Table 2. Equations used to describe the evolution of spontaneous in-plane and bending strain as a function of modulus.

	In plane	Bending
Constitutive relation	$N_{\alpha \beta }=C({ϵ}_{\alpha \beta }-{ϵ}_{\alpha \beta }^m)$	$M_{\alpha \beta }=B({\kappa }_{\alpha \beta }-{\kappa }_{\alpha \beta }^m)$
Modulus	C = ${\mathcal{M}}^0$(E)	B = $\mathcal{M}$2(E) − $\mathcal{M}$1(E)2/$\mathcal{M}$0(E)
Spontaneous strain and curvature	${ϵ}_{\alpha \beta }^m={\mathcal{M}}^0(E{\widehat{ϵ}}_{\alpha \beta })/{\mathcal{M}}^0(E)$	${\kappa }_{\alpha \beta }^m=\frac{1}{B}[{\mathcal{M}}^1(E{\widehat{ϵ}}_{\alpha \beta })-\frac{{\mathcal{M}}^1(E){\mathcal{M}}^0(E{\widehat{ϵ}}_{\alpha \beta })}{{\mathcal{M}}^0(E)}]$
Above, ${\mathcal{M}}^p(f)={\int }_{-h/2}^{h/2}{z}^{p}f(z)dz$ is the p-th moment through the thickness