Visual Analysis of the Relation Between Stiffness Tensor and the Cauchy-Green Tensor

Abstract

Stress and strain tensors, two well-known quantities in mechanical engineering, are linked through a fourth-order stiffness tensor, which is not considered by many visualizations due to its complexity. Considering an orthotropic material, the tensor naturally decomposes into nine known material properties.We used fiber surfaces to analyze a data set representing a biological tissue. A sphere is pushed into the material to confirm the mathematical link as well as the possibility to extract highly deformed regions even if only the stiffness tensor is available.