growth.js

/**
 * @page Growth
 * Growth functions
 *
 * Grow functions affect the rest configuration of the model's geometry
 *
 * Depends on algebra.js and geometry.js
 */

function myGrowth() {
    // Variables storing growth parametres
    this.g={};    // growth tensor in material coordinates (a 3x3 matrix)
    this.T=0;    // time constant
}

function initGrowth(params) {
    var gr=new myGrowth();
    gr.G=params.G;
    gr.T=params.T;
    return gr;
}
/**
 * @function growHomogeneous
 */
function growHomogeneous(ge,gr) {
    var nt=ge.nt;
    var t=ge.t;
    var p=ge.p;
    var r=ge.r;
    var H=gr.G;    // homogeneous growth factor
    
    var i,j,k,m,n;
    
    // for each tetrahedron
    for(i=0;i<nt;i++) {
        // for each tetra. node
        for(j=0;j<4;j++) {
            n=t[4*i+j];    // material node indices
            m=4*i+j;    // rest node indices
            // growth function: homogeneous growth
            for(k=0;k<3;k++) {
                r[m*3+k]=p[n*3+k]*H;
            }
        }
    }
}
/**
 * @function growBlockBorderInstantaneous
 */
function growBlockBorderInstantaneous(ge,gr) {
    var nw=ge.nw;
    var nh=ge.nh;
    var nd=ge.nd;
    var t=ge.t;
    var p=ge.p;
    var r=ge.r;
    var H=gr.G;

    var i,j,k,l,m,n;
    var numbox,numtet,im,ir;
    
    // tetrahedral boxes
    j=nh-2;
    for(i=0;i<nw-1;i++)
    for(k=0;k<nd-1;k++)
    {
        // box element index
        numbox=i*(nh-1)*(nd-1)+j*(nd-1)+k;
        // box's tetrahedral element index
        for(l=0;l<5;l++) {
            numtet=numbox*5+l;
            // tetrahedron's node index
            for(m=0;m<4;m++) {
                im=t[numtet*4+m];    // material vertex index
                ir=numtet*4+m;        // rest vertex index
                for(n=0;n<3;n++)
                    r[ir*3+n]=p[im*3+n]*H;
            }
        }
    }
}

/**
 * @function growRingBorderInstantaneous
 */
function growRingBorderInstantaneous(ge,gr) {
    var ntheta=ge.ntheta;
    var nxy=ge.nxy;
    var nz=ge.nz;
    var t=ge.t;
    var p=ge.p;
    var r=ge.r;
    var H=gr.G;

    var i,j,k,l,m,n;
    var numbox,numtet,im,ir;
    
    // tetrahedral boxes
    j=nxy-2;
    for(i=0;i<ntheta;i++)
    for(k=0;k<nz-1;k++)
    {
        // box element index
        numbox=i*(nxy-1)*(nz-1)+j*(nz-1)+k;
        // box's tetrahedral element index
        for(l=0;l<5;l++) {
            numtet=numbox*5+l;
            // tetrahedron's node index
            for(m=0;m<4;m++) {
                im=t[numtet*4+m];    // material vertex index
                ir=numtet*4+m;        // rest vertex index
                for(n=0;n<3;n++)
                    r[ir*3+n]=p[im*3+n]*H;
            }
        }
    }
}
/**
 * @function growRingBorderProgressive
 */
function growRingBorderProgressive(ge,gr,time) {
    var ntheta=ge.ntheta;
    var nxy=ge.nxy;
    var nz=ge.nz;
    var t=ge.t;
    var p=ge.p;
    var r=ge.r;
    var H=gr.G;
    var T=gr.T;
    
    var i,j,k,l,m,n;
    var numbox,numtet,im,ir;
    
    if(time>T)
        return;

    // tetrahedral boxes
    j=nxy-2;
    for(i=0;i<ntheta;i++)
    for(k=0;k<nz-1;k++)
    {
        // box element index
        numbox=i*(nxy-1)*(nz-1)+j*(nz-1)+k;
        // box's tetrahedral element index
        for(l=0;l<5;l++) {
            numtet=numbox*5+l;
            // tetrahedron's node index
            for(m=0;m<4;m++) {
                im=t[numtet*4+m];    // material vertex index
                ir=numtet*4+m;        // rest vertex index
                for(n=0;n<3;n++)
                    r[ir*3+n]=p[im*3+n]*Math.pow(H,1/(T/dt));
            }
        }
    }
}
/**
 * @function growRingTangentialInstantaneous
 * @description Each vertex in the original ring has coordinates x,y,z. The coordinates x,y are in the plane of the ring, z is in the plane of its thickness. The function growTangential produces a tangential expansion of the ring at rest, i.e., it alters the x,y coordinates, without changing the z coordinate (thickness), nor the radial size of each finite element. WRONG FOLLOWS: This is achieved by displacing each x,y point radially. The amount of displacement is such that the angle supported by each finite element will be multiplied by the dilatation parametre D. The total perimeter of a ring at a distance R from the central axis is 2*pi*R and will become 2*pi*R*D. Then, each point x,y at distance R has to be displaced to a distance R*D, i.e., they have to be multiplied by a factor D such that (x*D)^2+(y*D)^2=(R*D)^2.
 */
function growRingTangentialInstantaneous(ge,gr) {
    var ntheta=ge.ntheta;
    var nxy=ge.nxy;
    var nz=ge.nz;
    var t=ge.t;
    var r=ge.r;
    var Ro=ge.Ro;
    var Ri=ge.Ri;
    var D=gr.G;

    var i,j,k,l,m,n;
    var numbox,numtet;
    var im,ir;
    var theta,R,z;
    var a,di,dj,dtheta;
    
    for(i=0;i<ntheta;i++)
    for(j=0;j<nxy-1;j++)
    for(k=0;k<nz-1;k++)
    {
        numbox=i*(nxy-1)*(nz-1)+j*(nz-1)+k;
        for(l=0;l<5;l++) {
            numtet=numbox*5+l;
            a=tetraTopo[l].split(" ");
            for(m=0;m<4;m++) {
                ir=numtet*4+m;        // index of rest vertex
                di=parseInt(a[m].charAt(0));
                dj=parseInt(a[m].charAt(1));
                theta=2*Math.PI*(i+di)/ntheta;
                R=Ro*((j+dj)/nxy)+Ri*(1-(j+dj)/nxy);
                dtheta=(D-1)*(Math.PI/ntheta)*(2*di-1);
                r[ir*3+0]=R*Math.cos(theta+dtheta);
                r[ir*3+1]=R*Math.sin(theta+dtheta);
            }
        }
    }
}
/**
 * @function growSurface
 */
function growSurfaceHomogeneousInstantaneous(ge,gr) {
    var nt=ge.nt;
    var r=ge.r;
    var H=gr.G;          // homogeneous growth

    var i,j,k,ir;
    
    for(i=0;i<nt;i++)    // each tetrahedron
    for(j=0;j<4;j++) {
        ir=4*i+j;        // rest vertex
        for(k=0;k<3;k++) {
            r[3*ir+k]*=H;
        }
    }
}