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--- doc:user:elements:volumes:hyper_functionbased [2025/11/14 16:30] – [Holzapfel-Gasser-Ogden Anisotropic Material] vanhulle
+++ doc:user:elements:volumes:hyper_functionbased [2025/11/14 17:04] (current) – [Bonet-Burton Transversely-Isotropic Material] vanhulle
@@ Line 154: / Line 154: @@
 ==== Bonet-Burton Transversely-Isotropic Material ====
+Here we create a Bonet-Burton transversely isotropic hyperelastic material as presented in [[https://www.sciencedirect.com/science/article/pii/S0045782597003393 | Bonet J., Burton A. J., 1998, A simple orthotropic, transversely isotropic hyperelastic constitutive equation for large strain computations,
+Computer Methods in Applied Mechanics and Engineering, 162, 151-164.]]
+For this material, the strain-energy density function writes
+$$
+W = \frac{\mu}{2}\left(\bar{I}_1 - 3\right) + \left[\alpha + \beta \left( \bar{I}_1-3 \right) + \gamma \left( \bar{I}^{(i)}_4 -1\right)\right]\left(\bar{I}^{(i)}_4 - 1\right) - \frac{1}{2}\alpha \left(\bar{I}^{(i)}_5 -1\right) + \frac{\lambda}{2}(J-1)^2
+$$
+The different constants from $W$ are related to the engineering material constants from the matrix ($E$, $\nu$, $G$) and from the fibers ($E_a$, $G_a$, $\nu_a$) as
+$$
+n = \frac{E_a}{E} ~~~~|~~~~ m=1-\nu-2\nu^2
+$$
+$$
+\mu = G = 2C_1 = \frac{E}{2(1+\nu)} ~~~~|~~~~ \lambda = k_0 = \frac{E(\nu+n\nu^2)}{m(1+\nu)}
+$$
+$$
+\alpha = \mu - G_a = \mu - \frac{E_a}{2(1+\nu_a)} ~~~~|~~~~ \beta= \frac{E\nu^2(1-n)}{4m(1+\nu)} ~~~~|~~~~ \gamma=\frac{E_a(1-\nu)}{8m}-\frac{\lambda+2\mu}{8}+\frac{\alpha}{2}-\beta
+$$
+  ## Bonet-Burton Material
+  materialset.define(1, FunctionBasedHyperMaterial)
+  materialset(1).put(MASS_DENSITY, rho)
+  materialset(1).put(RUBBER_PENAL, lambda)
+  materialset(1).put(HYPER_ELAST_POTENTIAL_NO, 1)
+  materialset(1).put(HYPER_VOL_POTENTIAL_NO, 2)
+The elastic deviatoric potential is the sum of the ''NeoHookeanHyperPotential'' (isotropic matrix part) and BonetBurtonHyperPotential with one fiber directions. The addition between the two potentials is made using the CombinedElasticPotential.
+  ## Elastic (deviatoric) potential
+  materlawset = domain.getMaterialLawSet()
+  materlawset.define(1, CombinedElasticPotential)
+  materlawset(1).put(HYPER_POTENTIAL1_NO, 3) #Neo-Hookean
+  materlawset(1).put(HYPER_POTENTIAL2_NO, 4) #Bonet-Burton
+Isotropic Neo-Hookean potential
+  materlawset.define(3, NeoHookeanHyperPotential)
+  materlawset(3).put(HYPER_C1, mu/2.) #mu=2C1
+Transversely isotropic Bonet-Burton potential with one fiber family
+  materlawset.define(4, BonetBurtonHyperPotential)
+  materlawset(4).put(HYPER_BB_ALPHA, alpha)
+  materlawset(4).put(HYPER_BB_BETA, beta)
+  materlawset(4).put(HYPER_BB_GAMMA, gamma)
+  materlawset(4).put(HYPER_BB_USE_LNJ, false)
+  # first fiber family with beta orientation
+  materlawset(4).put(HYPER_FIB1_X, np.cos(beta))
+  materlawset(4).put(HYPER_FIB1_Y, np.sin(beta))
+The volumetric potential is the ''QuadraticVolumicPotential''
+  ## Volumetric potential
+  materlawset.define(2, QuadraticVolumicPotential)