Contacts - Types and Formulations in Ansys Mechanical

What do we say for a “contact” in general? We define two bodies to be in contact, when their surfaces touch each other. But the condition is not so easy in the world of simulation. There must be necessary conditions to be satisfied and formulations to be constructed to define a contact’s status. We shall have an in-depth understanding of the types of contacts and their formulations used in the current article. Here I will be discussing the contacts theory based on Ansys software.  

How do we define a contact? 

 When the surfaces of two different bodies touch such that they are mutually tangent to each other, then they are said to be in contact. These contacting surfaces transfer the compressive loads but not the tensile loads to each other. Certain contacts transfer the tangential frictional loads as well, which we will discuss in detail in the coming section. Thus, these two surfaces in contact are free to move away from each other, slide each other but not to penetrate. This is the general case of contact as we deal in real scenarios. Let us have a broader understanding of the type of contacts used in Ansys software. 

What are the types of contacts available in Ansys Mechanical?  

1. Bonded contact- Like the name suggests, bonded contact does not allow the interacting surfaces to move relative to each other. The contacting surfaces cannot penetrate, separate, or move tangentially to each other. These surfaces are used to simulate welded or glued surfaces. Since the contact length or area does not change during the loading conditions, this contact is categorized as linear contact. Any penetration will be ignored, or gaps will be closed once the contact is determined by the user.  

 

2. No separation contact – This contact allows the contacting surfaces not to separate or penetrate each other, that is, the contacting surfaces are restrained to move in normal direction. The surfaces are free to move in tangential direction without resistance. This type of contact is also a linear type of contact and is computationally less expensive to solve like the bonded contact.  

3. Frictionless contact – This contact allows the contacting surfaces to separate from each other but not to penetrate. The contacting surfaces are free to slide in tangential direction without resistance. Since there is a chance of change in area of contact during application of load, this contact is treated as nonlinear contact. This statement can be further explained by the contact pressure which equals zero value whenever separation occurs. Whereas this contact pressure remains nonzero value whenever the surfaces remain in contact. The stiffness matrix constantly needs to be updated considering the contact status. The case is the same for all the nonlinear types of contacts to be discussed further.  

4. Frictional contact – Unlike the frictionless contact, here in frictional contact, there is a resistance force acting in the tangential direction which act as a frictional resistance to the sliding motion. So, this type of contact can carry shear stresses up to a certain magnitude across their interface before they start sliding relative to each other. The state is called “sticking” The model defines an equivalent shear stress at which sliding on the geometry begins as a fraction of the contact pressure. Once the shear stress is exceeded, the two geometries will slide relative to each other. This type of contact is also a nonlinear contact. 

5. Rough contact – This is a modified form of frictional contact, where the coefficient of friction is infinitely high. So that, the contacting surfaces can separate from each other but not slide along tangential direction.  

How to numerically define a contact? The contacts are numerically interpreted using several formulations. There are two main types of formulation, Penalty method and Lagrange method. The formulations can be classified as. 

1. Pure Penalty method – Penalty method assumes a spring of constant stiffness between the contacting surfaces. The stiffness of spring is termed as “contact stiffness” which we can see in the tabular section of Ansys contact toolbox. This method assumes a small amount of penetration between the contacting surface and this penetration is treated as the deflection term in spring equation. Force = Stiffness x displacement, where stiffness is the contact stiffness and displacement are penetration. The greater the stiffness of spring, the less the deflection. Similar is the case here, where greater is the contact stiffness, lesser is the penetration. The product of contact stiffness and penetration results in transfer of force and thus results in contact pressure on the body surface. So, this numerically computed penetration is treated as a penalty, which does not happen in practical situations. The contact stiffness when goes to infinity, the penetration equals zero and more accurate it is, which is the ideal case. But this high value leads to chattering of contact and can lead to convergence issues. The lesser the value of contact stiffness, the penetration increases and the study deviates from real world scenario. So, optimum contact stiffness value must be maintained throughout without compromising the computation time and accuracy. 

2. Augmented Lagrange method – This is a modified form of penalty method where there is an additional term called “lambda” appears in the spring equation. The whole concept of penalty method is applied in the Augmented Lagrange method. Because of the extra term “lambda” Augmented Lagrange method is less sensitive to the magnitude of the contact stiffness. Ansys uses Augmented Lagrange method by default. Both Augmented Lagrange and Pure penalty methods use integration points for contact detection. 

 

3. Normal Lagrange method – This formulation works completely different from the above-mentioned penalty methods. In the above two methods, contact force and pressure are calculated from contact stiffness. In the Normal Lagrange method, contact pressure itself is treated as a separate degree of freedom to satisfy the contact compatibility. So, this method enforces zero penetration with a separate degree of freedom of contact pressure. There is no need of contact stiffness as well for this concept. The method is computationally much more expensive than the penalty method as it requires a direct solver than an iterative solver for solving the equilibrium equations. Chattering is an issue that often occurs in the Normal Lagrange method. Since there is no penetration in this method, the contact status is either open or closed. There is no immediate state in between them and it acts like a step function. So, there is a greater chance of oscillation of contact points between open and closed states. This can sometimes make convergence too difficult. The slight penetration allowed can make the convergence easier, which does not happen in this method. 

 

4. MPC method – This formulation is specifically used for “Bonded” and “No Separation” type of contact alone. This method internally adds multi point constraint equations between the nodes of surfaces in contact. These constraint equations tie the displacements between contacting surfaces. Both Normal Lagrange and MPC method use nodes for contact detection.