# 如何模拟超弹性材料的压缩

2018年 9月 5日

### Storakers 超弹性材料模型

Storakers材料模型通常用于模拟高度可压缩的泡沫材料。Storakers 材料模型的应变能密度函数为

(1)

W_s = \sum_
{k=1}^{N} \frac{2\mu_k}{\alpha_k^2}\left(\lambda_1^{\alpha_k}+\lambda_2^{alpha_k}+\lambda_3^{\alpha_k}-3+\frac{1}{\beta_k}\left(J_{el}^{-\alpha_k\beta_k-1}\right)\right)

#### 单轴测试

\lambda_1 = \lambda_3,\;\; \lambda_2 = \lambda\;\;\text{和}\;\; J = J_{el} = \lambda_1^2\lambda

(2)

\sigma_i = J^{-1}\lambda_i\frac{\partial W_s}{\partial \lambda_i}\;\;\;\;\;\;\;\;\;\;i = 1,2,3

\sigma_1 = J^{-1}\lambda_1\sum_{k=1}
^N\frac{2 \mu_k} {\alpha_k^2}\left(\alpha_k\lambda_1^{\alpha_k-1}\alpha_k J ^{\alpha_k\beta_k-1}\frac{\partial J}{\partial \lambda_1}\right)

(3)

\lambda_1 = \lambda^{-\beta/\left(1+2\beta\right)}\;\;\text{和}\;\;J = \lambda^{1/\left(1+2\beta\right)}

(4)

F_{uniaxial} = l_1l_3\sigma_2=\lambda_1^2l_{10}l_{30}\sigma_2

(5)

F_{uniaxial} = l_{10}l_{30}\sum_{k=1}^{N}\frac{2\mu_k}{\alpha_k}\left(1-\lambda^{-\alpha_k\frac{ \left(1+3\beta_k\right)}{\left(1+2\beta_k\right)}}\right)\lambda^{alpha_k-1}

#### 等双轴测试

\lambda_1 = \lambda_2 = \lambda,\;\;\; \lambda_3 = J\lambda^{-2}

(6)

\lambda_3 = \lambda^
{(-2\beta)/(1+\beta)}
\;\;\;\text
{和}
\;\;\;J = \lambda^
{2/(1+\beta)}

(7)

F_{equibiaxial}
= l_
{20}l_{30}\left(\lambda_2\lambda_3\right)\sigma_1

(8)

F_{equibiaxial} = l_{20}
l_
{30}
\sum_
{k=1}
^N\frac
{2\mu_k} {\alpha_k}
\left(1-\lambda^{-\alpha_k\frac
{(1+3\beta_k)}
{(1+\beta_k)}}\right)\lambda^
{\alpha_k-1}

### 使用优化接口计算 Storakers 材料参数

\mu_1 = 4329.6\;Pa,\;\mu_2 = 2502.9\;Pa,\;\alpha_1 = 19.328,\;\alpha_2 = 11.283,\;\beta_1 = 0.31998\;\text{, 和}\;\beta_2 = 0.082473

### 下一步

#### 评论 (1)

##### 炯 李
2020-12-21

Can you send me the raw data and model files? I want to learn from you! My email is lucklj2011@dlmu.edu.cn