Toward the characterization of anisotropic elastic nonlinear behavior under large deformations through a Data-Driven approach
Topic(s) : Special Sessions
Co-authors :
Annie MORCH (FRANCE), Michel CORET (FRANCE), Adrien LEYGUE (FRANCE), Julien RÉTHORÉ , Pauline LECOMTE-GROSBRAS , Jean-François WITZAbstract :
Mechanical symptoms, such as hypermobility or loss of stiffness, can occur in soft tissue pathologies. Surgical treatment often involves implanting a textile mesh that forms a biological composite with the pathological native tissue and scar tissue. The composite shows an anisotropic and non-linear mechanical response in large strains, that should mimick the physiological mechanical behavior in order to promote a successful in vivo integration [1,2].
In this study, we propose a method based on Data-Driven Identification (DDI) using rich experimental measurements to explore and compare the impact of the mesh on the composite.
The biological composite is replaced with a synthetic composite made of a mesh embedded in a silicon plate. Experimental testing consists in a complex loading (combination of in-plane rotation and translations) performed with an hexapod equipped with a multiaxial loadcell (6-axis sensor) coupled with images recording. The heterogeneous strain field is computed from the images with Digital Image Correlation (DIC) based on a Finite-Element method [3] (Figure 1).
DDI aims to compute admissible stresses in a material given the displacement field and the applied forces, without knowing the behavior law [4, 5]. It requires a large database of strain measurements. The input database of the DDI consists here in multiple sets of data, called « snapshots », coming from the experimental measure. Each snapshot contains the nodal displacements computed by the DIC in the FE-mesh and global forces as measured by the multiaxial loadcell. DDI associates stress state to each strain state computed with DIC, pairs are called mechanical states. A discrete description of the material behavior is introduced through a lower number of stress/strain tensors pairs called material states, which are additional unknowns of the problem. DDI can be seen as a clustering method which, under the equilibrium constraints with the applied forces, associates each mechanical state (from the experimental database) with a material state.
Thanks to the DDI, we can compute the Eulerian stress (Cauchy) associated with DIC computed dilatation (left Cauchy-Green) tensors in the sample. These tensors are symmetric and diagonalizable. If the material is anisotropic, the directions of principal stresses and strains will no longer be aligned. After diagonalization, the dot product between the eigenvectors of the strain and stress tensors allows the identification of the in-plane misalignment angle between the principal directions of stresses and deformations for each element of the FE-mesh (Figure 2).
Data-driven identification based on DIC experimental measurements revealed the anisotropic signature of the mesh. This method seems promising to evaluate and compare meshes with regards to their application. Thanks to the DDI computation of the stress field, current work now focus on the identification of anisotropic strain energy density.
In this study, we propose a method based on Data-Driven Identification (DDI) using rich experimental measurements to explore and compare the impact of the mesh on the composite.
The biological composite is replaced with a synthetic composite made of a mesh embedded in a silicon plate. Experimental testing consists in a complex loading (combination of in-plane rotation and translations) performed with an hexapod equipped with a multiaxial loadcell (6-axis sensor) coupled with images recording. The heterogeneous strain field is computed from the images with Digital Image Correlation (DIC) based on a Finite-Element method [3] (Figure 1).
DDI aims to compute admissible stresses in a material given the displacement field and the applied forces, without knowing the behavior law [4, 5]. It requires a large database of strain measurements. The input database of the DDI consists here in multiple sets of data, called « snapshots », coming from the experimental measure. Each snapshot contains the nodal displacements computed by the DIC in the FE-mesh and global forces as measured by the multiaxial loadcell. DDI associates stress state to each strain state computed with DIC, pairs are called mechanical states. A discrete description of the material behavior is introduced through a lower number of stress/strain tensors pairs called material states, which are additional unknowns of the problem. DDI can be seen as a clustering method which, under the equilibrium constraints with the applied forces, associates each mechanical state (from the experimental database) with a material state.
Thanks to the DDI, we can compute the Eulerian stress (Cauchy) associated with DIC computed dilatation (left Cauchy-Green) tensors in the sample. These tensors are symmetric and diagonalizable. If the material is anisotropic, the directions of principal stresses and strains will no longer be aligned. After diagonalization, the dot product between the eigenvectors of the strain and stress tensors allows the identification of the in-plane misalignment angle between the principal directions of stresses and deformations for each element of the FE-mesh (Figure 2).
Data-driven identification based on DIC experimental measurements revealed the anisotropic signature of the mesh. This method seems promising to evaluate and compare meshes with regards to their application. Thanks to the DDI computation of the stress field, current work now focus on the identification of anisotropic strain energy density.