// ContD computes D = dσ_new/dε_new continuous
func (o *VonMises) ContD(D [][]float64, s *State) (err error) {
// elastic part
err = o.SmallElasticity.CalcD(D, s)
if err != nil {
return
}
// only elastic
if !s.Loading {
return
}
// elastoplastic
σ := s.Sig
d1 := 3.0*o.G + o.H
a4 := 6.0 * o.G * o.G / d1
sno, _, _ := tsr.M_devσ(o.ten, σ) // ten := dev(σ)
for i := 0; i < o.Nsig; i++ {
for j := 0; j < o.Nsig; j++ {
D[i][j] -= a4 * o.ten[i] * o.ten[j] / (sno * sno)
}
}
return
}
// ContD computes D = dσ_new/dε_new continuous
func (o *DruckerPrager) ContD(D [][]float64, s *State) (err error) {
// elastic part
err = o.SmallElasticity.CalcD(D, s)
if err != nil {
return
}
// only elastic
if !s.Loading {
return
}
// elastoplastic
σ := s.Sig
d1 := o.K*o.Mb*o.M + 3.0*o.G + o.H
a1 := o.K * o.K * o.Mb * o.M / d1
a2 := tsr.SQ6 * o.K * o.G * o.Mb / d1
a3 := tsr.SQ6 * o.K * o.G * o.M / d1
a4 := 6.0 * o.G * o.G / d1
sno, _, _ := tsr.M_devσ(o.ten, σ) // ten := dev(σ)
for i := 0; i < o.Nsig; i++ {
for j := 0; j < o.Nsig; j++ {
D[i][j] -= a1*tsr.Im[i]*tsr.Im[j] +
a2*tsr.Im[i]*o.ten[j]/sno +
a3*o.ten[i]*tsr.Im[j]/sno +
a4*o.ten[i]*o.ten[j]/(sno*sno)
}
}
return
}
// CalcEps0 computes initial strains from stresses (s.Sig)
// Note: initial strains are elastic strains => εe_ini := ε0
func (o *HyperElast1) CalcEps0(s *State) {
s0 := make([]float64, o.Nsig)
s0no, p0, q0 := tsr.M_devσ(s0, s.Sig)
ev0 := -p0 / o.K0
ed0 := q0 / (3.0 * o.G0)
if !o.le {
var nls num.NlSolver
nls.Init(2, func(fx, x []float64) error { // ev=x[0], ed=x[1]
εv, εd := x[0], x[1]
p, q := o.Calc_pq(εv, εd)
fx[0] = p - p0
fx[1] = q - q0
return nil
}, nil, func(J [][]float64, x []float64) (err error) {
εv, εd := x[0], x[1]
pv := o.pa * math.Exp(-o.a*εv)
Dvv := o.a * (1.0 + 1.5*o.a*o.κb*εd*εd) * pv
Dvd := -3.0 * o.a * o.κb * εd * pv
Ddd := 3.0 * (o.G0 + o.κb*pv)
J[0][0] = -Dvv
J[0][1] = -Dvd
J[1][0] = Dvd
J[1][1] = Ddd
return nil
}, true, false, map[string]float64{"lSearch": 0})
x := []float64{ev0, ed0}
nls.SetTols(1e-10, 1e-10, 1e-14, num.EPS)
//nls.ChkConv = false
//nls.CheckJ(x, 1e-6, true, false)
silent := true
err := nls.Solve(x, silent)
if err != nil {
chk.Panic("HyperElast1: CalcEps0: non-linear solver failed:\n%v", err)
}
ev0, ed0 = x[0], x[1]
}
if s0no > 0 {
for i := 0; i < o.Nsig; i++ {
s.EpsE[i] = ev0*tsr.Im[i]/3.0 + tsr.SQ3by2*ed0*(s0[i]/s0no)
}
return
}
for i := 0; i < o.Nsig; i++ {
s.EpsE[i] = ev0 * tsr.Im[i] / 3.0
}
}