Kinetics of Martensitic Phase Transitions: Lattice model
Kinetics of Martensitic Phase Transitions: Lattice model
复制标题
马氏体相变动力学：晶格模型
DOI：
10.1137/040616942
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
A. Vainchtein
中科院分区：
文献类型：
--
作者：
L. Truskinovsky;A. Vainchtein
马氏体相变通常用混合型双曲-椭圆体系来模拟。这样的系统会导致不适定的初值问题，除非它们被附加的动力学关系所补充。本文用连续体模型的自然离散原型代替连续体模型，显式地计算出适当的闭合关系。这个过程可以看作是通过离散化进行的正则化，也可以看作是对潜在的离散微观结构的物理动机解释。我们用具有谐波远程相互作用的双稳定晶格的全惯性离散模型的行波解来模拟相边界。虽然微观模型是哈密顿模型，但它产生的宏观耗散可以用不连续速度与共轭构形力之间的关系来表示。这种动力学关系尊重熵不平等，但不是通常的Rankine-Hugoniot跳跃条件的结果。根据构造的解，在宏观水平上的耗散是由于晶格波携带能量远离传播锋的诱导辐射造成的。我们证明了晶格模型的足够强的非局域性可能是动力学关系的多值性的原因，并且可以定量地影响近声速区域的动力学。瞬态动力学的直接数值模拟表明，至少有些计算得到的行波是稳定的。
Martensitic phase transitions are often modeled by mixed-type hyperbolic-elliptic systems. Such systems lead to ill-posed initial-value problems unless they are supplemented by an additional kinetic relation. In this paper we explicitly compute an appropriate closing relation by replacing the continuum model with its natural discrete prototype. The procedure can be viewed as either regularization by discretization or a physically motivated account of underlying discrete microstructure. We model phase boundaries by traveling wave solutions of a fully inertial discrete model for a bi-stable lattice with harmonic long-range interactions. Although the microscopic model is Hamiltonian, it generates macroscopic dissipation which can be specified in the form of a rela- tion between the velocity of the discontinuity and the conjugate configurational force. This kinetic relation respects entropy inequality but is not a consequence of the usual Rankine-Hugoniot jump conditions. According to the constructed solution, the dissipation at the macrolevel is due to the induced radiation of lattice waves carrying energy away from the propagating front. We show that sufficiently strong nonlocality of the lattice model may be responsible for the multivaluedness of the kinetic relation and can quantitatively affect kinetics in the near-sonic region. Direct numerical simulations of the transient dynamics suggest stability of at least some of the computed traveling waves.