Catálogo de publicaciones - libros

By placing time on the same level as the space coordinates, governing balance and conservation laws are derived for elastodynamics. Both Lagrangian and Eulerian descriptions are used and the laws mentioned are derived by subjecting the Lagrangian (or its product with the coordinate four-vector) to operations of the gradient, divergence and curl. The 4 x 4 formalism employed leads to balance and conservation laws which are partly well known and partly seemingly novel.

The theory of configurational - or material - forces smells good of its mathematical-physical origins. This contribution outlines this characteristic trait with the help of a four-dimensional formalism in which energy and canonical momentum go along, with sources that prove to be jointly consistent in a dissipation inequality. This is what makes the formulation so powerful while automatically paving the way for an exploitation of irreversible thermodynamics, e.g., in the irreversible progress of a defect throughout matter

Kinematics in structural optimisation and configurational mechanics coincide as long as sufficiently smooth design variations of the material bodies are considered. Thus, variational techniques from design sensitivity analysis can be used to derive the well-known Eshelby tensor. The impact on numerical techniques including computer aided design (cad) and the finite element method (fern) is outlined.

In this paper we discuss models able to account for discontinuities of the temperature field across a immaterial interface. Our theory is based on a scalar interfacial field and cover two previously proposed theories of Pried and Shen [6] and Dascalu and Danescu [4]. We briefly present an application to the problem of solidification of an under-cooled liquid.

We study a fully inertial discrete model of a martensitic phase transition which takes into account interactions of first and second nearest neighbors. Although the model is Hamiltonian at the , it generates a nontrivial relation between the velocity of the martensitic phase boundary and the conjugate configurational force. The apparent dissipation is due to the induced radiation of lattice waves carrying energy away from the front.

I have been puzzled for a long time by the unnatural divide between the theory of bulk growth—strikingly underdeveloped—and that for surface growth—much better developed, along apparently independent lines. Recent advances in growth mechanics (DiCarlo and Quiligotti, 2002) make it now possible to subsume growth phenomena of both kinds under one and the same format, where surface growth is obtained as an infinitely intense bulk growth confined in a layer of vanishingly small thickness. This has allowed me to recover the results collected in Gurtin, 2000 from the standpoint of DiCarlo and Quiligotti, 2002. In particular, I am able to construe Gurtin’s technique of referential control volumes that evolve in time as a special application of the principle of virtual power.

We consider dislocations in the framework of Eringen’s nonlocal elasticity. The fundamental field equations of nonlocal elasticity are presented. Using these equations, the nonlocal force stresses of a straight screw and a straight edge dislocation are given. By the help of these nonlocal stresses, we are able to calculate the interaction forces between dislocations (Peach-Koehler forces). All classical singularities of the Peach-Koehler forces are eliminated. The extremum values of the forces are found near the dislocation line.

Remodelling of biological tissue, due to changes in microstructure, is treated in the continuum mechanical setting. Microstructural change is expressed as an evolution of the reference configuration. This evolution is expressed as a point-to-point map from the reference configuration to a remodelled configuration. A “preferred” change in configuration is considered in the form of a globally incompatible tangent map. This field could be experimentally determined, or specified from other insight. Issues of global compatibility and evolution equations for the resulting configurations are addressed. It is hypothesized that the tissue reaches local equilibrium with respect to changes in microstructure. A governing differential equation and boundary conditions are obtained for the microstructural changes by posing the problem in a variational setting. The Eshelby stress tensor, a separate configurational stress, and thermodynamic driving (material) forces arise in this formulation, which is recognized as describing a process of self-assembly. An example is presented to illustrate the theoretical framework.

Goal-oriented a posteriori error estimators are presented in this contribution for the error obtained while approximately evaluating the -integral, i.e. the material force acting at the crack tip, in nonlinear elastic fracture mechanics using the finite element method. The error estimators rest upon the strategy of solving an auxiliary dual problem and can be classified as equilibrated residual error estimators based on the solutions of Neumann boundary value problems on the element level. Finally, an illustrative numerical example is presented.

The numerical analysis of material forces in the context of continuum damage and thermo-hyperelasticity constitutes the central topic of this work. We consider the framework of geometrically non-linear spatial and material settings that lead to either spatial or material forces, respectively. Thereby material forces essentially represent the tendency of material defects to move relative to the ambient material. Material forces are thus important in the context of damage mechanics and thermo-elasticity, where an evolving damage variable or thermal effects can be understood as a potential source of heterogeneity. Thus the appearance of distributed material volume forces that are due to the damage or temperature gradient necessitates the discretization of the damage or temperature variable as an independent field in addition to the deformation field. Consequently we propose a monolithic solution strategy for the corresponding coupled problem. As a result in particular global discrete nodal quantities, the so-called material node point (surface) forces, are obtained and are studied for a number of computational examples.