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首页> 外文期刊>Zeitschrift fur Angewandte Mathematik und Mechanik >An energy-entropy-consistent time stepping scheme for nonlinear thermo-viscoelastic continua
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An energy-entropy-consistent time stepping scheme for nonlinear thermo-viscoelastic continua

机译：非线性热粘弹性连续体的能量熵一致时间步长方案

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This paper deals with an energy-entropy-consistent time integration of a thermo-viscoelastic continuum in Poissonian variables. The four differential evolution equations of first-order are transformed by a new General Equationfor Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) format into a matrix-vector notation. Since the entropy is a primary variable, we include thermal constraints to affect the temperatures at the boundary of the body. This enhanced GENERIC format with thermal constraints yields with the related degeneracy conditions structure preservation properties for a system with thermal constraints. The properties of an isolated system are in addition to a constant total linear and angular momentum, the constant total energy, an increasing total entropy and a decreasing Lyapunov function. The last one is a stability criterion for thermo-viscoelastic systems and also for unisolated systems without loads valid. The discretization in time is done with a new TC (Thermodynamically Consistent) integrator. This ETC integrator is constructed such, that the algorithmic structural properties after the space-time discretization reflect the underlying enhanced GENERIC format with thermal constraints. As discretization in space the finite element method is used. A projection of the test function of the thermal evolution equation is necessary for an energy-consistent discretization in space. The enhanced GENERIC format with thermal constraints, which is here given in the strong evolution equations, contains the external loads. The consistency properties are discussed for representative numerical examples with different boundary conditions. The coupled mechanical system is solved with a multi-level Newton-Raphson method based on a consistent linearization. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
机译：本文研究了泊松变量中热粘弹性连续体的能量熵常数时间积分。通过新的非平衡可逆-不可逆耦合（GENERIC）格式的通用方程将四个一阶微分演化方程转换为矩阵矢量表示法。由于熵是主要变量，因此我们包括热约束以影响人体边界处的温度。具有热约束的这种增强的GENERIC格式产生具有相关退化条件的具有热约束的系统的结构保留属性。孤立系统的特性除了具有恒定的总线性和角动量，恒定的总能量，增大的总熵和减小的Lyapunov函数之外。最后一个是热粘弹性系统以及没有有效载荷的非隔离系统的稳定性准则。时间的离散化是通过新的TC（热力学一致）积分器完成的。构造该ETC积分器，以使时空离散化后的算法结构特性反映具有热约束的潜在增强型GENERIC格式。作为空间离散化，使用了有限元方法。热演化方程的测试函数的投影对于能量一致的空间离散化是必需的。带有热约束的增强型GENERIC格式（在此处由强演化方程式给出）包含外部载荷。讨论了具有不同边界条件的代表性数值示例的一致性属性。用基于一致线性化的多级牛顿-拉夫森方法求解耦合的机械系统。 （C）2015 WILEY-VCH Verlag GmbH＆Co.KGaA，Weinheim

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