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.

Ravines in Angola. Causes and restraint methods

The Earth we know today was not always so. Over millions of years have undergone significant ch an g e s brought about by numerous geological phenomena aimed at your balance, some internal order, creating new geological formations and other external order smoothing formations previously created. From t h e tectonic standpoint, Angola is located in a relatively stable area which gives it a certain p ri v i l e g e w h e n compared with some Asian countries or even Americans where quite often occur earthquakes and volcanic eruptions. However, the same cannot be said in relation to the occurrence of an external geodynamics phenomena, such as the ravines, which in recent years has taken shape in many provinces, especially due to anthropogenic activity, giving rise to geological hazards, increasing the risk of damage in buildings and others infrastructures, losses direct or indirect in economic activities and loss of human lives. We understand that the reducing of these risks starts, in particular, by their identification, for later take preventive measures. This work is the result of some research work carried out by the authors through erosion courses of s o i l and stabilization of soils subject to erosion phenomena, carried out by Engineering Laboratory of Angola (LEA). For the realization of this work, we resorted to cartographic data query, literature, listening to s o m e o f the provincial representatives and local residents, as well as the observation in lo co o f s o m e af f e ct ed areas. The results allow us to infer that the main provinces affected by ravine phenomenon are located in Central and Northern highlands, as well as in the eastern region, and more recently in Cuando-Cub an go province. Not ruling out, however, other regions, such as in Luanda and Cabinda [1]. Relatively the causes, we can say that the ravines in Angola are primarily due to the combination of three natural factors: climate, topography and type of soil [2]. When we add the anthropogenic activit y , namely the execution of construction works, the drainage system obstructio n, exploration of m i n e ral s, agriculture and fires, it is verified an increasing of the phenomenon, often requiring immedi at e act i o n . These interventions can be done through structural or engineering measures and by the stabilization measures on the degraded soil cover [3]. We present an example of stabilization measures throu g h t h e deployment of a local vegetation called Pennisetum purpureum. It is expected that the results may contribute to a better understanding of the causes of the ravine phenomenon in Angola and that the adopted stabilization method can be adapted in other affected provinces in order to prevent and making the contention of the ravines.