## Abstract

Stochastic fluctuations of material properties, i.e. the elastic constants, result in stochastic fluctuations of the material's response to mechanical loading, i.e. the stresses. In this contribution, we present an analytical approach to the time-efficient and mathematically accurate modeling of the stochastic behavior of visco-elastic materials. The material behavior is modeled using a viscous strain as an internal variable whose evolution is described by a differential equation. Since the stochastic material properties enter the evolution equation, a stochastic differential equation has to be treated which renders the problem rather uncomfortable. However, we present a precise investigation of the problem that yields a treatment similar to the deterministic case but resulting in the analytical estimation both of the expectation value and the variance (and standard deviation) of the stresses. A numerical comparison to Monte Carlo simulations proves the reliability of our approach.

Original language | English |
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Pages (from-to) | 1249–1260 |

Number of pages | 12 |

Journal | Zeitschrift für Angewandte Mathematik und Mechanik |

Volume | 98 |

Issue number | 7 |

DOIs | |

Publication status | Published - Jul 2018 |

## Keywords

- Analytical solution
- Energy relaxation
- Stochastic material behavior
- Stress expectation and variance
- Visco-elastic material
- stochastic material behavior
- energy relaxation
- stress expectation and variance
- visco-elastic material
- analytical solution