Numerical integration on the sphere and its effect on the material symmetry of constitutive equations-A comparative study

2009 ◽  
pp. n/a-n/a ◽  
Author(s):  
A. E. Ehret ◽  
M. Itskov ◽  
H. Schmid
Keyword(s):  
Comparative Study ◽  
Numerical Integration ◽  
Constitutive Equations ◽  
Material Symmetry

Local material symmetry group for first- and second-order strain gradient fluids

2021 ◽  
pp. 108128652110216
Author(s):  
Victor A. Eremeyev
Keyword(s):  
Symmetry Group ◽  
Strain Gradient ◽  
Constitutive Equations ◽  
Strain Energy ◽  
Mass Density ◽  
Material Model ◽  
Second Order ◽  
Material Symmetry ◽  
Local Material ◽  
Current Mass

Using an unified approach based on the local material symmetry group introduced for general first- and second-order strain gradient elastic media, we analyze the constitutive equations of strain gradient fluids. For the strain gradient medium there exists a strain energy density dependent on first- and higher-order gradients of placement vector, whereas for fluids a strain energy depends on a current mass density and its gradients. Both models found applications to modeling of materials with complex inner structure such as beam-lattice metamaterials and fluids at small scales. The local material symmetry group is formed through such transformations of a reference placement which cannot be experimentally detected within the considered material model. We show that considering maximal symmetry group, i.e. material with strain energy that is independent of the choice of a reference placement, one comes to the constitutive equations of gradient fluids introduced independently on general strain gradient continua.

Material symmetry and constitutive equations

1980 ◽  
Vol 49 (5-6) ◽  
pp. 325-336 ◽  
Author(s):  
R. S. Rivlin
Keyword(s):  
Constitutive Equations ◽  
Material Symmetry

Dynamic Cloth Simulation: A Comparative Study of Explicit and Implicit Numerical Integration

2012 ◽  
Author(s):  
Laise Lima De Carvalho ◽  
Creto Augusto Vidal ◽  
Joaquim Bento Cavalcante-Neto ◽  
Suzana Matos Franca de Oliveira
Keyword(s):  
Comparative Study ◽  
Numerical Integration ◽  
Cloth Simulation
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