Classical Linear Constitutive Behavior

  • Tarek I. Zohdi
Part of the Lecture Notes in Applied and Computational Mechanics book series (LNACM, volume 64)


We now consider idealized linear material behavior.

The starting point to develop a constitutive theory is to assume that an energy function per unit volume exists, a nonnegative function denoted W. A linear constitutive relation can be derived from

\({\bf D}=\frac{\partial{W}}{\partial{\bf E}}\) (4.1)


\({W}\approx c_0+{\bf c}_1\cdot{\bf E}+ \frac{1}{2}{\bf E} \cdot{\bf \epsilon} \cdot{\bf E}+...\) (4.2)

which implies

D ≈ c 1 + ε·E + ... (4.3)


Energy Function Positive Eigenvalue Constitutive Theory Order Tensor Material Tensor 
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Copyright information

© Springer Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Dept. Mechanical EngineeringUniversity of CaliforniaBerkeleyUSA

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