Abstract In this paper the behaviour of rock-type materials is described with respect to the current configuration through rate-type constitutive equations, within the finite deformation framework, using the relative motion. The viscoplastic part of the constitutive equations concerns the long-time effects, i.e. the deformation by creep, while the instantaneous elastic response characterizes the short-time effect. The instantaneous elastic response expresses an appropriate objective time derivative of Cauchy stress tensor via the rate of strain, with the aid of fourth-order elastic stiffness tensor. Using mathematical arguments it follows that our new model extends, to finite strains, Cristescu’s rheological model Cristescu (1989)[2]. To solve boundary value problems for rock-type materials described by the proposed model, the appropriate variational equality for the velocity field, at a time t, is derived starting from the weak formulation of the incremental equilibrium problem. The rate form of the constitutive model is coupled with the variational equality, and serves to update the current state of the material.

中文翻译：

---

大变形下岩石类材料的流变模型。

摘要 在本文中，在有限变形框架内，使用相对运动，通过速率型本构方程相对于当前配置描述了岩石类材料的行为。本构方程的粘塑性部分涉及长期效应，即蠕变变形，而瞬时弹性响应表征短期效应。瞬时弹性响应借助四阶弹性刚度张量通过应变率表达柯西应力张量的适当客观时间导数。使用数学论证，我们的新模型将 Cristescu 的流变模型 Cristescu (1989) [2] 扩展到有限应变。为了解决所提出的模型描述的岩石类材料的边值问题，在时间 t 的速度场的适当变分等式是从增量平衡问题的弱公式导出的。本构模型的速率形式与变分等式相结合，用于更新材料的当前状态。