// Init initialises model
func (o *Ogden) Init(ndim int, pstress bool, prms fun.Prms) (err error) {
// basic data
o.Nsig = 2 * ndim
// parameters
for _, p := range prms {
if p.N == "K" {
o.K = p.V
}
if p.N[:3] == "alp" {
o.Alp = append(o.Alp, p.V)
}
if p.N[:3] == "mu" {
o.Mu = append(o.Mu, p.V)
}
}
if len(o.Alp) != len(o.Mu) {
return chk.Err("number of alp must be equal to number of mu. %d != %d\n", len(o.Alp), len(o.Mu))
}
// auxiliary
o.Fi = tsr.Alloc2()
o.b = tsr.Alloc2()
o.bm = make([]float64, o.Nsig)
o.λ = make([]float64, 3)
o.P = tsr.M_AllocEigenprojs(o.Nsig)
o.τ = make([]float64, 3)
return
}
// Connect connects rod/solid elements in this Rjoint
func (o *Rjoint) Connect(cid2elem []Elem, c *inp.Cell) (nnzK int, err error) {
// get rod and solid elements
rodId := c.JlinId
sldId := c.JsldId
o.Rod = cid2elem[rodId].(*Rod)
o.Sld = cid2elem[sldId].(*ElemU)
if o.Rod == nil {
err = chk.Err("cannot find joint's rod cell with id == %d", rodId)
return
}
if o.Sld == nil {
err = chk.Err("cannot find joint's solid cell with id == %d", sldId)
return
}
// total number of dofs
o.Ny = o.Rod.Nu + o.Sld.Nu
// material model name
matdata := o.Sim.MatParams.Get(o.Edat.Mat)
if matdata == nil {
err = chk.Err("materials database failed on getting %q material\n", o.Edat.Mat)
return
}
// initialise model
err = o.Mdl.Init(matdata.Prms)
if err != nil {
err = chk.Err("model initialisation failed:\n%v", err)
return
}
// parameters
for _, p := range matdata.Prms {
switch p.N {
case "h":
o.h = p.V
case "k1":
o.k1 = p.V
case "k2":
o.k2 = p.V
case "mu":
if p.V > 0.0 {
o.Coulomb = true
}
}
}
// auxiliary
nsig := 2 * o.Ndim
// rod data
rodH := o.Rod.Cell.Shp
rodNp := len(o.Rod.IpsElem)
rodNn := rodH.Nverts
rodNu := o.Rod.Nu
// solid data
sldH := o.Sld.Cell.Shp
sldS := sldH.S
sldNp := len(o.Sld.IpsElem)
sldNn := sldH.Nverts
sldNu := o.Sld.Nu
// shape functions of solid @ nodes of rod
o.Nmat = la.MatAlloc(sldNn, rodNn)
rodYn := make([]float64, o.Ndim)
rodRn := make([]float64, 3)
for m := 0; m < rodNn; m++ {
for i := 0; i < o.Ndim; i++ {
rodYn[i] = o.Rod.X[i][m]
}
err = sldH.InvMap(rodRn, rodYn, o.Sld.X)
if err != nil {
return
}
err = sldH.CalcAtR(o.Sld.X, rodRn, false)
if err != nil {
return
}
for n := 0; n < sldNn; n++ {
o.Nmat[n][m] = sldH.S[n]
}
}
// coulomb model => σc depends on p values of solid
if o.Coulomb {
// allocate variables
o.Pmat = la.MatAlloc(sldNn, rodNp)
o.Emat = la.MatAlloc(sldNn, sldNp)
o.rodRp = la.MatAlloc(rodNp, 3)
o.σNo = la.MatAlloc(sldNn, nsig)
o.σIp = make([]float64, nsig)
o.t1 = make([]float64, o.Ndim)
o.t2 = make([]float64, o.Ndim)
// extrapolator matrix
err = sldH.Extrapolator(o.Emat, o.Sld.IpsElem)
if err != nil {
return
}
// shape function of solid @ ips of rod
for idx, ip := range o.Rod.IpsElem {
rodYp := rodH.IpRealCoords(o.Rod.X, ip)
err = sldH.InvMap(o.rodRp[idx], rodYp, o.Sld.X)
if err != nil {
return
}
err = sldH.CalcAtR(o.Sld.X, o.rodRp[idx], false)
if err != nil {
return
}
for n := 0; n < sldNn; n++ {
o.Pmat[n][idx] = sldS[n]
}
}
}
// joint direction @ ip[idx]; corotational system aligned with rod element
o.e0 = la.MatAlloc(rodNp, o.Ndim)
o.e1 = la.MatAlloc(rodNp, o.Ndim)
o.e2 = la.MatAlloc(rodNp, o.Ndim)
π := make([]float64, o.Ndim) // Eq. (27)
Q := la.MatAlloc(o.Ndim, o.Ndim)
α := 666.0
Jvec := rodH.Jvec3d[:o.Ndim]
for idx, ip := range o.Rod.IpsElem {
// auxiliary
e0, e1, e2 := o.e0[idx], o.e1[idx], o.e2[idx]
// interpolation functions and gradients
err = rodH.CalcAtIp(o.Rod.X, ip, true)
if err != nil {
return
}
// compute basis vectors
J := rodH.J
π[0] = Jvec[0] + α
π[1] = Jvec[1]
e0[0] = Jvec[0] / J
e0[1] = Jvec[1] / J
if o.Ndim == 3 {
π[2] = Jvec[2]
e0[2] = Jvec[2] / J
}
la.MatSetDiag(Q, 1)
la.VecOuterAdd(Q, -1, e0, e0) // Q := I - e0 dyad e0
la.MatVecMul(e1, 1, Q, π) // Eq. (29) * norm(E1)
la.VecScale(e1, 0, 1.0/la.VecNorm(e1), e1)
if o.Ndim == 3 {
e2[0] = e0[1]*e1[2] - e0[2]*e1[1]
e2[1] = e0[2]*e1[0] - e0[0]*e1[2]
e2[2] = e0[0]*e1[1] - e0[1]*e1[0]
}
// compute auxiliary tensors
if o.Coulomb {
e1_dy_e1 := tsr.Alloc2()
e2_dy_e2 := tsr.Alloc2()
for i := 0; i < o.Ndim; i++ {
for j := 0; j < o.Ndim; j++ {
e1_dy_e1[i][j] = e1[i] * e1[j]
e2_dy_e2[i][j] = e2[i] * e2[j]
}
}
}
}
// auxiliary variables
o.ΔuC = la.MatAlloc(rodNn, o.Ndim)
o.Δw = make([]float64, o.Ndim)
o.qb = make([]float64, o.Ndim)
o.fC = make([]float64, rodNu)
// temporary Jacobian matrices. see Eq. (57)
o.Krr = la.MatAlloc(rodNu, rodNu)
o.Krs = la.MatAlloc(rodNu, sldNu)
o.Ksr = la.MatAlloc(sldNu, rodNu)
o.Kss = la.MatAlloc(sldNu, sldNu)
// debugging
//if true {
if false {
o.debug_print_init()
}
// success
return o.Ny * o.Ny, nil
}
