From 38f969edc46d072e30db0c5c60514f13a03fd90f Mon Sep 17 00:00:00 2001
From: Patrick Jaap <patrick.jaap@tu-dresden.de>
Date: Tue, 4 Oct 2022 11:08:16 +0200
Subject: [PATCH] Adjust Mooney-Rivlin energy in the Ciarlet case s.t. W(I)=0
This is done by subtracting "dim" or "1" at the given terms.
Now it is consistent with the other 2 cases of MR energy.
---
dune/elasticity/materials/mooneyrivlindensity.hh | 12 ++++++++----
test/mooneyrivlintest.cc | 2 +-
2 files changed, 9 insertions(+), 5 deletions(-)
diff --git a/dune/elasticity/materials/mooneyrivlindensity.hh b/dune/elasticity/materials/mooneyrivlindensity.hh
index a14f96f..644fa44 100644
--- a/dune/elasticity/materials/mooneyrivlindensity.hh
+++ b/dune/elasticity/materials/mooneyrivlindensity.hh
@@ -66,9 +66,11 @@ public:
C = F^TF and B = FF^T have the same eigenvalues - we can use either one of them.
There are three Mooney-Rivlin-Variants:
- ciarlet: W(F) = mooneyrivlin_a*(normF)^2 + mooneyrivlin_b*(normFinv)^2*detF^2 + mooneyrivlin_c*(detF)^2 -
- (2*mooneyrivlin_a + 4*mooneyrivlin_b + 2*mooneyrivlin_c)*ln(detF),
- where the last term is chosen s.t. W( t*I ) is minimal for t=1
+ ciarlet: W(F) = mooneyrivlin_a * [ (normF)^2 - dim ] # -dim for w(I) = 0
+ + mooneyrivlin_b * [ (normFinv)^2*detF^2 - dim ] # -dim for w(I) = 0
+ + mooneyrivlin_c * [ (detF)^2 - 1 ] # -1 for W(I) = 0
+ + (2*mooneyrivlin_a + 4*mooneyrivlin_b + 2*mooneyrivlin_c)*ln(detF),
+ where the last term is chosen s.t. W( t*I ) is minimal for t=1.
log: W(F) = \sum_{i,j=0}^{i+j<=n} mooneyrivlin_ij * (I1 - 3)^i * (I2 - 3)^j + mooneyrivlin_k * ln(det(F))^2
square: W(F) = \sum_{i,j=0}^{i+j<=n} mooneyrivlin_ij * (I1 - 3)^i * (I2 - 3)^j + mooneyrivlin_k * 0.5 * (det(F) - 1)^2
@@ -100,7 +102,9 @@ public:
gradientInverse.invert();
field_type frobeinusNormFInverseSquared = gradientInverse.frobenius_norm2();
using std::log;
- return mooneyrivlin_a*frobeniusNormFsquared + mooneyrivlin_b*frobeinusNormFInverseSquared*detF*detF + mooneyrivlin_c*detF*detF
+ return mooneyrivlin_a * ( frobeniusNormFsquared - dim )
+ + mooneyrivlin_b * ( frobeinusNormFInverseSquared*detF*detF - dim )
+ + mooneyrivlin_c * ( detF*detF - 1.0 )
- (2.0*mooneyrivlin_a + 4.0*mooneyrivlin_b + 2.0*mooneyrivlin_c)*log(detF);
}
else
diff --git a/test/mooneyrivlintest.cc b/test/mooneyrivlintest.cc
index 89a0471..58ddbd1 100644
--- a/test/mooneyrivlintest.cc
+++ b/test/mooneyrivlintest.cc
@@ -165,7 +165,7 @@ int main (int argc, char *argv[])
parameters["mooneyrivlin_a"] = "2.42e+6";
parameters["mooneyrivlin_b"] = "6.52e+6";
parameters["mooneyrivlin_c"] = "-7.34e+6";
- expectedEnergy = 76302830.4;
+ expectedEnergy = 56822830.4;
expectedGradientTwoNorm = 40670527.3;
expectedGradientInfinityNorm = 11116511.8;
expectedMatrixFrobeniusNorm = 2.1978108e+09;
--
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