I'm learning piezoelectricity right now and got an equation I can't understand. It writes the newton's sencond law for the stresses in materials due to elastic and piezoelectric contribution. The equation is in the attachment. In this equation I'd like to ask what is the partial derivative between stress and the coordiante? And if density*(u_i)" means 'ma' in newton's sencond law, does it mean the volume is an unit which equals to 1? Or there is another explaination?