scholarly journals A nonintrusive distributed reduced‐order modeling framework for nonlinear structural mechanics—Application to elastoviscoplastic computations

2019 ◽  
Vol 121 (1) ◽  
pp. 32-53 ◽  
Author(s):  
Fabien Casenave ◽  
Nissrine Akkari ◽  
Felipe Bordeu ◽  
Christian Rey ◽  
David Ryckelynck
Keyword(s):  
Structural Mechanics ◽  
Reduced Order Modeling ◽  
Modeling Framework ◽  
Reduced Order ◽  
Nonlinear Structural ◽  
Nonlinear Structural Mechanics

scholarly journals A Proper Generalized Decomposition (PGD) approach to crack propagation in brittle materials: with application to random field material properties

2019 ◽  
Vol 65 (2) ◽  
pp. 451-473 ◽  
Author(s):  
Hasini Garikapati ◽  
Sergio Zlotnik ◽  
Pedro Díez ◽  
Clemens V. Verhoosel ◽  
E. Harald van Brummelen
Keyword(s):  
Crack Propagation ◽  
Material Properties ◽  
Computational Cost ◽  
Brittle Materials ◽  
Energy Criterion ◽  
Reduced Order Modeling ◽  
Proper Generalized Decomposition ◽  
Modeling Framework ◽  
Global Energy ◽  
Reduced Order

Abstract Understanding the failure of brittle heterogeneous materials is essential in many applications. Heterogeneities in material properties are frequently modeled through random fields, which typically induces the need to solve finite element problems for a large number of realizations. In this context, we make use of reduced order modeling to solve these problems at an affordable computational cost. This paper proposes a reduced order modeling framework to predict crack propagation in brittle materials with random heterogeneities. The framework is based on a combination of the Proper Generalized Decomposition (PGD) method with Griffith’s global energy criterion. The PGD framework provides an explicit parametric solution for the physical response of the system. We illustrate that a non-intrusive sampling-based technique can be applied as a post-processing operation on the explicit solution provided by PGD. We first validate the framework using a global energy approach on a deterministic two-dimensional linear elastic fracture mechanics benchmark. Subsequently, we apply the reduced order modeling approach to a stochastic fracture propagation problem.

Self-correcting incremental approach in nonlinear structural mechanics.

AIAA Journal ◽  
1971 ◽  
Vol 9 (12) ◽  
pp. 2464-2466 ◽  
Author(s):  
DONALD A. MASSETT ◽  
JAMES A. STRICKLIN
Keyword(s):  
Structural Mechanics ◽  
Incremental Approach ◽  
Nonlinear Structural ◽  
Nonlinear Structural Mechanics
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