We know that the pressure p is a scalar, that is, a zero-order tensor. For a point in space, given a position, there is a pressure value. Then start to do the pressure gradient field. Scalar gradient field is a vector, namely 1 tensor. At this point, we can still say that there is a vector value in a position in space, which is a fact. But what's more significant is that for a position and any unit vector in space, we can find out the change of pressure in the field at this point along the direction of this unit vector, that is, the value of pressure gradient point multiplied by the unit vector. Back to elasticity. Why do you need a second-order tensor to describe stress and strain? Because for the stress state of a particle, our requirement is that for a particle in space, for any unit vector, we need to know the magnitude and direction of the force along this unit vector direction. It is strange here why a force along a certain direction still has a direction. This is because when we discuss the force in a certain direction, there are not only positive forces along the normal direction, but also shear forces perpendicular to the normal direction. What is a point multiplied by a vector or a vector? That's a second-order tensor. In fact, the definition of second-order tensor is complicated, so you can refer to the first chapter of "A Course in Elasticity" published by Peking University Press. There is also a fourth-order tensor in elasticity, which is the modulus in the constitutive model. This is because for a particle, given any second-order tensor strain, we can get some second-order tensor stress. What is the point multiplied by the second tensor equal to the second tensor? Fourth-order tensor. It's just that we generally use the strong and weak symmetry of this fourth-order tensor to write a 6×6 matrix by Voigt notation. When studying damage mechanics, we need something to map a certain modulus to a certain damage modulus. Theoretically, this thing should be an eighth-order tensor. However, this is generally not done in research.