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.

Summary and Conclusion

This monograph outlines the process and results of development of a common educational programme at masters level in health and social care management, which was supported by the Erasmus Life Long Education project CareMan (Cul- ture and Care Management). The CareMan project brought together university partners actively involved in educating social and health care professionals in leadership and management at master’s level in Europe. The five partners of the consortium were Lahti University of Applied Sciences – Lahti UAS (administra- tive and academic coordinator, Finland), Charles University – CU (the Czech Republic), Edinburgh Napier University – ENU (Scotland), Hammeline University of Applied Sciences – HAMK (Finland), and University of Évora – UoE (Portugal). The objectives of the project were to achieve lower -level educational goals that included the development through education cultural and value -driven leadership, quality of care and quality management to effectively manage an integrated health and social care service. Through mapping the situation in the field and comparing curricula of all participating universities the overall aim was to develop a joint masters programme in social and healthcare management. After the detailed understanding of national and institutional specifics of each of the individual academic entities it was recognised that, due to a number of regulation issues, the original aim was not achievable. Following subsequent analytical work, it was decided to develop a set of three master’s level modules. At the end of the project it was intended that all created modules would be available virtually to the participating programmes and would contribute some added value to existing curricula. In the future these ready -to -use modules are intended to be taught in cooperation with the participating universities or as a separate module in each university. The chosen theoretical framework of the project that underpinned the devel- opment, management and evaluation of the inter -cultural educational provision relied on the combination of two learning theories – ‘cooperative collaborative and social learning’ and ’transformational’ (Mezirow, 2009). This theoretical framework helped to align with European collaborative policy and its application on all levels of implementation of the project.