Prev Subsubsection 4.1.3.12: Orthotropic Elastic Up Subsection 4.1.3: Unconstrained Materials Subsubsection 4.1.3.14: Osmotic Pressure from Virial Expansion Next
4.1.3.13 Orthotropic CLE
The material type for a conewise linear elastic (CLE) material with orthtropic symmetry is orthotropic CLE. The following parameters must be defined:
<lp11> | Tensile diagonal first Lamé coefficient along direction 1 | [P] |
<lp22> | Tensile diagonal first Lamé coefficient along direction 2 | [P] |
<lp11> | Tensile diagonal first Lamé coefficient along direction 3 | [P] |
<lm11> | Compressive diagonal first Lamé coefficient along direction 1 | [P] |
<lm22> | Compressive diagonal first Lamé coefficient along direction 2 | [P] |
<lm33> | Compressive diagonal first Lamé coefficient along direction 3 | [P] |
<l12> | Off-diagonal first Lamé coefficient in 1-2 plane | [P] |
<l23> | Off-diagonal first Lamé coefficient in 2-3 plane | [P] |
<l31> | Off-diagonal first Lamé coefficient in 3-1 plane | [P] |
<mu1> | Second Lamé coefficient along direction 1 | [P] |
<mu2> | Second Lamé coefficient along direction 2 | [P] |
<mu3> | Second Lamé coefficient along direction 3 | [P] |
This bimodular elastic material is the orthotropic conewise linear elastic material described by Curnier et al. [25]. It is derived from the following hyperelastic strain-energy function: where and Here, is the Lagrangian strain tensor and , where ( are orthonormal vectors aligned with the material axes. This material response was originally formulated for infinitesimal strain analyses; its behavior under finite strains may not be physically realistic.
Example:
<material id="1" type=" orthotropic CLE"> <density>1</density> <lp11>13.01</lp11> <lp22>13.01</lp22> <lp33>13.01</lp33> <lm11>0.49</lm11> <lm22>0.49</lm22> <lm33>0.49</lm33> <l12>0.66</l12> <l23>0.66</l23> <l31>0.66</l31> <mu1>0.16</mu1> <mu2>0.16</mu2> <mu3>0.16</mu3> </material>