Showing papers on "Mixture theory published in 1984"

Bulk modulus and thermal expansivity of melt polymer composites: Statistical versus macro‐mechanics

Abstract: Physical properties of composites as a function of filler content have been described in the past through models requiring the solution of macroscopic equations of motion for an elastic continuum or, on a more empirical level, by the assumption of various compositional averaging schemes. We discuss a model drawn from our molecular mixture theory. This allows us to avoid the formal problems attending concentrated suspensions and introduces molecular filler-medium interaction parameters. Comparisons with experimental material and empirical equations involving bulk modulus and thermal expansivity will be given. The theory opens the possibility of determining interfacial strengths from appropriate mechanical and thermal measurements and of predicting one set from another set of data.

A Thermomechanical Theory for a Porous Anisotropic Elastic Solid with Inclusions

Abstract: We construct a mixture theory which describes a porous elastic anisotropic solid with inclusions. Thermal effects are taken into account. The theory is in accord with classical thermodynamics. Fully nonlinear isotropic and anisotropic materials are considered, and field equations are also given for a nontrivial special case which, though nonlinear, is controlled by a few material functions. When properly specialized, the theory reduces to the P-α model, a model widely used to describe porous solids.

New approach to the effective stress principle

Abstract: A definition of the effective stress emerges naturally from mixture theory for a fluid saturated porous solid. The effective stress definition suggested by the mixture theory arises before any particular behavior for the matrix has been stipulated. In contrast, many definitions in common usage are tied to specific constitutive models and are thus extraneous to the theory of stress. This difference is illustrated by specializing the mixture theory to the case of a linear elastic solid matrix, for which the well-established consolidation, or poroelasticity, theory of Biot is recovered exactly.

Foundations of Mixture Theory

Abstract: We here present an axiomatic derivation of the field equations of continuum thermodynamics. In this derivation, in which we also employ the usual continuity assumptions of continuum theory, our cardinal precept is TRUESDELL’S metaphysical principle number 2, taken quite literally: not only each component body of the mixture but also each subbody of each component body and by extension each combination of subbodies of component bodies is required to obey the laws of thermodynamics. From this prospectus one may expect the occurrence of many fields not found in the classical theory and correspondingly more balance equations. However we show in the end how the derived fields and equations reduce to those of Lecture 5, leading in particular to two important observations about the classical theory. First, one should note that thepeculiar quantities of the classical theory should not be interpreted in the naive way suggested by the form in which they appear in the balance equations. For example, the partial heat flux ha • n integrated over a surface cannot reasonably be interpreted as the heat flux into component a from the totality of components located on the opposite side of that surface, but as a more complicated average of effects occurring among elements on the same side and on opposite sides of the surface. Second, although we necessarily arrive at individual entropy inequalities, there is no rational argument that they should take the classical form.

Application of mixture theory to shock initiation of porous hns explosive

Abstract: A specific microstructural model for the chemical decomposition of shock-loaded HNS explosive has been implemented in a mixture theory. Interaction terms in the mass balance equations have been made consistent with known decomposition kinetics and interaction terms in the energy balance laws are formulated to describe the conjectured microstructural processes. Results of calculations compare favorably with experiments. This study identifies a way in which nonequilibrium processes in the shock environment can be studied and highlights an ambiguity which exists in data interpretation.

Growth and decay of one-dimensional shock waves in multiphase mixtures

Abstract: We examine the behavior of one-dimensional shock waves in a chemically reacting, nondiffusing multiphase mixture, i.e., one in which the constituents may possess individual microstructure such as porosity and granularity. Essential to this investigation is the introduction of the shock-evolution equation, which determines the local growth or decay of the shock wave in view of the dissipative and enhancive mechanisms involved. This equation accounts for the immiscibility and energy exchange between the constituents as associated with the microstructural properties of the mixture, along with the chemical reactivity at the shock front. Also presented are the constituent Hugoniot properties and associated remarks within the context of a multiphase mixture theory.

Numerical modeling of the mechanics of nonlinear porous media under dynamic loading

Abstract: A multiphase continuum model that couples nonlinear deformation to porous flow has been developed and adapted for numerical analyses of dynamic and quasistatic behavior in the explicit finit-difference code TENSOR In a physical sense the model describes a solid skeletal material containing flaws configured either as pores or stress-induced tensil cracks These flaws may be filled with a multiphase fluid (eg, air and water) whose transient behavior is governed by a dynamic flow model that reduces to classical Darcy flow for a single-phase fluid in the limit of quasistatic behavior Dynamic mixture theory is used to account for coupling effects between phases Nonlinear material behavior representing the drained response of the porous solid has been combined with the multiphase flow model to account for the effects of pore pressure on compaction, shear failure, and tensile failure Numerical calculations are presented using both the multiphase model and a single-phase model to simulate the spherical response from explosive experiments performed on grout spheres Good agreement with the measured particle velocity is obtained with both models However, the phenomenology associated with explosively generated cavities using the multiphase model differs markedly from that obtained with a single-phase model Notably, a region of liquefaction surroundingmore » the cavity is created as a result of pore-pressure-induced tensile failure during shock wave passage This precludes the development of a residual stress field adjacent to the cavity, as typically calculated with a single-phase model A small residual stress field is formed beyond the liquefied region The formation of the residual stress field using the multiphase model and its stability during subsequent readjustment caused by pore-fluid migration is greatly enhanced with a small initial amount of air-filled porosity 46 references, 15 figures« less

Development of Advanced Constitutive Model for Reinforced Concrete

Abstract: : The objective of this research was to develop an advanced, nonlinear, multiaxial constitutive theory for reinforced concrete which provides a modeling capability that is superior to existing models, especially in the nonlinear response regime. The problem of constructing such a theory is partitioned into two major tasks, which have been pursued concurrently. One task consists of formulating a procedure (mixture theory) for analytically mixing reinforcing steel and plain concrete, so that the interaction between the two, which plays a key role in the overall behavior of reinforced concrete, is properly modeled. The other task consists of developing a model of plain concrete, which accurately portrays its nonlinear, multiaxial behavior and which is computationally feasible for use in conjunction with the mixture theory. The mixture theory is designed to synthesize the global constitutive properties of reinforced concrete from the properties of plain concrete, steel, interfaces and reinforcing geometry. The progress made during the course of the program toward achieving the above research objectives is summarized. A detailed account of the accomplishments made during the third year of the program are given, since these are not available elsewhere. Finally, a list of the publications and technical interactions which resulted from this research is given.