An electronic circuit device having a circuit stack, such as an electronic display device with a display stack, includes a protective backing having multiple layers or with a graded layer that protects the electronic circuits from both low velocity impacts and high velocity impacts. The protective backing may have an elastic layer and a viscoelastic layer or have a graded layer with a graded structure that gradually transitions between an elastic region on a first side and a viscoelastic region on a second side. The elastic first layer or region protects the display stack from low velocity impacts while the viscoelastic layer or region protects the display stack from high velocity impacts. The elastic layer or region may be arranged such that it does not add substantial stiffness to the overall circuit stack when it is flexed relatively slowly under normal use.