Large Displacement Analysis using PDE Toolbox

Hello,

I am looking for a method of incorporating large displacement analysis using the PDE toolbox (for displacements large enough to alter the material properties of a compliant beam over the course of the displacement).

I am currently using the PDE toolbox to create a static, structural model (plane stress), fix one end while displacing the other, and solving for nodal displacement, stress, strain, and specifically VonMisses stress.

For small displacements I believe I have no issues; however, for larger displacements, the solution differs depending on if the displacement is performed in one step, or performed in several steps (see figure below).

As can be seen, while the center of the free end (the point of displacement) is consistent among the solutions, the configuration of the model differs based on how many load steps are used. This is likely due to material properties changing as the shape is deformed. I believe that the more load steps performed, the more accurate the model is. Thus, if I want to ensure that a compliant beam made out of a chosen material will not yield, it is better if I perform this analysis over several steps.

While it would be nice to recreate the model and mesh each step (as done above), and simply add the VM stress of each node over all the steps, I cannot, as I can not guarantee that the mesh is the same at each step (i.e. the initial node positions at each step is the final node positions of the step before) . I am therefore wondering if there is another way to perform this "large displacement" analysis using the PDE toolbox.

I have played around using the geometryfromMesh() function, which allows you to define your own mesh given known nodes and elements, but the function also creates the geometry, and takes away the control I have over vertex displacement, meaning I can't guarantee the existance of the vertex I want to displace (center of free end).

Any guidance is appreciated. Code for how I solve the problem is below.

model = createpde('structural','static-planestress'); % create structure plane stress model

G = [2,length(poly),poly(1,:) poly(2,:)]'; % geometry description matrix using outline of of desired shape
GM = decsg(G); % creating geometry matrix (GM) from geometry description matrix (G) 
geometryFromEdges(model,GM); % creating analytical geometry

mesh = generateMesh(model,'GeometricOrder','linear'); % creating mesh

structuralProperties(model,'YoungsModulus',E,'PoissonsRatio',nu,'MassDensity',rho); % material properties - mass density not needed
structuralBC(model,'Edge',FixedE,'Constraint','fixed'); % fixing left edge 

structuralBC(model,'Vertex',FreeV,'YDisplacement',DispY,'XDisplacement',DispX); % displacing model at vertex "FreeV"

structuralresults = solve(model); % solving model for disp, stress, strain, VM stress