + 2$
Minimizer	$s = − 1 2 a (b − c) + sign (b)$
Abbreviations	$(b − c) + = 0 for b ≤ c b − c for b > c$
	$sign (b) = b b for b ≠ 0$