Exemple #1
0
// add_natbcs_to_rhs adds natural boundary conditions to rhs
func (o ElemP) add_natbcs_to_rhs(fb []float64, sol *Solution) (ok bool) {

	// compute surface integral
	var tmp float64
	var ρl, pl, fl, plmax, g, rmp, rx, rf float64
	for idx, nbc := range o.NatBcs {

		// tmp := plmax shift or qlb
		tmp = nbc.Fcn.F(sol.T, nil)

		// loop over ips of face
		for jdx, ipf := range o.IpsFace {

			// interpolation functions and gradients @ face
			iface := nbc.IdxFace
			if LogErr(o.Shp.CalcAtFaceIp(o.X, ipf, iface), "add_natbcs_to_rhs") {
				return
			}
			Sf := o.Shp.Sf
			Jf := la.VecNorm(o.Shp.Fnvec)
			coef := ipf.W * Jf

			// select natural boundary condition type
			switch nbc.Key {
			case "ql":
				// flux prescribed
				ρl = 0
				for i, m := range o.Shp.FaceLocalV[iface] {
					ρl += Sf[i] * o.ρl_ex[m]
				}
				for i, m := range o.Shp.FaceLocalV[iface] {
					fb[o.Pmap[m]] -= coef * ρl * tmp * Sf[i]
				}
			case "seep":

				// variables extrapolated to face
				ρl, pl, fl = o.fipvars(iface, sol)
				plmax = o.Plmax[idx][jdx] - tmp
				if plmax < 0 {
					plmax = 0
				}

				// compute residuals
				g = pl - plmax // Eq. (24)
				rmp = o.ramp(fl + o.κ*g)
				rx = ρl * rmp // Eq. (30)
				rf = fl - rmp // Eq. (26)
				for i, m := range o.Shp.FaceLocalV[iface] {
					μ := o.Vid2seepId[m]
					fb[o.Pmap[m]] -= coef * Sf[i] * rx
					fb[o.Fmap[μ]] -= coef * Sf[i] * rf
				}
			}
		}
	}
	return true
}
Exemple #2
0
// add_natbcs_to_jac adds contribution from natural boundary conditions to Jacobian
func (o ElemUP) add_natbcs_to_jac(sol *Solution) (ok bool) {

	// compute surface integral
	ndim := Global.Ndim
	u_nverts := o.U.Shp.Nverts
	var shift float64
	var pl, fl, plmax, g, rmp float64
	for idx, nbc := range o.P.NatBcs {

		// plmax shift
		shift = nbc.Fcn.F(sol.T, nil)

		// loop over ips of face
		for jdx, ipf := range o.P.IpsFace {

			// interpolation functions and gradients @ face
			iface := nbc.IdxFace
			if LogErr(o.P.Shp.CalcAtFaceIp(o.P.X, ipf, iface), "up: add_natbcs_to_jac") {
				return
			}
			Sf := o.P.Shp.Sf
			Jf := la.VecNorm(o.P.Shp.Fnvec)
			coef := ipf.W * Jf

			// select natural boundary condition type
			switch nbc.Key {
			case "seep":

				// variables extrapolated to face
				_, pl, fl = o.P.fipvars(iface, sol)
				plmax = o.P.Plmax[idx][jdx] - shift
				if plmax < 0 {
					plmax = 0
				}

				// compute derivatives
				g = pl - plmax // Eq. (24)
				rmp = o.P.ramp(fl + o.P.κ*g)
				for i, m := range o.P.Shp.FaceLocalV[iface] {
					for n := 0; n < u_nverts; n++ {
						for j := 0; j < ndim; j++ {
							c := j + n*ndim
							for l, r := range o.P.Shp.FaceLocalV[iface] {
								o.Kpu[m][c] += coef * Sf[i] * Sf[l] * o.dρldus_ex[r][c] * rmp
							}
						}
					}
				}
			}
		}
	}
	return true
}
Exemple #3
0
// contact_add_to_rhs adds contribution to rhs due to contact modelling
func (o *ElemU) contact_add_to_rhs(fb []float64, sol *Solution) (err error) {

	// compute surface integral
	var qb, db, rmp, rx, rq float64
	for _, nbc := range o.NatBcs {

		// loop over ips of face
		for _, ipf := range o.IpsFace {

			// interpolation functions and gradients @ face
			iface := nbc.IdxFace
			err = o.Cell.Shp.CalcAtFaceIp(o.X, ipf, iface)
			if err != nil {
				return
			}
			Sf := o.Cell.Shp.Sf
			nvec := o.Cell.Shp.Fnvec

			// select natural boundary condition type
			switch nbc.Key {

			// contact
			case "contact":

				// variables extrapolated to face
				qb = o.fipvars(iface, sol)
				xf := o.Cell.Shp.FaceIpRealCoords(o.X, ipf, iface)
				la.VecAdd(xf, 1, o.us) // add displacement: x = X + u
				db = o.contact_g(xf)

				// compute residuals
				coef := ipf[3] * o.Thickness
				Jf := la.VecNorm(nvec)
				rmp = o.contact_ramp(qb + o.κ*db)
				rx = rmp
				rq = qb - rmp
				for j, m := range o.Cell.Shp.FaceLocalVerts[iface] {
					μ := o.Vid2contactId[m]
					fb[o.Qmap[μ]] -= coef * Sf[j] * rq * Jf // -residual
					for i := 0; i < o.Ndim; i++ {
						r := o.Umap[i+m*o.Ndim]
						fb[r] -= coef * Sf[j] * rx * nvec[i] // -extra term
					}
				}
			}
		}
	}
	return
}
Exemple #4
0
// CalcAtIp calculates volume data such as S and G at natural coordinate r
//  Input:
//   x[ndim][nverts+?] -- coordinates matrix of solid element
//   ip                -- integration point
//  Output:
//   S, DSdR, DxdR, DRdx, G, and J
func (o *Shape) CalcAtIp(x [][]float64, ip *Ipoint, derivs bool) (err error) {

	// S and dSdR
	o.Func(o.S, o.dSdR, ip.R, ip.S, ip.T, derivs)
	if !derivs {
		return
	}

	if o.Gndim == 1 {
		// calculate Jvec3d == dxdR
		for i := 0; i < len(x); i++ {
			o.Jvec3d[i] = 0.0
			for m := 0; m < o.Nverts; m++ {
				o.Jvec3d[i] += x[i][m] * o.dSdR[m][0] // dxdR := x * dSdR
			}
		}

		// calculate J = norm of Jvec3d
		o.J = la.VecNorm(o.Jvec3d)

		// calculate G
		for m := 0; m < o.Nverts; m++ {
			o.Gvec[m] = o.dSdR[m][0] / o.J
		}

		return
	}

	// dxdR := sum_n x * dSdR   =>  dx_i/dR_j := sum_n x^n_i * dS^n/dR_j
	for i := 0; i < len(x); i++ {
		for j := 0; j < o.Gndim; j++ {
			o.dxdR[i][j] = 0.0
			for n := 0; n < o.Nverts; n++ {
				o.dxdR[i][j] += x[i][n] * o.dSdR[n][j]
			}
		}
	}

	// dRdx := inv(dxdR)
	o.J, err = la.MatInv(o.dRdx, o.dxdR, MINDET)
	if err != nil {
		return
	}

	// G == dSdx := dSdR * dRdx  =>  dS^m/dR_i := sum_i dS^m/dR_i * dR_i/dx_j
	la.MatMul(o.G, 1, o.dSdR, o.dRdx)
	return
}
Exemple #5
0
func Test_geninvs01(tst *testing.T) {

	//verbose()
	chk.PrintTitle("geninvs01")

	// coefficients for smp invariants
	smp_a := -1.0
	smp_b := 0.5
	smp_β := 1e-1 // derivative values become too high with
	smp_ϵ := 1e-1 // small β and ϵ @ zero

	// constants for checking derivatives
	dver := chk.Verbose
	dtol := 1e-6
	dtol2 := 1e-6

	// run tests
	nd := test_nd
	for idxA := 0; idxA < len(test_nd); idxA++ {
		//for idxA := 10; idxA < 11; idxA++ {

		// tensor and eigenvalues
		A := test_AA[idxA]
		a := M_Alloc2(nd[idxA])
		Ten2Man(a, A)
		L := make([]float64, 3)
		M_EigenValsNum(L, a)

		// SMP derivs and SMP director
		dndL := la.MatAlloc(3, 3)
		dNdL := make([]float64, 3)
		d2ndLdL := utl.Deep3alloc(3, 3, 3)
		N := make([]float64, 3)
		F := make([]float64, 3)
		G := make([]float64, 3)
		m := SmpDerivs1(dndL, dNdL, N, F, G, L, smp_a, smp_b, smp_β, smp_ϵ)
		SmpDerivs2(d2ndLdL, L, smp_a, smp_b, smp_β, smp_ϵ, m, N, F, G, dNdL, dndL)
		n := make([]float64, 3)
		SmpUnitDirector(n, m, N)

		// SMP invariants
		p, q, err := GenInvs(L, n, smp_a)
		if err != nil {
			chk.Panic("SmpInvs failed:\n%v", err)
		}

		// output
		io.PfYel("\n\ntst # %d ###################################################################################\n", idxA)
		io.Pfblue2("L = %v\n", L)
		io.Pforan("n = %v\n", n)
		io.Pforan("p = %v\n", p)
		io.Pforan("q = %v\n", q)

		// check invariants
		tvec := make([]float64, 3)
		GenTvec(tvec, L, n)
		proj := make([]float64, 3) // projection of tvec along n
		tdn := la.VecDot(tvec, n)  // tvec dot n
		for i := 0; i < 3; i++ {
			proj[i] = tdn * n[i]
		}
		norm_proj := la.VecNorm(proj)
		norm_tvec := la.VecNorm(tvec)
		q_ := GENINVSQEPS + math.Sqrt(norm_tvec*norm_tvec-norm_proj*norm_proj)
		io.Pforan("proj = %v\n", proj)
		io.Pforan("norm(proj) = %v == p\n", norm_proj)
		chk.Scalar(tst, "p", 1e-14, math.Abs(p), norm_proj)
		chk.Scalar(tst, "q", 1e-13, q, q_)

		// dt/dL
		var tmp float64
		N_tmp := make([]float64, 3)
		n_tmp := make([]float64, 3)
		tvec_tmp := make([]float64, 3)
		dtdL := la.MatAlloc(3, 3)
		GenTvecDeriv1(dtdL, L, n, dndL)
		for i := 0; i < 3; i++ {
			for j := 0; j < 3; j++ {
				dnum, _ := num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
					tmp, L[j] = L[j], x
					m_tmp := SmpDirector(N_tmp, L, smp_a, smp_b, smp_β, smp_ϵ)
					SmpUnitDirector(n_tmp, m_tmp, N_tmp)
					GenTvec(tvec_tmp, L, n_tmp)
					L[j] = tmp
					return tvec_tmp[i]
				}, L[j], 1e-6)
				chk.AnaNum(tst, io.Sf("dt/dL[%d][%d]", i, j), dtol, dtdL[i][j], dnum, dver)
			}
		}

		// d²t/dLdL
		io.Pfpink("\nd²t/dLdL\n")
		dNdL_tmp := make([]float64, 3)
		dndL_tmp := la.MatAlloc(3, 3)
		dtdL_tmp := la.MatAlloc(3, 3)
		for i := 0; i < 3; i++ {
			for j := 0; j < 3; j++ {
				for k := 0; k < 3; k++ {
					dnum, _ := num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
						tmp, L[k] = L[k], x
						m_tmp := SmpDerivs1(dndL_tmp, dNdL_tmp, N_tmp, F, G, L, smp_a, smp_b, smp_β, smp_ϵ)
						SmpUnitDirector(n_tmp, m_tmp, N_tmp)
						GenTvecDeriv1(dtdL_tmp, L, n_tmp, dndL_tmp)
						L[k] = tmp
						return dtdL_tmp[i][j]
					}, L[k], 1e-6)
					dana := GenTvecDeriv2(i, j, k, L, dndL, d2ndLdL[i][j][k])
					chk.AnaNum(tst, io.Sf("d²t[%d]/dL[%d]dL[%d]", i, j, k), dtol2, dana, dnum, dver)
				}
			}
		}

		// change tolerance
		dtol_tmp := dtol
		switch idxA {
		case 5, 11:
			dtol = 1e-5
		case 12:
			dtol = 0.0013
		}

		// first order derivatives
		dpdL := make([]float64, 3)
		dqdL := make([]float64, 3)
		p_, q_, err := GenInvsDeriv1(dpdL, dqdL, L, n, dndL, smp_a)
		if err != nil {
			chk.Panic("%v", err)
		}
		chk.Scalar(tst, "p", 1e-17, p, p_)
		chk.Scalar(tst, "q", 1e-17, q, q_)
		var ptmp, qtmp float64
		io.Pfpink("\ndp/dL\n")
		for j := 0; j < 3; j++ {
			dnum, _ := num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
				tmp, L[j] = L[j], x
				m_tmp := SmpDirector(N_tmp, L, smp_a, smp_b, smp_β, smp_ϵ)
				SmpUnitDirector(n_tmp, m_tmp, N_tmp)
				ptmp, _, err = GenInvs(L, n_tmp, smp_a)
				if err != nil {
					chk.Panic("DerivCentral: SmpInvs failed:\n%v", err)
				}
				L[j] = tmp
				return ptmp
			}, L[j], 1e-6)
			chk.AnaNum(tst, io.Sf("dp/dL[%d]", j), dtol, dpdL[j], dnum, dver)
		}
		io.Pfpink("\ndq/dL\n")
		for j := 0; j < 3; j++ {
			dnum, _ := num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
				tmp, L[j] = L[j], x
				m_tmp := SmpDirector(N_tmp, L, smp_a, smp_b, smp_β, smp_ϵ)
				SmpUnitDirector(n_tmp, m_tmp, N_tmp)
				_, qtmp, err = GenInvs(L, n_tmp, smp_a)
				if err != nil {
					chk.Panic("DerivCentral: SmpInvs failed:\n%v", err)
				}
				L[j] = tmp
				return qtmp
			}, L[j], 1e-6)
			chk.AnaNum(tst, io.Sf("dq/dL[%d]", j), dtol, dqdL[j], dnum, dver)
		}

		// recover tolerance
		dtol = dtol_tmp

		// change tolerance
		io.Pforan("dtol2 = %v\n", dtol2)
		dtol2_tmp := dtol2
		switch idxA {
		case 5:
			dtol2 = 1e-5
		case 10:
			dtol2 = 0.72
		case 11:
			dtol2 = 1e-5
		case 12:
			dtol2 = 544
		}

		// second order derivatives
		dpdL_tmp := make([]float64, 3)
		dqdL_tmp := make([]float64, 3)
		d2pdLdL := la.MatAlloc(3, 3)
		d2qdLdL := la.MatAlloc(3, 3)
		GenInvsDeriv2(d2pdLdL, d2qdLdL, L, n, dpdL, dqdL, p, q, dndL, d2ndLdL, smp_a)
		io.Pfpink("\nd²p/dLdL\n")
		for i := 0; i < 3; i++ {
			for j := 0; j < 3; j++ {
				dnum, _ := num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
					tmp, L[j] = L[j], x
					m_tmp := SmpDerivs1(dndL_tmp, dNdL_tmp, N_tmp, F, G, L, smp_a, smp_b, smp_β, smp_ϵ)
					SmpUnitDirector(n_tmp, m_tmp, N_tmp)
					GenInvsDeriv1(dpdL_tmp, dqdL_tmp, L, n_tmp, dndL_tmp, smp_a)
					L[j] = tmp
					return dpdL_tmp[i]
				}, L[j], 1e-6)
				chk.AnaNum(tst, io.Sf("d²p/dL[%d][%d]", i, j), dtol2, d2pdLdL[i][j], dnum, dver)
			}
		}
		io.Pfpink("\nd²q/dLdL\n")
		for i := 0; i < 3; i++ {
			for j := 0; j < 3; j++ {
				dnum, _ := num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
					tmp, L[j] = L[j], x
					m_tmp := SmpDerivs1(dndL_tmp, dNdL_tmp, N_tmp, F, G, L, smp_a, smp_b, smp_β, smp_ϵ)
					SmpUnitDirector(n_tmp, m_tmp, N_tmp)
					GenInvsDeriv1(dpdL_tmp, dqdL_tmp, L, n_tmp, dndL_tmp, smp_a)
					L[j] = tmp
					return dqdL_tmp[i]
				}, L[j], 1e-6)
				chk.AnaNum(tst, io.Sf("d²q/dL[%d][%d]", i, j), dtol2, d2qdLdL[i][j], dnum, dver)
			}
		}

		// recover tolerance
		dtol2 = dtol2_tmp
	}
}
Exemple #6
0
// add_natbcs_to_jac adds contribution from natural boundary conditions to Jacobian
func (o ElemP) add_natbcs_to_jac(sol *Solution) (ok bool) {

	// clear matrices
	if o.HasSeep {
		for i := 0; i < o.Np; i++ {
			for j := 0; j < o.Nf; j++ {
				o.Kpf[i][j] = 0
				o.Kfp[j][i] = 0
			}
		}
		la.MatFill(o.Kff, 0)
	}

	// compute surface integral
	nverts := o.Shp.Nverts
	var shift float64
	var ρl, pl, fl, plmax, g, rmp, rmpD float64
	var drxdpl, drxdfl, drfdpl, drfdfl float64
	for idx, nbc := range o.NatBcs {

		// plmax shift
		shift = nbc.Fcn.F(sol.T, nil)

		// loop over ips of face
		for jdx, ipf := range o.IpsFace {

			// interpolation functions and gradients @ face
			iface := nbc.IdxFace
			if LogErr(o.Shp.CalcAtFaceIp(o.X, ipf, iface), "add_natbcs_to_jac") {
				return
			}
			Sf := o.Shp.Sf
			Jf := la.VecNorm(o.Shp.Fnvec)
			coef := ipf.W * Jf

			// select natural boundary condition type
			switch nbc.Key {
			case "seep":

				// variables extrapolated to face
				ρl, pl, fl = o.fipvars(iface, sol)
				plmax = o.Plmax[idx][jdx] - shift
				if plmax < 0 {
					plmax = 0
				}

				// compute derivatives
				g = pl - plmax // Eq. (24)
				rmp = o.ramp(fl + o.κ*g)
				rmpD = o.rampD1(fl + o.κ*g)
				drxdpl = ρl * o.κ * rmpD // first term in Eq. (A.4) (without Sn)
				drxdfl = ρl * rmpD       // Eq. (A.5) (without Sn)
				drfdpl = -o.κ * rmpD     // Eq. (A.6) (corrected with κ and without Sn)
				drfdfl = 1.0 - rmpD      // Eq. (A.7) (without Sn)
				for i, m := range o.Shp.FaceLocalV[iface] {
					μ := o.Vid2seepId[m]
					for j, n := range o.Shp.FaceLocalV[iface] {
						ν := o.Vid2seepId[n]
						o.Kpp[m][n] += coef * Sf[i] * Sf[j] * drxdpl
						o.Kpf[m][ν] += coef * Sf[i] * Sf[j] * drxdfl
						o.Kfp[μ][n] += coef * Sf[i] * Sf[j] * drfdpl
						o.Kff[μ][ν] += coef * Sf[i] * Sf[j] * drfdfl
					}
					for n := 0; n < nverts; n++ { // Eqs. (18) and (22)
						for l, r := range o.Shp.FaceLocalV[iface] {
							o.Kpp[m][n] += coef * Sf[i] * Sf[l] * o.dρldpl_ex[r][n] * rmp
						}
					}
				}
			}
		}
	}
	return true
}
Exemple #7
0
// 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
}
Exemple #8
0
func Test_smpinvs02(tst *testing.T) {

	//verbose()
	chk.PrintTitle("smpinvs02")

	// coefficients for smp invariants
	smp_a := -1.0
	smp_b := 0.5
	smp_β := 1e-1 // derivative values become too high with
	smp_ϵ := 1e-1 // small β and ϵ @ zero

	// constants for checking derivatives
	dver := chk.Verbose
	dtol := 1e-9
	dtol2 := 1e-8

	// run tests
	nd := test_nd
	for idxA := 0; idxA < len(test_nd); idxA++ {
		//for idxA := 0; idxA < 1; idxA++ {
		//for idxA := 10; idxA < 11; idxA++ {

		// tensor and eigenvalues
		A := test_AA[idxA]
		a := M_Alloc2(nd[idxA])
		Ten2Man(a, A)
		L := make([]float64, 3)
		M_EigenValsNum(L, a)

		// SMP director
		N := make([]float64, 3)
		n := make([]float64, 3)
		m := SmpDirector(N, L, smp_a, smp_b, smp_β, smp_ϵ)
		SmpUnitDirector(n, m, N)

		// output
		io.PfYel("\n\ntst # %d ###################################################################################\n", idxA)
		io.Pforan("L = %v\n", L)
		io.Pforan("N = %v\n", N)
		io.Pforan("m = %v\n", m)
		io.Pfpink("n = %v\n", n)
		chk.Vector(tst, "L", 1e-12, L, test_λ[idxA])
		chk.Scalar(tst, "norm(n)==1", 1e-15, la.VecNorm(n), 1)
		chk.Scalar(tst, "m=norm(N)", 1e-14, m, la.VecNorm(N))

		// dN/dL
		var tmp float64
		N_tmp := make([]float64, 3)
		dNdL := make([]float64, 3)
		SmpDirectorDeriv1(dNdL, L, smp_a, smp_b, smp_β, smp_ϵ)
		io.Pfpink("\ndNdL = %v\n", dNdL)
		for i := 0; i < 3; i++ {
			dnum, _ := num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
				tmp, L[i] = L[i], x
				SmpDirector(N_tmp, L, smp_a, smp_b, smp_β, smp_ϵ)
				L[i] = tmp
				return N_tmp[i]
			}, L[i], 1e-6)
			chk.AnaNum(tst, io.Sf("dN/dL[%d][%d]", i, i), dtol, dNdL[i], dnum, dver)
		}

		// dm/dL
		n_tmp := make([]float64, 3)
		dmdL := make([]float64, 3)
		SmpNormDirectorDeriv1(dmdL, m, N, dNdL)
		io.Pfpink("\ndmdL = %v\n", dmdL)
		for j := 0; j < 3; j++ {
			dnum, _ := num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
				tmp, L[j] = L[j], x
				m_tmp := SmpDirector(N_tmp, L, smp_a, smp_b, smp_β, smp_ϵ)
				L[j] = tmp
				return m_tmp
			}, L[j], 1e-6)
			chk.AnaNum(tst, io.Sf("dm/dL[%d]", j), dtol, dmdL[j], dnum, dver)
		}

		// dn/dL
		dndL := la.MatAlloc(3, 3)
		SmpUnitDirectorDeriv1(dndL, m, N, dNdL, dmdL)
		io.Pfpink("\ndndL = %v\n", dndL)
		for i := 0; i < 3; i++ {
			for j := 0; j < 3; j++ {
				dnum, _ := num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
					tmp, L[j] = L[j], x
					m_tmp := SmpDirector(N_tmp, L, smp_a, smp_b, smp_β, smp_ϵ)
					SmpUnitDirector(n_tmp, m_tmp, N_tmp)
					L[j] = tmp
					return n_tmp[i]
				}, L[j], 1e-6)
				chk.AnaNum(tst, io.Sf("dn/dL[%d][%d]", i, j), dtol, dndL[i][j], dnum, dver)
			}
		}

		// change tolerance
		dtol2_tmp := dtol2
		if idxA == 10 || idxA == 11 {
			dtol2 = 1e-6
		}

		// d²m/dLdL
		dNdL_tmp := make([]float64, 3)
		dmdL_tmp := make([]float64, 3)
		d2NdL2 := make([]float64, 3)
		d2mdLdL := la.MatAlloc(3, 3)
		SmpDirectorDeriv2(d2NdL2, L, smp_a, smp_b, smp_β, smp_ϵ)
		SmpNormDirectorDeriv2(d2mdLdL, L, smp_a, smp_b, smp_β, smp_ϵ, m, N, dNdL, d2NdL2, dmdL)
		io.Pfpink("\nd2mdLdL = %v\n", d2mdLdL)
		for i := 0; i < 3; i++ {
			for j := 0; j < 3; j++ {
				dnum, _ := num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
					tmp, L[j] = L[j], x
					m_tmp := SmpDirector(N_tmp, L, smp_a, smp_b, smp_β, smp_ϵ)
					SmpDirectorDeriv1(dNdL_tmp, L, smp_a, smp_b, smp_β, smp_ϵ)
					SmpNormDirectorDeriv1(dmdL_tmp, m_tmp, N_tmp, dNdL_tmp)
					L[j] = tmp
					return dmdL_tmp[i]
				}, L[j], 1e-6)
				chk.AnaNum(tst, io.Sf("d2m/dL[%d]dL[%d]", i, j), dtol2, d2mdLdL[i][j], dnum, dver)
			}
		}

		// d²N/dLdL
		io.Pfpink("\nd²N/dLdL\n")
		for i := 0; i < 3; i++ {
			dnum, _ := num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
				tmp, L[i] = L[i], x
				SmpDirectorDeriv1(dNdL_tmp, L, smp_a, smp_b, smp_β, smp_ϵ)
				L[i] = tmp
				return dNdL_tmp[i]
			}, L[i], 1e-6)
			chk.AnaNum(tst, io.Sf("d²N[%d]/dL[%d]dL[%d]", i, i, i), dtol2, d2NdL2[i], dnum, dver)
		}

		// d²n/dLdL
		io.Pfpink("\nd²n/dLdL\n")
		dndL_tmp := la.MatAlloc(3, 3)
		d2ndLdL := utl.Deep3alloc(3, 3, 3)
		SmpUnitDirectorDeriv2(d2ndLdL, m, N, dNdL, d2NdL2, dmdL, n, d2mdLdL, dndL)
		for i := 0; i < 3; i++ {
			for j := 0; j < 3; j++ {
				for k := 0; k < 3; k++ {
					dnum, _ := num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
						tmp, L[k] = L[k], x
						m_tmp := SmpDirector(N_tmp, L, smp_a, smp_b, smp_β, smp_ϵ)
						SmpDirectorDeriv1(dNdL_tmp, L, smp_a, smp_b, smp_β, smp_ϵ)
						SmpNormDirectorDeriv1(dmdL_tmp, m_tmp, N_tmp, dNdL_tmp)
						SmpUnitDirectorDeriv1(dndL_tmp, m_tmp, N_tmp, dNdL_tmp, dmdL_tmp)
						L[k] = tmp
						return dndL_tmp[i][j]
					}, L[k], 1e-6)
					chk.AnaNum(tst, io.Sf("d²n[%d]/dL[%d]dL[%d]", i, j, k), dtol2, d2ndLdL[i][j][k], dnum, dver)
				}
			}
		}

		// recover tolerance
		dtol2 = dtol2_tmp

		// SMP derivs
		//if false {
		if true {
			io.Pfpink("\nSMP derivs\n")
			dndL_ := la.MatAlloc(3, 3)
			dNdL_ := make([]float64, 3)
			d2ndLdL_ := utl.Deep3alloc(3, 3, 3)
			N_ := make([]float64, 3)
			F_ := make([]float64, 3)
			G_ := make([]float64, 3)
			m_ := SmpDerivs1(dndL_, dNdL_, N_, F_, G_, L, smp_a, smp_b, smp_β, smp_ϵ)
			SmpDerivs2(d2ndLdL_, L, smp_a, smp_b, smp_β, smp_ϵ, m_, N_, F_, G_, dNdL_, dndL_)
			chk.Scalar(tst, "m_", 1e-14, m_, m)
			chk.Vector(tst, "N_", 1e-15, N_, N)
			chk.Vector(tst, "dNdL_", 1e-15, dNdL_, dNdL)
			chk.Matrix(tst, "dndL_", 1e-13, dndL_, dndL)
			chk.Deep3(tst, "d2ndLdL_", 1e-11, d2ndLdL_, d2ndLdL)
		}
	}
}
Exemple #9
0
// contact_add_to_jac adds coupled equations due to contact modelling to Jacobian
func (o *ElemU) contact_add_to_jac(Kb *la.Triplet, sol *Solution) (err error) {

	// clear matrices
	for i := 0; i < o.Nq; i++ {
		for j := 0; j < o.Nq; j++ {
			o.Kqq[i][j] = 0
		}
		for j := 0; j < o.Nu; j++ {
			o.Kqu[i][j] = 0
			o.Kuq[j][i] = 0
		}
	}

	// compute surface integral
	var qb, db, Hb float64
	dddu := make([]float64, o.Ndim)
	for _, nbc := range o.NatBcs {

		// loop over ips of face
		for _, ipf := range o.IpsFace {

			// contact
			switch nbc.Key {
			case "contact":

				// interpolation functions and gradients @ face
				iface := nbc.IdxFace
				err = o.Cell.Shp.CalcAtFaceIp(o.X, ipf, iface)
				if err != nil {
					return
				}
				Sf := o.Cell.Shp.Sf
				nvec := o.Cell.Shp.Fnvec
				coef := ipf[3] * o.Thickness
				Jf := la.VecNorm(nvec)

				// variables extrapolated to face
				qb = o.fipvars(iface, sol)
				xf := o.Cell.Shp.FaceIpRealCoords(o.X, ipf, iface)
				la.VecAdd(xf, 1, o.us) // add displacement: x = X + u
				db = o.contact_g(xf)
				o.contact_dgdx(dddu, xf)

				// compute derivatives
				Hb = o.contact_rampD1(qb + o.κ*db)
				for i, m := range o.Cell.Shp.FaceLocalVerts[iface] {
					μ := o.Vid2contactId[m]
					for j, n := range o.Cell.Shp.FaceLocalVerts[iface] {
						ν := o.Vid2contactId[n]
						o.Kqq[μ][ν] += coef * Jf * Sf[i] * Sf[j] * (1.0 - Hb)
						for k := 0; k < o.Ndim; k++ {
							r := k + m*o.Ndim
							c := k + n*o.Ndim
							val := coef * Sf[i] * Sf[j] * Hb * o.κ * dddu[k] * Jf
							o.Kuq[r][ν] += coef * Sf[i] * Sf[j] * Hb * nvec[k]
							o.Kqu[μ][c] -= val
							o.K[r][c] += val
						}
					}
				}
			}
		}
	}

	// add Ks to sparse matrix Kb
	for i, I := range o.Qmap {
		for j, J := range o.Qmap {
			Kb.Put(I, J, o.Kqq[i][j])
		}
		for j, J := range o.Umap {
			Kb.Put(I, J, o.Kqu[i][j])
			Kb.Put(J, I, o.Kuq[j][i])
		}
	}
	for i, I := range o.Umap {
		for j, J := range o.Umap {
			Kb.Put(I, J, o.K[i][j])
		}
	}
	return
}