Aeta/V[echanica 44, 299--317 (1982) ACTA MECHANICA 9by Springer-Verlag 1982 A Continuum Theory for Two Phase Media By G. Ahmadi, Potsdam, New York (Received May 17, 1980; revised December 10, 1980) Summary A continuum theory of a two phase solid-fluid media is formulated. Th 9 basic balance laws for the solid phase as well as for the fluid phase are presented. Based on thermo- dynamical consideration a set of constitutive equations are derived and the basic equations of motions of the distributed solid and fluid continua are obtained and discussed. It is shown that the theory contains as its special cases, Mohr-Coulomb criterion of limiting equilibrium of granular materials, Saffman theory of dusty gas, as well as Darcy's law of flow through porous media. It is then concluded that the present theory covers the full spectrum of two phase solid-fluid media from tow porosity granular media with Darey's law of fluid motion to low and high concentration two phase flows such as dusty gas and blood flow. 1. Introduction The mechanics of two phase solid-fluid mixtures is of fundamental importance in several fields of engineering. For instance, the limit of small porosity is of inter- est to the fields of soil mechanics, foundation engineering and ground water engineering. On the other hand, the limit of low concentration finds applications in the area of air and water polution and flow of dusty gas. High concentration two phase flow occurs in blood flow, sediment transport as well as many other fields in mechanical and chemical engineering. Although all these problems appear to be similar, they have been treated independent of each other in the past. The first study of the mechanical behavior of soil including granular material was carried out by Coulomb [1]. The Mohr-Coulomb theory of limiting equi- librium was formulated by KStter [2]. Further generalizations have been carried out by Sokolovskii [3]. Drucker ~nd Prager [4], Shield [5], among others, applied the theory of elastic-plastic solid for describing the mechanics of granular material. A theory of fluid saturated porous media was developed by Blot [6], [7] and further studied by Deresiweicz [8]. The continuum theory of mixture was studied by Truesdell and Toupin [9], Truesdell [10], Eringen and Ingrain [11], Green and Naghdi [12] and Bown [13]. The flow of viscous fluids through porous solids was considered by Crochet and Naghdi [14], Ahmadi and Manvi [15] and Ahmadi and Farshad [16]. An interesting continuum theory of granular materials was formu- lated by Goodman and Cowin [17], [18], and later extended by Jenkins [19], Passman [20], Ahmadi and Sohrabpour [21], Shahinpoor and Ahmadi [22] and Ahmadi [23], [24]. The Goodman-Cowin theory is based on the theory of struc- 0001-5970/82/0044/0299/$03.80