Non–convex potentials and microstructures in finite–strain plasticity
Non–convex potentials and microstructures in finite–strain plasticity
复制标题
有限应变塑性中的非凸势和微观结构
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
A. Mielke
中科院分区：
文献类型：
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作者：
C. Carstensen;K. Hackl;A. Mielke
建立了有限应变弹塑性演化问题的数学模型，其中隐式时间离散化的一个时间步长导致一般的非凸极小化问题。通过消除所有内部变量，可以在变分和非线性偏微分方程组的一般框架内对简化的问题进行数学和数值分析。对单一滑移系统和von Mise塑性的结果表明，有限应变弹塑性产生了非拟凸能量密度的简化问题，因此允许不达到能量最小化和微观结构。
A mathematical model for a finite–strain elastoplastic evolution problem is proposed in which one time–step of an implicit time–discretization leads to generally non–convex minimization problems. The elimination of all internal variables enables a mathematical and numerical analysis of a reduced problem within the general framework of calculus of variations and nonlinear partial differential equations. The results for a single slip–system and von Mises plasticity illustrate that finite–strain elastoplasticity generates reduced problems with non–quasiconvex energy densities and so allows for non–attainment of energy minimizers and microstructures.