Numerical models of steady rolling for non‐linear viscoelastic structures in finite deformations
Numerical models of steady rolling for non‐linear viscoelastic structures in finite deformations
复制标题
有限变形中非线性粘弹性结构稳定滚动的数值模型
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
C. Rahler
中科院分区：
文献类型：
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作者：
P. Tallec;C. Rahler
首次提出了基于不可逆热力学的粘弹性材料本构定律的拉格朗日公式。这些定律由控制内部变量演化的非线性微分方程表示。然后根据连续介质力学守恒定律得到描述轴对称粘弹性结构稳定滚动的方程。提出了代数系统的有限元近似和求解技术。内部变量的消除允许人们保持一种具有粘弹性方程独立解的类弹性算法。数值测试表明了该方法在大型三维情况下的可行性和效率。
A Lagrangian formulation of constitutive laws for a viscoelastic material based on irreversible thermodynamics is first presented. These laws are expressed by a non-linear differential equation governing the evolution of an internal variable. Then equations describing the steady rolling of an axisymmetric viscoelastic structure are obtained from the conservation laws of continuum mechanics. A finite element approximation and a solution technique of the algebraic system is proposed. The eiimination of the internal variable allows one to keep an elastic-like algorithm with an independent solution of the viscoelastic equation. Numerical tests show the feasibility and the efficiency of the proposed methods in large three-dimensional situations.