论文标题
在亚临界胁迫假设下的磁弹性中的准演化
Quasistatic evolution in magnetoelasticity under subcritical coercivity assumptions
论文作者
论文摘要
我们研究了在静态和准危机中的磁弹性变异模型。该模型具有混合的欧拉格朗日公式，因为在实际空间中的变形配置上定义了磁化。磁饱和约束在参考配置中配制，涉及变形的雅各布决定因素。这些属于Barchiesi，Henao和Mora-Corral引入的空化不连续变形的可能性不连续变形的类别。我们建立了一个紧凑的结果，特别是，该结果产生了磁化物与变形的组成的收敛性。在静态环境中，这使我们能够通过经典的较低的半持续方法来证明最小化器的存在。我们的紧凑性结果还使我们能够在准危机环境中解决分析，在该设置中，我们检查了由施加的载荷和边界条件驱动的与速率无关的演变。在这种情况下，我们证明了能量解决方案的存在。
We study a variational model of magnetoelasticity both in the static and in the quasistatic setting. The model features a mixed Eulerian-Lagrangian formulation, as magnetizations are defined on the deformed configuration in the actual space. The magnetic saturation constraint is formulated in the reference configuration and involves the Jacobian determinant of deformations. These belong to the class of possibility discontinuous deformations excluding cavitation introduced by Barchiesi, Henao and Mora-Corral. We establish a compactness result which, in particular, yields the convergence of the compositions of magnetizations with deformations. In the static setting, this enables us to prove the existence of minimizers by means of classical lower semicontinuity methods. Our compactness result also allows us to address the analysis in the quasistatic setting, where we examine rate-independent evolutions driven by applied loads and boundary conditions. In this case, we prove the existence of energetic solutions.
