Benchmark solution
=====================


Calculation method
-----------------

The analytical solution for this hydro-mechanical load has not been developed. Also, the reference solution is obtained numerically using the Scilab 2.7.2 software for BETON_UMLV or python for BETON_BURGER. Each deformation component is calculated separately:


* endogenous shrinkage deformities are determined from the relationship:


*

    .. image:: images/Object_19.svg
        :width: 78
        :height: 24


    .. _RefImage_Object_19.svg:

where

    .. image:: images/Object_20.svg
        :width: 78
        :height: 24


    .. _RefImage_Object_20.svg:

refers to the degree of hydration of the material


* the desiccation shrinkage deformations are determined from the relationship:


*

    .. image:: images/Object_21.svg
        :width: 78
        :height: 24


    .. _RefImage_Object_21.svg:

where

    .. image:: images/Object_22.svg
        :width: 78
        :height: 24


    .. _RefImage_Object_22.svg:

refers to the water content of the material


*the natural creep deformations are calculated numerically using a discretization identical to that implemented in the*Code_Aster* for BETON_UMLV and an layout according to an explicit diagram for BETON_BURGER. The time discretization is then necessarily finer for the explicit schema.


*


Reference quantities and results
------------------------

The test is homogeneous. The deformation is tested at any node.


Uncertainty about the solution
----------------------------

Numerical result obtained with Scilab 2.7.2 or python (SSNV174B .44)


Bibliographical references
---------------------------


1. THE PAPE Y.: UMLV behavioral relationship for the clean creep of concrete, *Code_Aster* Reference Documentation, [:ref:`R7.01.06 <R7.01.06>`] 16 p (2002).


2. FOUCAULT A.: BETON_BURGER behavioral relationship for the clean creep of concrete, Code-Aster Reference Documentation, [:ref:`R7.01.35 <R7.01.35>`], 2011.