Simulation of the responses of materials under simple shear

In this project, the second-order responses of homogeneous materials under simple shear were being analysed. D.Murnaghan (1951) suggested that the simple shear displacement U along the x-axis is a function of Y only. Hence, hypothesis stating that U could be a function of X, Y and Z was made and investigation based on the development of second-order nonlinear elastic models were carried out to verify the hypothesis. It was found out that the displacement U must not be a function of X in order for the volume of the homogeneous material to be preserved during simple shear. However, it was discovered that U could be a function of Z due to the second-order effects from the non-linear displacement w(Y, Z). Thereafter, the General Solution of Displacement U(Y, Z) was derived in term of , where is any non-linear displacement equation (function of Z) prescribed on the top plane. With the known linear displacement u(Y, Z) and non-linear displacement w(Y, Z), the General Solution of Cauchy’s Stress Tensor T was also worked out for the ease of tabulating T if any is chosen. Many works had been done for the simple shear deformation in homogeneous materials. Hence, the overall conditions for the elastic constants between two homogeneous materials, which allow any kind of volume preserving simple shear deformation in heterogeneous materials (i.e composite materials), were also investigated based on the derived General Solution of Cauchy’s Stress Tensor T.Bachelor of Engineering (Mechanical Engineering