Bi-modulus constitutive law assumes that material constants have different values in tension and compression. It is known that finding an equilibrium state of an elastic body consisting of a bi-modulus material is recast as a semidefinite programming problem, which can be solved with a primal-dual interior-point method. As an alternative approach, this paper presents a fast first-order optimization method. Specifically, we propose an accelerated proximal gradient method for solving a minimization problem of the total potential energy. This algorithm is easy to implement, and free from numerical solution of linear equations. Numerical experiments demonstrate that the proposed method outperforms the semidefinite programming approach with a standard solver implementing a primal-dual interior-point method.

双模本构律假设材料常数在拉伸和压缩时具有不同的值。已知将由双模量材料构成的弹性体的平衡状态重铸为半确定的编程问题，可以用原始对偶内点法解决该问题。作为一种替代方法，本文提出了一种快速的一阶优化方法。具体来说，我们提出了一种加速的近端梯度方法，用于解决总势能最小化的问题。该算法易于实现，并且没有线性方程的数值解。数值实验表明，所提出的方法优于采用半对偶内点法的标准求解器的半定规划方法。