As a computational analyst, one of the most important steps in building a model is ensuring the appropriate constitutive behavior is chosen to replicate the “real world” material behavior of the item being virtually evaluated. Even after the appropriate constitutive law is chosen, determining the input parameters are often a non-trivial task depending on the complexity of the material behavior.
This is especially true for computational models involving human tissues, as they are often nonlinear and anisotropic in nature. Calibration of these materials “by-hand” can often be time-consuming and inaccurate. Therefore, an automated process to explore the appropriate material parameters is generally much more efficient and accurate. The Data Matching capability in Isight is ideally suited for determining the material input parameters for even the most complex constitutive laws.
As an illustrative example, the mechanical behavior of human skin is calibrated using a combination of Abaqus and Isight.
Step 1: Create the Abaqus Simulation of the In Vivo Testing of Skin Tissue
Briefly, a 40 mm diameter circular area of shell elements (S4R and S3) represents the tested area. The nodes along the circumference were fixed in all translational and rotational degrees-of-freedom.
A central region of 4 mm in diameter represents the area of contact between the experimental probe and skin. The thickness of the shell elements is 1.5mm, representing a typical skin thickness of the arm. The movement of the probe is simulated by applying the appropriate displacement and rotational boundary conditions to the nodes within the probe contact area.
The material is assumed to be nonlinear elastic and isotropic; therefore, the Ogden strain energy potential of order 2 is chosen. Additionally, the material is assumed to be viscoelastic; therefore, the basic hereditary integral formulation for linear isotropic viscoelasticity is included in the material definition.
Step 2: Material Identification using Isight
There are 8 parameters resulting from the constitutive behavior assumptions (2 components of initial stress, 4 Ogden parameters, and viscoelastic parameters (g and τ)).
In order to determine the numerical value of these parameters, we will use optimization techniques found within iSight to match the Abaqus simulation results to in vivo experimental results. An iSight workflow is created using two components.
The Abaqus and Data Matching components are utilized sequentially to run the simulation and compare those results to in vivo experimental values, respectively. The optimization technique utilized is Hooke-Jeeves. After 40 iterations through the workflow, the error of the difference between simulation and in vivo results reduces significantly.
Further, if we compare the load-deflection between initial and final simulation results to the in vivo experimental data, a much improved response after the Data Matching exercise is observed.
