function [exxb,eyyb,exyb,exxd,eyyd,exyd]=CalcNodalStrainRates(MUA,ub,vb,ud,vd)

Calculates horizontal strain rates given horizontal velocities.

  [exxb,eyyb,exyb,exxd,eyyd,exyd]=CalcNodalStrainRates(MUA,ub,vb,ud,vd)

Returns nodal values.

Note: The strain rates are calculated at integration points and then projected onto nodes.

The projection does not conserve positivity and positve integration values can become negative at nodes. The effective strain rate , e, is for this reason calculated directly from nodal values, ensuring that e is always positive.

Example:

Read data, calculate nodal strain rates, and then plot over FE mesh at roughly equal spaced grid.

load ('GaussPeak_Example_Restartfile.mat','MUA','CtrlVarInRestartFile','F','GF','BCs');  % load data
CtrlVar=CtrlVarInRestartFile; x=MUA.coordinates(:,1) ; y=MUA.coordinates(:,2);
[exx,eyy,exy]=CalcNodalStrainRates(MUA,F.ub,F.vb);                             % calculate strain rates
[X,Y]=ndgrid(linspace(min(x),max(x),10),linspace(min(y),max(y),10));
I=nearestNeighbor(MUA.TR,[X(:) Y(:)]);  % find nodes within computational grid closest to the regularly scape X and Y grid points.
figure
CtrlVar.PlotNodes=0; PlotMuaMesh(CtrlVar,MUA,[],'color','k') ;                           % Plot FE mesh
hold on
scale=1e5; LineWidth=2 ;
PlotTensor(x(I)/CtrlVar.PlotXYscale,y(I)/CtrlVar.PlotXYscale,exx(I),exy(I),eyy(I),scale,LineWidth);  % plot strain rates
axis equal

See also CalcNodalStrainRatesAndStresses

narginchk(3,5)

if nargin==4
       fprintf("The parameter list no longer contains CtrlVar \n")
end

if ~nargin==3 || ~nargin==5
    error('Ua:CalcNodalStrainRates','Wrong number of input arguments')
end

if ~isempty(ub)

    [dubdx,dubdy]=calcFEderivativesMUA(ub,MUA);
    [dvbdx,dvbdy]=calcFEderivativesMUA(vb,MUA);
    exxb=dubdx;
    eyyb=dvbdy;
    exyb=0.5*(dubdy+dvbdx);
    [exxb,eyyb,exyb]=ProjectFintOntoNodes(MUA,exxb,eyyb,exyb);
else
    exxb=[] ; eyyb=[] ; exyb=[];
end

if nargin == 5
    if ~isempty(ud)
        [duddx,duddy]=calcFEderivativesMUA(ud,MUA);
        [dvddx,dvddy]=calcFEderivativesMUA(vd,MUA);

        exxd=duddx;
        eyyd=dvddy;
        exyd=0.5*(duddy+dvddx);

        [exxd,eyyd,exyd]=ProjectFintOntoNodes(MUA,exxd,eyyd,exyd);
    end
else
    exxd=[] ; eyyd=[] ; exyd=[];
end

end

Published with MATLAB® R2025b