// SmpDirectorDeriv1 computes the first order derivative of the SMP director
// Notes: Only non-zero components are returned; i.e. dNdL[i] := dNdL[i][i]
func SmpDirectorDeriv1(dNdL []float64, L []float64, a, b, β, ϵ float64) {
if SMPUSESRAMP {
dNdL[0] = -b * fun.SrampD1(a*L[0], β) * math.Pow(ϵ+fun.Sramp(a*L[0], β), -b-1.0)
dNdL[1] = -b * fun.SrampD1(a*L[1], β) * math.Pow(ϵ+fun.Sramp(a*L[1], β), -b-1.0)
dNdL[2] = -b * fun.SrampD1(a*L[2], β) * math.Pow(ϵ+fun.Sramp(a*L[2], β), -b-1.0)
} else {
eps := β
dNdL[0] = -b * fun.SabsD1(a*L[0], eps) * math.Pow(ϵ+fun.Sabs(a*L[0], eps), -b-1.0)
dNdL[1] = -b * fun.SabsD1(a*L[1], eps) * math.Pow(ϵ+fun.Sabs(a*L[1], eps), -b-1.0)
dNdL[2] = -b * fun.SabsD1(a*L[2], eps) * math.Pow(ϵ+fun.Sabs(a*L[2], eps), -b-1.0)
}
}
// SmpDirector computes the director (normal vector) of the spatially mobilised plane
// Notes:
// 1) the norm of N is returned => m := norm(N)
// 2) if !SMPUSESRAMP, β==eps and must be a small quantity
func SmpDirector(N, L []float64, a, b, β, ϵ float64) (m float64) {
if SMPUSESRAMP {
N[0] = a / math.Pow(ϵ+fun.Sramp(a*L[0], β), b)
N[1] = a / math.Pow(ϵ+fun.Sramp(a*L[1], β), b)
N[2] = a / math.Pow(ϵ+fun.Sramp(a*L[2], β), b)
} else {
eps := β
N[0] = a / math.Pow(ϵ+fun.Sabs(a*L[0], eps), b)
N[1] = a / math.Pow(ϵ+fun.Sabs(a*L[1], eps), b)
N[2] = a / math.Pow(ϵ+fun.Sabs(a*L[2], eps), b)
}
m = math.Sqrt(N[0]*N[0] + N[1]*N[1] + N[2]*N[2])
return
}
// SmpDirectorDeriv2 computes the second order derivative of the SMP director
// Notes: Only the non-zero components are returned; i.e.: d²NdL2[i] := d²N[i]/dL[i]dL[i]
func SmpDirectorDeriv2(d2NdL2 []float64, L []float64, a, b, β, ϵ float64) {
var F_i, G_i, H_i float64
for i := 0; i < 3; i++ {
if SMPUSESRAMP {
F_i = fun.Sramp(a*L[i], β)
G_i = fun.SrampD1(a*L[i], β)
H_i = fun.SrampD2(a*L[i], β)
} else {
eps := β
F_i = fun.Sabs(a*L[i], eps)
G_i = fun.SabsD1(a*L[i], eps)
H_i = fun.SabsD2(a*L[i], eps)
}
d2NdL2[i] = a * b * ((b+1.0)*G_i*G_i - (ϵ+F_i)*H_i) * math.Pow(ϵ+F_i, -b-2.0)
}
}
// ramp implements the ramp function
func (o *ElemP) ramp(x float64) float64 {
if o.Macaulay {
return fun.Ramp(x)
}
return fun.Sramp(x, o.βrmp)
}