Catálogo de publicaciones - libros

The overall stiffness of a truss is optimized by choosing the nodal coordinates of the undeformed truss such that the strain energy of the loaded truss attains a minimum. The derivatives of the strain energy with respect to the nodal coordinates are interpreted as material forces acting on the nodes of the undeformed truss in “design space”.

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.

The concept of a balance law for an elastic fractured body, in Euclidean and material space, is used to investigate the propagation of a circular crack in an elastic body. In the spirit of modern continuum mechanics, a rigorous localization process results in the local equations in the smooth parts of the body and, in addition, in the relations holding at the crack tip. The latter are used in establishing relations concerning the energy release rates.

The aim of this study is to establish a criteria based on an energy threshold corresponding to crack initiation in the case of dilatational symmetry of a structure under thermomechanical loading. On the base of the J, L, M integrals presented by Knowles and Sternberg, respectively in the case of translational, rotational and scaling symmetry in the light of Noether’s theory, many path independent integrals have been defined with applications in fracture mechanics. By the formulation of an adequate Lagrangian formulation, the thermoplastic behaviour is introduced in the M integral through the null Lagrangian theorem. Such an integral finds a physical interpretation as an energy release rate in analogy to the J integral. It equals the change in total available energy due to expansion of an existing cavity. A modification of the M* integral is proposed, in order to have the path-domain independence. A new path-domain independent is described in order to obtain the path domain independence for any transformation of the dilatation group.

Two basic peeling problems formulated by Ericksen (1991) are studied, both in statics and in dynamics. While equilibrium is treated variationally, the evolution of the tape tip is modeled as the result of a configurational force balance.

The propagation of moving surface inside a body is analysed in the framework of thermodynamics, when the moving surface is associated with an irreversible change of mechanical properties. The thermodynamical force associated to the propagation has the form of an energy release rate. Quasistatic rate boundary value problem is given when the propagation of the interface is governed by a normality rule. Extension to generalised media to study delamination is also investigated.

We formulate a general frame for modelling of processes with phase changes. Then we discuss some kinetic equations for phase transformations in steels. We compare some of them with experimental data of pearlite transformation in 100Cr6 steel.

The paper determines the forms of equations of force equilibrium and Maxwell’s relation for stable coherent phase interfaces in isotropic two-dimensional solids. If any of the two principal stretches of the first phase differs from the two principal stretches of the second phase, one obtains the equality of two scalar forces and of a Gibbs function. The forms of these quantities depend on whether the two principal stretches both increase (decrease) when crossing the interface or whether one of the stretches increases and the other decreases. Apart from this nondegenerate case, also the degenerate cases are discussed. The proofs use the rank 1 convexity condition for isotropic materials.

Dynamics of martensitic phase transition fronts in solids is determined by the driving force (a material force acting at the phase boundary). Additional constitutive information needed to describe such a dynamics is introduced by means of non-equilibrium jump conditions at the phase boundary. The relation for the driving force is also used for the modeling of the entropy production at the phase boundary.

We formulate a general frame for modelling of processes with phase changes. Then we discuss some kinetic equations for phase transformations in steels. We compare some of them with experimental data of pearlite transformation in 100Cr6 steel.