A unified full field solution for indentation of an anisotropic piezoelectric half-plane by multiple rigid punches

Consider the indentation of an anisotropic piezoelectric half-plane by multiple rigid punches. By using the Stroh's formalism for anisotropic piezoelasticity and the analytical continuation method for complex function's manipulation, a unified full-field solution is obtained for four different contact conditions including adhesive contact with conducting punches, adhesive contact with insulating punches, frictional contact with conducting punches, and frictional contact with insulating punches. To demonstrate the generality and applicability of the unified general solution, the closed-form solutions for some benchmark problems such as indentation by one flat-ended punch, one parabolic punch, or multiple flat-ended punches are then derived. With the numerical results evaluated by the closed-form solutions, the effects of anisotropy, poling direction, frictional coefficient, contact condition, applied loads, and punch interaction are also studied and discussed.