CauchyGreenStrain

Author: softmattertheory

src/geometry/functional.c

@@ -3882,6 +3882,7 @@ typedef struct {
     value *fields;
     value *originalfields; // Original fields
     value method; // Method dictionary
+    objectmesh *mref; // Reference mesh
     vm *v;
 } integralref;
 
@@ -4115,21 +4116,69 @@ static value integral_gradfn(vm *v, int nargs, value *args) {
     return out;
 }
 
+/* -------------------
+ * Cauchy green strain
+ * ------------------- */
+
+int cauchygreenhandle; // TL storage handle for CG tensor
+
+/** Evaluates the cg strain tensor */
+void integral_evaluatecg(vm *v, value *out) {
+    objectintegralelementref *elref = integral_getelementref(v);
+    
+    if (!elref || !elref->iref->mref) {
+        morpho_runtimeerror(v, INTEGRAL_SPCLFN, CGTENSOR_FUNCTION); return;
+    }
+    
+    int gdim=elref->nv-1; // Dimension of Gram matrix
+    
+    objectmatrix *cg=object_newmatrix(gdim, gdim, true);
+    if (!cg) { morpho_runtimeerror(v, ERROR_ALLOCATIONFAILED); return; }
+    
+    double gramrefel[gdim*gdim], gramdefel[gdim*gdim], qel[gdim*gdim], rel[gdim*gdim];
+    objectmatrix gramref = MORPHO_STATICMATRIX(gramrefel, gdim, gdim); // Gram matrices
+    objectmatrix gramdef = MORPHO_STATICMATRIX(gramdefel, gdim, gdim); //
+    objectmatrix q = MORPHO_STATICMATRIX(qel, gdim, gdim); // Inverse of Gram in source domain
+    objectmatrix r = MORPHO_STATICMATRIX(rel, gdim, gdim); // Intermediate calculations
+    
+    linearelasticity_calculategram(elref->iref->mref->vert, elref->mesh->dim, elref->nv, elref->vid, &gramref);
+    linearelasticity_calculategram(elref->mesh->vert, elref->mesh->dim, elref->nv, elref->vid, &gramdef);
+    
+    if (matrix_inverse(&gramref, &q)!=MATRIX_OK) return false;
+    if (matrix_mul(&gramdef, &q, &r)!=MATRIX_OK) return false;
+
+    matrix_identity(cg);
+    matrix_scale(cg, -0.5);
+    matrix_accumulate(cg, 0.5, &r);
+    
+    vm_settlvar(v, cauchygreenhandle, MORPHO_OBJECT(cg));
+    *out = MORPHO_OBJECT(cg);
+}
+
+static value integral_cgfn(vm *v, int nargs, value *args) {
+    value out=MORPHO_NIL;
+
+    vm_gettlvar(v, cauchygreenhandle, &out);
+    if (MORPHO_ISNIL(out)) integral_evaluatecg(v, &out);
+    
+    return out;
+}
+
 /* ----------------------
  * General initialization
  * ---------------------- */
 
 /** Clears threadlocal storage */
 void integral_cleartlvars(vm *v) {
-    int handles[] = { elementhandle, normlhandle, tangenthandle, -1 };
+    int handles[] = { elementhandle, normlhandle, tangenthandle, cauchygreenhandle, -1 };
 
     for (int i=0; handles[i]>=0; i++) {
         vm_settlvar(v, handles[i], MORPHO_NIL);
     }
 }
 
 void integral_freetlvars(vm *v) {
-    int handles[] = { normlhandle, tangenthandle, -1 };
+    int handles[] = { normlhandle, tangenthandle, cauchygreenhandle, -1 };
 
     for (int i=0; handles[i]>=0; i++) {
         value val;
@@ -4150,17 +4199,23 @@ value functional_methodproperty;
 bool integral_prepareref(objectinstance *self, objectmesh *mesh, grade g, objectselection *sel, integralref *ref) {
     bool success=false;
     value func=MORPHO_NIL;
+    value mref=MORPHO_NIL;
     value field=MORPHO_NIL;
     value method=MORPHO_NIL;
     ref->v=NULL;
     ref->nfields=0;
     ref->method=MORPHO_NIL;
+    ref->mref=NULL;
 
     if (objectinstance_getpropertyinterned(self, scalarpotential_functionproperty, &func) &&
         MORPHO_ISCALLABLE(func)) {
         ref->integrand=func;
         success=true;
     }
+    if (objectinstance_getpropertyinterned(self, linearelasticity_referenceproperty, &mref) &&
+        MORPHO_ISMESH(mref)) {
+        ref->mref=MORPHO_GETMESH(mref);
+    }
     if (objectinstance_getpropertyinterned(self, functional_methodproperty, &method)) {
         ref->method=method;
     }
@@ -4290,10 +4345,13 @@ value LineIntegral_init(vm *v, int nargs, value *args) {
     int nparams = -1;
     int nfixed;
     value method=MORPHO_NIL;
+    value mref=MORPHO_NIL;
 
-    if (builtin_options(v, nargs, args, &nfixed, 1,
-                        functional_methodproperty, &method)) {
+    if (builtin_options(v, nargs, args, &nfixed, 2,
+                        functional_methodproperty, &method,
+                        linearelasticity_referenceproperty, &mref)) {
         if (MORPHO_ISDICTIONARY(method)) objectinstance_setproperty(self, functional_methodproperty, method);
+        if (MORPHO_ISMESH(mref)) objectinstance_setproperty(self, linearelasticity_referenceproperty, mref);
     } else {
         morpho_runtimeerror(v, LINEINTEGRAL_ARGS);
         return MORPHO_NIL;
@@ -4638,6 +4696,7 @@ void functional_initialize(void) {
     builtin_addfunction(TANGENT_FUNCTION, integral_tangent, BUILTIN_FLAGSEMPTY);
     builtin_addfunction(NORMAL_FUNCTION, integral_normal, BUILTIN_FLAGSEMPTY);
     builtin_addfunction(GRAD_FUNCTION, integral_gradfn, BUILTIN_FLAGSEMPTY);
+    builtin_addfunction(CGTENSOR_FUNCTION, integral_cgfn, BUILTIN_FLAGSEMPTY);
 
     morpho_defineerror(FUNC_INTEGRAND_MESH, ERROR_HALT, FUNC_INTEGRAND_MESH_MSG);
     morpho_defineerror(FUNC_ELNTFND, ERROR_HALT, FUNC_ELNTFND_MSG);
@@ -4672,6 +4731,7 @@ void functional_initialize(void) {
     elementhandle=vm_addtlvar();
     tangenthandle=vm_addtlvar();
     normlhandle=vm_addtlvar();
+    cauchygreenhandle=vm_addtlvar();
 
     morpho_addfinalizefn(functional_finalize);
 }

src/geometry/functional.h

@@ -56,6 +56,7 @@
 #define TANGENT_FUNCTION               "tangent"
 #define NORMAL_FUNCTION                "normal"
 #define GRAD_FUNCTION                  "grad"
+#define CGTENSOR_FUNCTION              "cgtensor"
 
 /* Functional names */
 #define LENGTH_CLASSNAME               "Length"

test/functionals/areaintegral/cgtensor.morpho

@@ -0,0 +1,24 @@
+import constants
+import meshtools
+
+var mb = MeshBuilder() 
+mb.addvertex([0,0])
+mb.addvertex([1,0])
+mb.addvertex([0,1])
+mb.addface([0,1,2])
+
+var m = mb.build() 
+
+var mref = m.clone() 
+
+m.setvertexmatrix(2*m.vertexmatrix())
+
+var phi = Field(m, fn (x,y) 1+x)
+
+fn integrand(x, f) {
+    var cg = cgtensor()
+    return cg.trace()
+}
+
+var a = AreaIntegral(integrand, phi, reference=mref)
+print a.total(m) // expect: 6