The energy jump condition for thermomechanical media in the presence of configurational forces

In the context of a propagating surface of discontinuity in a thermomechanical medium, this brief communication establishes a relationship between the supplies of material momentum, linear momentum, energy and entropy. The relationship is equivalent to the jump condition in energy and is also framed in the context of a driving traction.      

Configurational forces in discrete elastic systems

The concept of configurational forces is applied to a simple, one-dimensional problem that is solved by finite elements. Both the exact solution and its finite-element approximation are provided in closed form. The total energy according to the approximate solution depends on the choice of the nodes. Any virtual shift of a node results in a virtual change of energy, which can be interpreted as the virtual work done by a configurational force acting on that node. It is shown that, in the case of equidistant nodes, the configurational forces acting on the interior nodes vanish. Also, the relation between the nodal configurational forces and the Eshelby stress resultant along the rod is investigated.     

Gravitational forces in dual-porosity systems: I. Model derivation by homogenization

We consider the problem of modeling flow through naturally fractured porous media. In this type of media, various physical phenomena occur on disparate length scales, so it is difficult to properly average their effects. In particular, gravitational forces pose special problems. In this paper we develop a general understanding of how to incorporate gravitational forces into the dual-porosity concept. We accomplish this through the mathematical technique of formal two-scale homogenization. This technique enables us to average the single-porosity, Darcy equations that govern the flow on the finest (fracture thickness) scale. The resulting homogenized equations are of dual-porosity type. We consider three flow situations, the flow of a single component in a single phase, the flow of two fluid components in two completely immiscible phases, and the completely miscible flow of two components.This work was supported in part by the National Science Foundation and by the State of Texas Governor's Energy Office.     

A continuum model accounting for defect and mass densities in solids with inelastic material behaviour

In this paper the analysis of structures with inelastic material behaviour is considered taking into account the evolution of defects and changes in mass density. The underlying kinematical concept of an oriented continuum is general enough to describe the micro- and macrobehaviour of material bodies appropriately. Based on the logical and consistent variational arguments for a Lagrangian functional the dynamic balance laws, boundary and transversality conditions, all related to the evolution of defect density and mass changes, are derived for macro- and microstresses of deformational as well as of configurational type. The adopted procedure, which formally leaves the balance laws unaltered, leads to the additional balance law for changes in defect density and additional boundary conditions for the changes in mass and defect densities. Driving forces or affinities, associated with the evolution of defect and mass densities, and a generalization of the J-integral representing the thermodynamic forces on defects are obtained. A nonlocal constitutive model accounting for changes in the defect density is presented.     

Gravitational forces in dual-porosity systems: II. Computational validation of the homogenized model

Three models are considered for single component, single phase flow in naturally fractured porous media. The microscopic model holds on the Darcy scale, and it is considered to govern the system. The macroscopic, dual-porosity model was derived in Part I of this work from the microscopic model by two-scale mathematical homogenization. In this paper, we show that the dual-porosity model predicts well the behavior of the microscopic model by comparing their computed solutions in certain reasonable test cases. Homogenization gives a complex formula for a key parameter in the dual-porosity model; herein a simple approximation to this formula is presented. The third model considered is a single-porosity model with averaged parameters. It is shown that this type of model cannot predict the behavior of the microscopic flow.This work was supported in part by the National Science Foundation and by the State of Texas Governor's Energy Office.     

Investigation on thermomechanical fracture in the framework of configurational forces

A configurational force approach is developed for providing a fresh look onto classical aspects of thermomechanical fracture. The theoretical framework is based on the finite deformation and makes no restrictions on the material response. The integral form of configurational force balance at the crack tip is constructed, and the concentrated configurational body force is decomposed into the inertial and internal parts. The energy release rate is evaluated through the generalized second law of thermodynamics applicable to configurational force system. The theoretical investigation shows that the negative of the projection of the internal configurational force concentrated at the crack tip along the direction of crack propagation plays the role of the energy release rate and acts directly in response to crack propagation. This finding enables us to deal with the thermomechanical fracture problems in material space.     

Failure theory via the concept of material configurational forces associated with the M-integral

A new failure theory based on the material configuration forces associated with the invariant M-integral is proposed to describe the content and evolution of the multi-defects localized in the body. The physical interpretation of the global M-integral is as the sum of the local energy release rate due to the self-similar expansion for each specific defect. It does provide an effective measure for the evaluation of damage level. It is found that the unique parameter of the M-integral cannot be used as a unified failure criterion to predict the damage evolution and the final failure due to the major obstacle that the critical value of the M-integral is not a problem-invariant constant and shows an apparent defect configuration-dependence. Consequently, a new failure parameter referred as the configurational damage parameter (abbreviated as Π-parameter) is proposed by the appropriate formulation via the M-integral, the remote uni-axial load, and the inner variable of the damaged area. A series of numerical examples are carried out to demonstrate that the critical value of Π-parameter is a material constant regardless of defect configurations. Furthermore, it is performed to validate the applicability of the Π-parameter as a failure criterion to predict the final failure of the locally damaged materials. Finally, a protocol of experimental measurement of the Π-parameter is proposed by method of digital image correlation to facilitate the wide application of the new failure criterion. It is concluded that the present failure theory via the configurational forces associated with the M-integral provides some outside variable features and has the advantage of predicting the structural integrity of damaged materials containing the locally distributed defects.     

Material forces in thermoelastic ferromagnets

A systematic construction of the canonical balance of momentum (“pseudomomentum” on the material manifold) and energy is presented for materially inhomogeneous thermoelastic hard ferromagnets in which both exchange forces and magnetic-spin inertia are taken into account. The latter is of the gyroscopic type and endows the sources of quasi-inhomogeneities in the balance of pseudomomentum with special properties. The equations obtained will prove useful in further studies of the fracture of hard ferromagnets and of the propagation of phase-transition fronts in such materials. Received January 23, 1996