Notation system and list of symbols

Notation system

• An underline, e.g. $\underline{u}$, denotes a vector
• A double underline, e.g. $\underline{\underline{\sigma}}$, denotes a second-order tensor.
• A double-struck capital letter, e.g. $\mathbb{C}$, denotes a fourth-order tensor.
• A capital letter in square brackets, e.g. $[M]$, denotes a matrix
• An asterisk superscript, e.g. $\theta^*$, denotes a trial function

List of symbols

• $\Omega$: 3D domain occupied by the studied solid
• $\partial\Omega$: external boundary of $\Omega$
• $\textrm{div}(.)$: divergence operator
• $\nabla , . , (.)$: gradient operator