| Symbol 符号 | Description 描述 |
|---|---|
| 𝑎 | unbolded, lowercase letter is a scalar 标量 |
| 𝐴 | unbolded, uppercase letter is (still) a scalar 仍然是标量 |
| 𝐚 | bolded, lowercase letter is a vector 向量 |
| 𝐀 | bolded, uppercase letter is a matrix 矩阵 |
| 𝐚 ∊ ℛ^n | is an n-dimensional vector n维向量 |
| 𝐀 ∊ ℛ^{m×n} | 𝐀 is an m by n vector {m×n}矩阵 |
| 𝔸 ∊ ℛ^{m×n×o×...} | 𝔸 is a higher-order(3rd and above)tensor 高维张量 |
| Symbol 符号 | Description 描述 |
|---|---|
 |
2-norm (§C.1.1) |
 |
Frobenius norm 弗罗贝尼乌斯范数(§C.3) |
| 𝐀∶𝐁 | Double-contraction of matrices 矩阵双收缩 𝐀 and 𝐁 |
| 𝔸∶𝐁 | Double-contraction of higher-order tensor 𝔸 and matrix 𝐁 双收缩高阶张量 𝔸 与双收缩矩阵 𝐁 §3.2,§.3) |
| 𝐀⊗𝐁 | A Kronecker product between two matrices 两矩阵的克罗内克积 (§C.5) |
| 𝑡𝑟 𝐀 | trace of matrix 𝐀, i.e. the sum of its diagonal entries, 对角线条目的总和 (§C.2) |
| 𝚍𝚎𝚝 𝐀 | determinant of matrix 𝐀 矩阵行列式 |
| 𝚟𝚎𝚌 (⋅) | flattening or vectorization of a matrix or tensor 矩阵和张量的扁平化和向量化(§3) |
| 𝟶 | The zero matrix, a.k.a. the null matrix. Nothing but zeros 零矩阵又称零矩阵，除了零什么都没有 |
| 𝚰 | The identity matrix. A diagonal matrix of all ones 特征矩阵。全为对角矩阵 |
These symbols are reserved for the following deformation-specific phenomena: 符号保留用于以下 特定-变形🫠 现象：
| Symbol | Description |
|---|---|
| rest vertex, before deformation 变形前的静止顶点 | |
| deformed vertex 变形定点 | |
𝐅 =  |
deformation gradient, in 3D 3维变形梯度 |
𝐅 =  |
deformation gradient, in 2D 2维变形梯度 |
| 𝑪 | right Cauchy-Green tensor, 右柯西格林张量 𝐂 = |
| 𝑬 | Green's strain, 格林应变 |
| 𝒕 | translation 移动 |
| 𝒂 | anisotropic fiber direction from 各向异性纤维方向 |
| 𝚥 | 𝚥 = 𝑑𝑒𝑡 𝐅, the current relative volume of 𝐅 𝐅当前的相对体积 |
| 𝑔_{1} | flattened gradient of 𝐼_{1} invariant from(§5.5) 𝐼_{1}的拍平梯度 不变 形式 |
| 𝑔_{2} | flattened gradient of 𝐼_{2} invariant from(§5.5) 𝐼_{2}的拍平梯度 不变 形式 |
| 𝑔_{𝚥} ≡ g_{3} | flattened gradient of 𝚥 ≡ 𝐼_{3} invariant from(§4.2.2.1) |