摘要：The cohesive surface method has been used intensively on numerical simulations of fracture of metals and brittle materials. However, the constitutive cohesive laws (or traction versus crack opening relationships) used for these materials are not adequate to simulate the concrete behavior because they do not take into consideration effects related to the size of the finite elements and other phenomena that characterize concrete rupture (e.g. development of a process zone at the crack tip). In this work, some well-known post-peak constitutive equations for the cohesive surface are explored. The shape of these equations changes overall results and it seems to be linked with the development of the process zone, so the shape can be considered a material property as the fracture energy. However, the present work also explores the effect of the pre-peak part of the cohesive law. It is demonstrated that this part of the curve must be related to the size of the finite elements, in order to have a mesh independent result. As practical applications, cases in Mode I of propagation are presented (three-point bending), where the effect of the post-peak relationship on load versus crack opening is shown. It could be concluded that post-peak relationship is important to define maximum rupture load. Besides that, different sizes of bodies were analyzed and the scale effect of concrete was captured (the smaller the body, the greater the toughness). A good fit with literature results was obtained. It is demonstrated also that results are mesh independent, depending on the pre-peak part of the cohesive law. Concrete properties are not considered random fields.
其他摘要：The cohesive surface method has been used intensively on numerical simulations of fracture of metals and brittle materials. However, the constitutive cohesive laws (or traction versus crack opening relationships) used for these materials are not adequate to simulate the concrete behavior because they do not take into consideration effects related to the size of the finite elements and other phenomena that characterize concrete rupture (e.g. development of a process zone at the crack tip). In this work, some well-known post-peak constitutive equations for the cohesive surface are explored. The shape of these equations changes overall results and it seems to be linked with the development of the process zone, so the shape can be considered a material property as the fracture energy. However, the present work also explores the effect of the pre-peak part of the cohesive law. It is demonstrated that this part of the curve must be related to the size of the finite elements, in order to have a mesh independent result. As practical applications, cases in Mode I of propagation are presented (three-point bending), where the effect of the post-peak relationship on load versus crack opening is shown. It could be concluded that post-peak relationship is important to define maximum rupture load. Besides that, different sizes of bodies were analyzed and the scale effect of concrete was captured (the smaller the body, the greater the toughness). A good fit with literature results was obtained. It is demonstrated also that results are mesh independent, depending on the pre-peak part of the cohesive law. Concrete properties are not considered random fields.
