弯曲状态下弹塑性杆的降维
Dimension reduction for elastoplastic rods in the bending regime
AI总结：
该研究从三维有限塑性出发，依托率无关系统演化Γ-收敛框架，基于Cosserat杆假设的乘法分解提出新思路，严格推导了弹塑性杆的有效弯曲模型，给出了弯曲状态下互恢复序列的假设形式。
摘要：
我们从三维有限塑性出发，严格推导了弹塑性杆的有效弯曲模型。推导过程中我们依托率无关系统的演化Γ-收敛框架。本文的主要贡献是提出了弯曲状态下互恢复序列的一个假设形式。与以往处理极限中无穷小变形的研究不同，在弯曲状态下我们研究的是具有无穷小应变但大转动的有限变形。为克服这些难点，我们基于Cosserat杆假设的乘法分解提出了新思路。作为正则化项，我们在能量中引入了随杆厚度趋于零而消失的应变梯度项。
英文摘要：
We rigorously derive an effective bending model for elastoplastic rods starting from three-dimensional finite plasticity. For the derivation we lean on a framework of evolutionary $Γ$-convergence for rate-independent systems. The main contribution of this paper is an ansatz for the mutual recovery sequence in the bending regime. In difference to previous works that deal with infinitesimal deformations in the limit, in the bending regime we are concerned with finite deformations that admit infinitesimally small strain but large rotations. To overcome these difficulties we provide new ideas based on a multiplicative decomposition for the Cosserat rod ansatz. As regularizing terms, we introduce strain gradient terms into the energy that vanish as the thickness of the rod tends to zero.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
