Thermal models, lithosphere thickness and heat flow in South Portugal. Some comments about the subject

Reinterpretation of old heat flow data or use of new data and new techniques of detection of the temperature under the surface have conducted to new heat flow density values in some regions of the globe. The problem of ice melting in Greenland and Antarctica caught the public's attention to the importance of knowledge on heat flow values and thermal structure of the globe. In the last years, several models were presented trying to obtain lithosphere and Moho thickness of the Iberia Peninsula. The work we intend to present is related with the SW part of the Iberia Peninsula ( south of the Ossa Morena zone, South Portuguese Zone and Algarve). The results obtained show a decrease in the thickness of the crust and the lithosphere in this region. Density anomalies in the crust are also referred. I intend to make the connection between the results of these models and the heat flow thermal conductivity, heat production and geological data available for the region, trying to explain the results of heat flow density data obtained.

Abstraction and use of groundwater for heating buildings in a hard rock environment

In order to turn more efficient the heating of class rooms in the lower floor of the old building of the University of Évora (a XVI century building), five drillings were organised inside the area of the university (Figure 1). The purpose was to use the temperature differential of groundwater in relation to air, by means of a heat exchanger, and use this process to heat the rooms using less energy, turning the heating process less expensive. The wells were drilled in fractured rocks (gneisses), and the purpose was to locate them at least around 100 m one from each other, whilst trying to have a hydraulic connection in-between. From the five initial wells, four were successful in terms of productivity, but just two of them (RA1 and RA2) proved to be hydraulically connected. The wells were equipped with screens for all their drilled depth (100 m), except for the first six meters and some two or three pipes of six meters each, to allow space for the installation for submersible pumps. The length of the installed screens guarantees a good efficiency of the system. In the wells with no connection, the heating system can work using each single well for abstraction and injection, but the process is much less efficient than in the cases where interaction between wells is possible through the rock’s fracture network.

A finite-strain solid–shell using local Löwdin frames and least-squares strains

A finite-strain solid–shell element is proposed. It is based on least-squares in-plane assumed strains, assumed natural transverse shear and normal strains. The singular value decomposition (SVD) is used to define local (integration-point) orthogonal frames-of-reference solely from the Jacobian matrix. The complete finite-strain formulation is derived and tested. Assumed strains obtained from least-squares fitting are an alternative to the enhanced-assumed-strain (EAS) formulations and, in contrast with these, the result is an element satisfying the Patch test. There are no additional degrees-of-freedom, as it is the case with the enhanced-assumed-strain case, even by means of static condensation. Least-squares fitting produces invariant finite strain elements which are shear-locking free and amenable to be incorporated in large-scale codes. With that goal, we use automatically generated code produced by AceGen and Mathematica. All benchmarks show excellent results, similar to the best available shell and hybrid solid elements with significantly lower computational cost.

A finite-strain solid–shell using local Löwdin frames and least-squares strains

A finite-strain solid–shell element is proposed. It is based on least-squares in-plane assumed strains, assumed natural transverse shear and normal strains. The singular value decomposition (SVD) is used to define local (integration-point) orthogonal frames-of- reference solely from the Jacobian matrix. The complete finite-strain formulation is derived and tested. Assumed strains obtained from least-squares fitting are an alternative to the enhanced-assumed-strain (EAS) formulations and, in contrast with these, the result is an element satisfying the Patch test. There are no additional degrees-of-freedom, as it is the case with the enhanced- assumed-strain case, even by means of static condensation. Least-squares fitting produces invariant finite strain elements which are shear-locking free and amenable to be incorporated in large-scale codes. With that goal, we use automatically generated code produced by AceGen and Mathematica. All benchmarks show excellent results, similar to the best available shell and hybrid solid elements with significantly lower computational cost.

Semi-implicit finite strain constitutive integration and mixed strain/stress control based on intermediate configurations

A new semi-implicit stress integration algorithm for finite strain plasticity (compatible with hyperelas- ticity) is introduced. Its most distinctive feature is the use of different parameterizations of equilibrium and reference configurations. Rotation terms (nonlinear trigonometric functions) are integrated explicitly and correspond to a change in the reference configuration. In contrast, relative Green–Lagrange strains (which are quadratic in terms of displacements) represent the equilibrium configuration implicitly. In addition, the adequacy of several objective stress rates in the semi-implicit context is studied. We para- metrize both reference and equilibrium configurations, in contrast with the so-called objective stress integration algorithms which use coinciding configurations. A single constitutive framework provides quantities needed by common discretization schemes. This is computationally convenient and robust, as all elements only need to provide pre-established quantities irrespectively of the constitutive model. In this work, mixed strain/stress control is used, as well as our smoothing algorithm for the complemen- tarity condition. Exceptional time-step robustness is achieved in elasto-plastic problems: often fewer than one-tenth of the typical number of time increments can be used with a quantifiable effect in accuracy. The proposed algorithm is general: all hyperelastic models and all classical elasto-plastic models can be employed. Plane-stress, Shell and 3D examples are used to illustrate the new algorithm. Both isotropic and anisotropic behavior is presented in elasto-plastic and hyperelastic examples.