We discuss some aspects of using the spatial description and the finite volume method as applied to the solid mechanics problems. The main objective is to study the differential equation relating the strain measure to the velocity gradient. We show that this equation can be reduced to an integral form and the obtained equation has the structure of the balance equation without a source term. On the one hand, such form of equation for the strain measure is convenient when dynamical problems of solid mechanics are solved by using the finite volume method. On the other hand, the balance equation allows us to look at the strain measure as a parameter of state in a broader sense, not as the purely geometrical characteristic. We believe that this interpretation of the strain measure may open up new prospects for describing the processes connected with the substance supply into solids. In order to solve such problems, we suggest to add a source term into the balance equation for the strain measure. We discuss this idea from different points of view. We also solve some problems where the stress–strain state of solids is caused by the source terms in the balance equation for the strain measure.

我们讨论了将空间描述和有限体积方法应用于固体力学问题的某些方面。主要目的是研究将应变测量与速度梯度相关的微分方程。我们表明，该方程可以简化为整数形式，并且所获得的方程具有不带源项的平衡方程的结构。一方面，当使用有限体积法解决固体力学的动力学问题时，这种形式的应变测量方程很方便。另一方面，平衡方程式使我们可以将应变量度视为广义上的状态参数，而不是纯粹的几何特征。我们认为，这种应变测量方法的解释可能会开辟新的前景，以描述与将物质供给固体相关的过程。为了解决此类问题，我们建议将源项添加到应变测量的平衡方程中。我们从不同的角度讨论这个想法。我们还解决了一些问题，其中固体的应力-应变状态是由应变测量的平衡方程中的源项引起的。