弹粘塑性孔隙介质在冲击荷载作用下的一种本构关系——第一部分:状态方程

CONSTITUTIVE RELATION OF ELASTOVISCOPLASTIC POROUS MEDIA SUBJECTED TO SHOCK ——PART I:STATE EQUATION

利用弹塑性介质的不可逆热力学的普遍关系,对弹粘塑性孔隙介质在冲击静水压力作用下的力学行为进行了研究。在本构关系中,使用了对于固体来讲更为合理的德拜形式的自由能。利用等效应变法,考虑了孔隙率对孔隙介质在冲击静水压力作用下的力学行为的影响,并得到了孔隙率演化方程。最终得到的本构关系符合不可逆热力学定律,形式相对简单,物理意义明确。数值计算结果与已有结果吻合很好。

The process of deformation and fracture of deformable solid media subjected to shock is accompanied by many irreversible dissipative mechanical, physical and chemical processes. The constitutive equations of solid subjected to shock should express these irreversible features. The mechanical behaviors of elastoviscoplastic porous media subjected to hydrostatic shock are studied in the framework of irreversible thermodynamics of elastoviscoplastic media. The corresponding constitutive equations are expressed by Helmholtz free energy of Debye form, as it is more rational for solid. The influence of porosity on the mechanical behaviors of elastoviscoplastic porous media subjected to hydrostatic shock is remarkable, and it is considered by means of effective strain method. The evolution equation of porosity is also obtained on this basis. The constitutive equations presented here are relatively simple, and their physical meaning is clear, corresponding to irreversible thermodynamics. In order to validate the proposed constitutive relations, a numerical example is given, and the agreement is good with the existing results.