// L_update computes principal stresses for given principal strains
func (o *HyperElast1) L_update(σ, ε []float64) (p, q float64) {
eno, εv, εd := tsr.M_devε(o.e, ε) // using principal values since len(ε)=3
p, q = o.Calc_pq(εv, εd)
if eno > o.EnoMin {
for i := 0; i < 3; i++ {
σ[i] = -p*tsr.Im[i] + tsr.SQ2by3*q*o.e[i]/eno
}
return
}
for i := 0; i < 3; i++ {
σ[i] = -p * tsr.Im[i]
}
return
}
// Update updates stresses for given strains
func (o *HyperElast1) Update(s *State, ε, dummy []float64, eid, ipid int, time float64) (err error) {
eno, εv, εd := tsr.M_devε(o.e, ε)
p, q := o.Calc_pq(εv, εd)
if eno > o.EnoMin {
for i := 0; i < o.Nsig; i++ {
s.Sig[i] = -p*tsr.Im[i] + tsr.SQ2by3*q*o.e[i]/eno
}
return
}
for i := 0; i < o.Nsig; i++ {
s.Sig[i] = -p * tsr.Im[i]
}
return
}
// L_CalcD computes De in principal components for given principal elastic strains
// D -- [ncp][ncp] elastic modulus
// ε -- [ncp] elastic strains
//
// Note: this method works also for non-principal components
//
func (o *HyperElast1) L_CalcD(D [][]float64, ε []float64) {
// number of components
ncp := len(ε)
if ncp == 0 {
ncp = o.Nsig
}
// elastic modulus
I, Psd := tsr.Im, tsr.Psd
if o.le {
for i := 0; i < ncp; i++ {
for j := 0; j < ncp; j++ {
D[i][j] = o.K0*I[i]*I[j] + 2.0*o.G0*Psd[i][j]
}
}
return
}
// invariants of strain and normalised deviatoric direction
eno, εv, εd := tsr.M_devε(o.e, ε)
if eno > o.EnoMin {
for i := 0; i < ncp; i++ {
o.e[i] /= eno
}
} else {
for i := 0; i < ncp; i++ {
o.e[i] = 0
}
}
// Dvv = ∂²ψ/(∂εve ∂εve)
// DvdS = (∂²ψ/(∂εve ∂εde)) * sqrt(2/3)
// Ddd2 = (∂²ψ/(∂εde ∂εde)) * 2 / 3
pv := o.pa * math.Exp(-o.a*εv)
Dvv := o.a * (1.0 + 1.5*o.a*o.κb*εd*εd) * pv
DvdS := -3.0 * o.a * o.κb * εd * pv * tsr.SQ2by3
Ddd2 := 2.0 * (o.G0 + o.κb*pv)
for i := 0; i < ncp; i++ {
for j := 0; j < ncp; j++ {
D[i][j] = Dvv*I[i]*I[j] + Ddd2*Psd[i][j] + DvdS*(I[i]*o.e[j]+o.e[i]*I[j])
}
}
}
// Plot runs the plot generation (basic set)
func (o *Plotter) Plot(keys []string, res []*State, sts [][]float64, first, last bool) {
// auxiliary variables
nr := imax(len(res), len(sts))
if nr < 1 {
return
}
x := make([]float64, nr)
y := make([]float64, nr)
o.P = make([]float64, nr)
o.Q = make([]float64, nr)
o.W = make([]float64, nr)
o.Ev = make([]float64, nr)
o.Ed = make([]float64, nr)
// compute invariants
for i := 0; i < len(res); i++ {
if len(res[i].Sig) < 4 {
chk.Panic("number of stress components is incorrect: %d", len(res[i].Sig))
}
o.P[i], o.Q[i], o.W[i] = tsr.M_pqw(res[i].Sig)
}
nsig := len(res[0].Sig)
devε := make([]float64, nsig)
for i := 0; i < len(sts); i++ {
if len(sts[i]) < 4 {
chk.Panic("number of strain components is incorrect: %d", len(sts[i]))
}
_, o.Ev[i], o.Ed[i] = tsr.M_devε(devε, sts[i])
}
// clear previous figure
if first {
plt.Clf()
plt.SplotGap(0.35, 0.35)
if o.Hspace > 0 {
plt.SetHspace(o.Hspace)
}
if o.Vspace > 0 {
plt.SetVspace(o.Vspace)
}
}
// number of points for contour
if o.NptsPq < 2 {
o.NptsPq = 61
}
if o.NptsOct < 2 {
o.NptsOct = 41
}
if o.NptsSig < 2 {
o.NptsSig = 41
}
// subplot variables
o.Pidx = 1
o.Ncol, o.Nrow = utl.BestSquare(len(keys))
if len(keys) == 2 {
o.Ncol, o.Nrow = 1, 2
}
if len(keys) == 3 {
o.Ncol, o.Nrow = 1, 3
}
// do plot
for _, key := range keys {
o.Subplot()
switch key {
case "ed,q":
o.QdivP = false
o.Plot_ed_q(x, y, res, sts, last)
case "ed,q/p":
o.QdivP = true
o.Plot_ed_q(x, y, res, sts, last)
case "p,q":
o.WithYs = false
o.Plot_p_q(x, y, res, sts, last)
case "p,q,ys":
o.WithYs = true
o.Plot_p_q(x, y, res, sts, last)
case "ed,ev":
o.Plot_ed_ev(x, y, res, sts, last)
case "p,ev":
o.LogP = false
o.Plot_p_ev(x, y, res, sts, last)
case "log(p),ev":
o.LogP = true
o.Plot_p_ev(x, y, res, sts, last)
case "i,f":
o.Plot_i_f(x, y, res, sts, last)
case "i,alp":
o.Plot_i_alp(x, y, res, sts, last)
case "Dgam,f":
o.Plot_Dgam_f(x, y, res, sts, last)
case "oct":
o.WithYs = false
o.Plot_oct(x, y, res, sts, last)
case "oct,ys":
o.WithYs = true
o.Plot_oct(x, y, res, sts, last)
case "s3,s1":
o.WithYs = false
o.Plot_s3_s1(x, y, res, sts, last)
case "s3,s1,ys":
o.WithYs = true
o.Plot_s3_s1(x, y, res, sts, last)
case "empty":
continue
default:
chk.Panic("cannot handle key=%q", key)
}
if o.Split && last {
o.Save("_", key)
}
}
// save figure
if !o.Split && last {
o.Save("", "")
}
}