Top ↑
Researches
Modeling  Simulating  Governing
Monodimensional  Multidimensional
Energy  Equations  Graphs  States
Equations
Mathematical representations Table of contents
Energetic tensors
Constitution of the reality: half square of the behaviour tensor minus the unit tensor
Internal energy
Double tensorial contraction of the stress tensor by the behaviour tensor
The stress tensor has a global part and a frontal part
The power is the time derivative of the energy
The power comports an irreversible part and a reversible part
Elements
Elastic reality of Hook: a fourth order elasticity tensor
Viscous reality of Newton: a fourth order viscosity tensor
Flow connections
Stress on reversible reality
Stress on irreversible reality
Differential equation of reality: sum of the reversible and irreversible parts
Kelvin reality: a sudden application of stress does not produce an immediate deformation because the irreversible part does not react instantaneously
Potential connections
Stress on reversible reality
Stress on irreversible reality
Total stress: sum of stresses
Differential equation of reality
Maxwell reality: a sudden application of stress produces an immediate deformation due to the reversible part and a creep due to the irreversible part
Tensor bond graphs
Tensorial differential equation of the reality of Kelvin
Tensor bond graph of the reality of Kelvin
Tensorial differential equation of the reality of Maxwell
Tensor bond graph of the reality of Maxwell