Experimental modeling of nonuniform deformation in finite volume evaluation region of heterogeneous material

The objective of the present study is to establish the experimental modeling process of the nonuniform deformation behavior of heterogeneous materials. For this purpose, the constant stress moment, which is the work conjugate quantity of the constant strain gradient for the finite volume evaluation region, is introduced. The proposed stress moment can be evaluated from the stress field. The extended constitutive equation that relates the strain, stress, strain gradient, and stress moment is then formulated to predict the nonuniform deformation behavior of heterogeneous materials. In order to confirm that the proposed method is appropriate to represent the nonuniform deformation, finite element method (FEM) simulations of bending of macroscopically and microscopically heterogeneous materials were performed. The proposed method could predict the bending deformation of macroscopically heterogeneous material as precisely as the homogeneous case because the distribution of the heterogeneity is introduced in the extended constitutive equation. A bending simulation of a laminated cantilever was then performed using the extended constitutive equation for the microscopically heterogeneous material. The proposed method was capable of representing the analytically verified size-dependent bending deformation of the laminated cantilever.